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Merge branch 'devel' of github.com:SheffieldML/GPy into devel

Browse source 
Conflicts:
	GPy/core/fitc.py
This commit is contained in:
Ricardo 2013-06-05 16:37:57 +01:00
commit c774432fee
56 changed files with 783 additions and 807 deletions
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16
GPy/core/fitc.py
View file

@ -14,7 +14,7 @@ class FITC(SparseGP):
sparse FITC approximation
:param X: inputs
:type X: np.ndarray (N x Q)
:type X: np.ndarray (num_data x Q)
:param likelihood: a likelihood instance, containing the observed data
:type likelihood: GPy.likelihood.(Gaussian | EP)
:param kernel : the kernel (covariance function). See link kernels
@ -57,7 +57,7 @@ class FITC(SparseGP):
self.V_star = self.beta_star * self.likelihood.Y
# The rather complex computations of self.A
tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.num_data)))
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
self.A = tdot(tmp)
@ -113,7 +113,7 @@ class FITC(SparseGP):
self._dpsi1_dX_jkj = 0
self._dpsi1_dtheta_jkj = 0
for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.N),self.V_star,alpha,gamma_2,gamma_3):
for i,V_n,alpha_n,gamma_n,gamma_k in zip(range(self.num_data),self.V_star,alpha,gamma_2,gamma_3):
K_pp_K = np.dot(Kmmipsi1[:,i:(i+1)],Kmmipsi1[:,i:(i+1)].T)
_dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:]
_dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
@ -137,14 +137,14 @@ class FITC(SparseGP):
aux_1 = self.likelihood.Y.T * np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1)
aux_2 = np.dot(LBiLmipsi1.T,self._LBi_Lmi_psi1V)
dA_dnoise = 0.5 * self.D * (dbstar_dnoise/self.beta_star).sum() - 0.5 * self.D * np.sum(self.likelihood.Y**2 * dbstar_dnoise)
dA_dnoise = 0.5 * self.input_dim * (dbstar_dnoise/self.beta_star).sum() - 0.5 * self.input_dim * np.sum(self.likelihood.Y**2 * dbstar_dnoise)
dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T)
dC_dnoise = -0.5 * np.sum(mdot(self.LBi.T,self.LBi,Lmi_psi1) * Lmi_psi1 * dbstar_dnoise.T)
dD_dnoise_1 = mdot(self.V_star*LBiLmipsi1.T,LBiLmipsi1*dbstar_dnoise.T*self.likelihood.Y.T)
alpha = mdot(LBiLmipsi1,self.V_star)
alpha_ = mdot(LBiLmipsi1.T,alpha)
dD_dnoise_2 = -0.5 * self.D * np.sum(alpha_**2 * dbstar_dnoise )
dD_dnoise_2 = -0.5 * self.input_dim * np.sum(alpha_**2 * dbstar_dnoise )
dD_dnoise_1 = mdot(self.V_star.T,self.psi1.T,self.Lmi.T,self.LBi.T,self.LBi,self.Lmi,self.psi1,dbstar_dnoise*self.likelihood.Y)
dD_dnoise_2 = 0.5*mdot(self.V_star.T,self.psi1.T,Hi,self.psi1,dbstar_dnoise*self.psi1.T,Hi,self.psi1,self.V_star)
@ -154,7 +154,7 @@ class FITC(SparseGP):
def log_likelihood(self):
""" Compute the (lower bound on the) log marginal likelihood """
A = -0.5 * self.N * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y)
A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y)
C = -self.output_dim * (np.sum(np.log(np.diag(self.LB))))
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
return A + C + D
@ -204,8 +204,8 @@ class FITC(SparseGP):
# q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
# Ci = I + (RPT0)Di(RPT0).T
# C = I - [RPT0] * (D+[RPT0].T*[RPT0])^-1*[RPT0].T
# = I - [RPT0] * (D + self.Qnn)^-1 * [RPT0].T
# C = I - [RPT0] * (input_dim+[RPT0].T*[RPT0])^-1*[RPT0].T
# = I - [RPT0] * (input_dim + self.Qnn)^-1 * [RPT0].T
# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
# = I - V.T * V
U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)

8
GPy/core/gp.py
View file

@ -33,8 +33,8 @@ class GP(GPBase):
self._set_params(self._get_params())
def _set_params(self, p):
self.kern._set_params_transformed(p[:self.kern.Nparam_transformed()])
self.likelihood._set_params(p[self.kern.Nparam_transformed():])
self.kern._set_params_transformed(p[:self.kern.num_params_transformed()])
self.likelihood._set_params(p[self.kern.num_params_transformed():])
self.K = self.kern.K(self.X)
self.K += self.likelihood.covariance_matrix
@ -46,12 +46,12 @@ class GP(GPBase):
#alpha = np.dot(self.Ki, self.likelihood.Y)
alpha,_ = linalg.lapack.flapack.dpotrs(self.L, self.likelihood.Y,lower=1)
self.dL_dK = 0.5 * (tdot(alpha) - self.input_dim * self.Ki)
self.dL_dK = 0.5 * (tdot(alpha) - self.output_dim * self.Ki)
else:
#tmp = mdot(self.Ki, self.likelihood.YYT, self.Ki)
tmp, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(self.likelihood.YYT), lower=1)
tmp, _ = linalg.lapack.flapack.dpotrs(self.L, np.asfortranarray(tmp.T), lower=1)
self.dL_dK = 0.5 * (tmp - self.input_dim * self.Ki)
self.dL_dK = 0.5 * (tmp - self.output_dim * self.Ki)
def _get_params(self):
return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))

28
GPy/core/gp_base.py
View file

@ -1,24 +1,24 @@
import numpy as np
import model
from .. import kern
from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D
import pylab as pb
from GPy.core.model import Model
class GPBase(model.model):
class GPBase(Model):
"""
Gaussian Process model for holding shared behaviour between
Gaussian Process Model for holding shared behaviour between
sprase_GP and GP models
"""
def __init__(self, X, likelihood, kernel, normalize_X=False):
self.X = X
assert len(self.X.shape) == 2
self.N, self.input_dim = self.X.shape
self.num_data, self.input_dim = self.X.shape
assert isinstance(kernel, kern.kern)
self.kern = kernel
self.likelihood = likelihood
assert self.X.shape[0] == self.likelihood.data.shape[0]
self.N, self.output_dim = self.likelihood.data.shape
self.num_data, self.output_dim = self.likelihood.data.shape
if normalize_X:
self._Xmean = X.mean(0)[None, :]
@ -28,7 +28,7 @@ class GPBase(model.model):
self._Xmean = np.zeros((1, self.input_dim))
self._Xstd = np.ones((1, self.input_dim))
model.model.__init__(self)
Model.__init__(self)
# All leaf nodes should call self._set_params(self._get_params()) at
# the end
@ -84,8 +84,8 @@ class GPBase(model.model):
Xnew, xmin, xmax, xx, yy = x_frame2D(self.X, plot_limits, resolution)
m, v = self._raw_predict(Xnew, which_parts=which_parts)
m = m.reshape(resolution, resolution).T
ax.contour(xx, yy, m, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
ax.scatter(self.X[:, 0], self.X[:, 1], 40, self.likelihood.Y, linewidth=0, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max())
ax.contour(xx, yy, m, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
ax.scatter(self.X[:, 0], self.X[:, 1], 40, self.likelihood.Y, linewidth=0, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max()) # @UndefinedVariable
ax.set_xlim(xmin[0], xmax[0])
ax.set_ylim(xmin[1], xmax[1])
else:
@ -94,9 +94,9 @@ class GPBase(model.model):
def plot(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None):
"""
TODO: Docstrings!
:param levels: for 2D plotting, the number of contour levels to use
is ax is None, create a new figure
"""
# TODO include samples
if which_data == 'all':
@ -111,7 +111,7 @@ class GPBase(model.model):
Xu = self.X * self._Xstd + self._Xmean # NOTE self.X are the normalized values now
Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
m, var, lower, upper = self.predict(Xnew, which_parts=which_parts)
m, _, lower, upper = self.predict(Xnew, which_parts=which_parts)
for d in range(m.shape[1]):
gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax)
ax.plot(Xu[which_data], self.likelihood.data[which_data, d], 'kx', mew=1.5)
@ -122,13 +122,13 @@ class GPBase(model.model):
elif self.X.shape[1] == 2: # FIXME
resolution = resolution or 50
Xnew, xx, yy, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
m, var, lower, upper = self.predict(Xnew, which_parts=which_parts)
m, _, lower, upper = self.predict(Xnew, which_parts=which_parts)
m = m.reshape(resolution, resolution).T
ax.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
ax.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
Yf = self.likelihood.Y.flatten()
ax.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.)
ax.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) # @UndefinedVariable
ax.set_xlim(xmin[0], xmax[0])
ax.set_ylim(xmin[1], xmax[1])

85
GPy/core/model.py
View file

@ -6,37 +6,32 @@ from .. import likelihoods
from ..inference import optimization
from ..util.linalg import jitchol
from GPy.util.misc import opt_wrapper
from parameterised import parameterised
from scipy import optimize
from parameterised import Parameterised
import multiprocessing as mp
import numpy as np
import priors
import re
import sys
import pdb
from GPy.core.domains import POSITIVE, REAL
# import numdifftools as ndt
class model(parameterised):
class Model(Parameterised):
def __init__(self):
parameterised.__init__(self)
Parameterised.__init__(self)
self.priors = None
self.optimization_runs = []
self.sampling_runs = []
self.preferred_optimizer = 'scg'
#self._set_params(self._get_params()) has been taken out as it should only be called on leaf nodes
# self._set_params(self._get_params()) has been taken out as it should only be called on leaf nodes
def _get_params(self):
raise NotImplementedError, "this needs to be implemented to use the model class"
raise NotImplementedError, "this needs to be implemented to use the Model class"
def _set_params(self, x):
raise NotImplementedError, "this needs to be implemented to use the model class"
raise NotImplementedError, "this needs to be implemented to use the Model class"
def log_likelihood(self):
raise NotImplementedError, "this needs to be implemented to use the model class"
raise NotImplementedError, "this needs to be implemented to use the Model class"
def _log_likelihood_gradients(self):
raise NotImplementedError, "this needs to be implemented to use the model class"
raise NotImplementedError, "this needs to be implemented to use the Model class"
def set_prior(self, regexp, what):
"""
Sets priors on the model parameters.
Sets priors on the Model parameters.
Arguments
---------
@ -65,7 +60,7 @@ class model(parameterised):
if len(tie_matches) > 1:
raise ValueError, "cannot place Prior across multiple ties"
elif len(tie_matches) == 1:
which = which[:1] # just place a Prior object on the first parameter
which = which[:1] # just place a Prior object on the first parameter
# check constraints are okay
@ -95,7 +90,7 @@ class model(parameterised):
def get_gradient(self, name, return_names=False):
"""
Get model gradient(s) by name. The name is applied as a regular expression and all parameters that match that regular expression are returned.
Get Model gradient(s) by name. The name is applied as a regular expression and all parameters that match that regular expression are returned.
"""
matches = self.grep_param_names(name)
if len(matches):
@ -135,7 +130,7 @@ class model(parameterised):
def randomize(self):
"""
Randomize the model.
Randomize the Model.
Make this draw from the Prior if one exists, else draw from N(0,1)
"""
# first take care of all parameters (from N(0,1))
@ -147,16 +142,16 @@ class model(parameterised):
if self.priors is not None:
[np.put(x, i, p.rvs(1)) for i, p in enumerate(self.priors) if not p is None]
self._set_params(x)
self._set_params_transformed(self._get_params_transformed()) # makes sure all of the tied parameters get the same init (since there's only one prior object...)
self._set_params_transformed(self._get_params_transformed()) # makes sure all of the tied parameters get the same init (since there's only one prior object...)
def optimize_restarts(self, Nrestarts=10, robust=False, verbose=True, parallel=False, num_processes=None, **kwargs):
def optimize_restarts(self, num_restarts=10, robust=False, verbose=True, parallel=False, num_processes=None, **kwargs):
"""
Perform random restarts of the model, and set the model to the best
Perform random restarts of the Model, and set the Model to the best
seen solution.
If the robust flag is set, exceptions raised during optimizations will
be handled silently. If _all_ runs fail, the model is reset to the
be handled silently. If _all_ runs fail, the Model is reset to the
existing parameter values.
Notes
@ -179,19 +174,19 @@ class model(parameterised):
try:
jobs = []
pool = mp.Pool(processes=num_processes)
for i in range(Nrestarts):
for i in range(num_restarts):
self.randomize()
job = pool.apply_async(opt_wrapper, args=(self,), kwds=kwargs)
jobs.append(job)
pool.close() # signal that no more data coming in
pool.join() # wait for all the tasks to complete
pool.close() # signal that no more data coming in
pool.join() # wait for all the tasks to complete
except KeyboardInterrupt:
print "Ctrl+c received, terminating and joining pool."
pool.terminate()
pool.join()
for i in range(Nrestarts):
for i in range(num_restarts):
try:
if not parallel:
self.randomize()
@ -200,10 +195,10 @@ class model(parameterised):
self.optimization_runs.append(jobs[i].get())
if verbose:
print("Optimization restart {0}/{1}, f = {2}".format(i + 1, Nrestarts, self.optimization_runs[-1].f_opt))
print("Optimization restart {0}/{1}, f = {2}".format(i + 1, num_restarts, self.optimization_runs[-1].f_opt))
except Exception as e:
if robust:
print("Warning - optimization restart {0}/{1} failed".format(i + 1, Nrestarts))
print("Warning - optimization restart {0}/{1} failed".format(i + 1, num_restarts))
else:
raise e
@ -218,11 +213,11 @@ class model(parameterised):
Ensure that any variables which should clearly be positive have been constrained somehow.
"""
positive_strings = ['variance', 'lengthscale', 'precision', 'kappa']
param_names = self._get_param_names()
# param_names = self._get_param_names()
currently_constrained = self.all_constrained_indices()
to_make_positive = []
for s in positive_strings:
for i in self.grep_param_names(".*"+s):
for i in self.grep_param_names(".*" + s):
if not (i in currently_constrained):
to_make_positive.append(i)
if len(to_make_positive):
@ -240,18 +235,18 @@ class model(parameterised):
Gets the gradients from the likelihood and the priors.
"""
self._set_params_transformed(x)
obj_grads = - self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients())
obj_grads = -self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients())
return obj_grads
def objective_and_gradients(self, x):
self._set_params_transformed(x)
obj_f = -self.log_likelihood() - self.log_prior()
obj_grads = - self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients())
obj_grads = -self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients())
return obj_f, obj_grads
def optimize(self, optimizer=None, start=None, **kwargs):
"""
Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors.
Optimize the Model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors.
kwargs are passed to the optimizer. They can be:
:max_f_eval: maximum number of function evaluations
@ -274,7 +269,7 @@ class model(parameterised):
def optimize_SGD(self, momentum=0.1, learning_rate=0.01, iterations=20, **kwargs):
# assert self.Y.shape[1] > 1, "SGD only works with D > 1"
sgd = SGD.StochasticGD(self, iterations, learning_rate, momentum, **kwargs)
sgd = SGD.StochasticGD(self, iterations, learning_rate, momentum, **kwargs) # @UndefinedVariable
sgd.run()
self.optimization_runs.append(sgd)
@ -291,7 +286,7 @@ class model(parameterised):
def f(x):
self._set_params(x)
return self.log_likelihood()
h = ndt.Hessian(f)
h = ndt.Hessian(f) # @UndefinedVariable
A = -h(x)
self._set_params(x)
# check for almost zero components on the diagonal which screw up the cholesky
@ -300,7 +295,7 @@ class model(parameterised):
return A
def Laplace_evidence(self):
"""Returns an estiamte of the model evidence based on the Laplace approximation.
"""Returns an estiamte of the Model evidence based on the Laplace approximation.
Uses a numerical estimate of the hessian if none is available analytically"""
A = self.Laplace_covariance()
try:
@ -310,12 +305,12 @@ class model(parameterised):
return 0.5 * self._get_params().size * np.log(2 * np.pi) + self.log_likelihood() - hld
def __str__(self):
s = parameterised.__str__(self).split('\n')
s = Parameterised.__str__(self).split('\n')
# add priors to the string
if self.priors is not None:
strs = [str(p) if p is not None else '' for p in self.priors]
else:
strs = ['']*len(self._get_params())
strs = [''] * len(self._get_params())
width = np.array(max([len(p) for p in strs] + [5])) + 4
log_like = self.log_likelihood()
@ -336,7 +331,7 @@ class model(parameterised):
def checkgrad(self, target_param=None, verbose=False, step=1e-6, tolerance=1e-3):
"""
Check the gradient of the model by comparing to a numerical estimate.
Check the gradient of the Model by comparing to a numerical estimate.
If the verbose flag is passed, invividual components are tested (and printed)
:param verbose: If True, print a "full" checking of each parameter
@ -389,7 +384,7 @@ class model(parameterised):
param_list = range(len(x))
else:
param_list = self.grep_param_names(target_param, transformed=True, search=True)
if not param_list:
if not np.any(param_list):
print "No free parameters to check"
return
@ -419,15 +414,15 @@ class model(parameterised):
def input_sensitivity(self):
"""
return an array describing the sesitivity of the model to each input
return an array describing the sesitivity of the Model to each input
NB. Right now, we're basing this on the lengthscales (or
variances) of the kernel. TODO: proper sensitivity analysis
where we integrate across the model inputs and evaluate the
effect on the variance of the model output. """
where we integrate across the Model inputs and evaluate the
effect on the variance of the Model output. """
if not hasattr(self, 'kern'):
raise ValueError, "this model has no kernel"
raise ValueError, "this Model has no kernel"
k = [p for p in self.kern.parts if p.name in ['rbf', 'linear']]
if (not len(k) == 1) or (not k[0].ARD):
@ -474,8 +469,8 @@ class model(parameterised):
ll_change = new_ll - last_ll
if ll_change < 0:
self.likelihood = last_approximation # restore previous likelihood approximation
self._set_params(last_params) # restore model parameters
self.likelihood = last_approximation # restore previous likelihood approximation
self._set_params(last_params) # restore Model parameters
print "Log-likelihood decrement: %s \nLast likelihood update discarded." % ll_change
stop = True
else:

48
GPy/core/parameterised.py
View file

@ -6,12 +6,10 @@ import numpy as np
import re
import copy
import cPickle
import os
from ..util.squashers import sigmoid
import warnings
import transformations
class parameterised(object):
class Parameterised(object):
def __init__(self):
"""
This is the base class for model and kernel. Mostly just handles tieing and constraining of parameters
@ -36,7 +34,7 @@ class parameterised(object):
"""
Returns a **copy** of parameters in non transformed space
:see_also: :py:func:`GPy.core.parameterised.params_transformed`
:see_also: :py:func:`GPy.core.Parameterised.params_transformed`
"""
return self._get_params()
@ -49,7 +47,7 @@ class parameterised(object):
"""
Returns a **copy** of parameters in transformed space
:see_also: :py:func:`GPy.core.parameterised.params`
:see_also: :py:func:`GPy.core.Parameterised.params`
"""
return self._get_params_transformed()
@ -113,7 +111,7 @@ class parameterised(object):
if hasattr(self, 'prior'):
pass
self._set_params_transformed(self._get_params_transformed()) # sets tied parameters to single value
self._set_params_transformed(self._get_params_transformed()) # sets tied parameters to single value
def untie_everything(self):
"""Unties all parameters by setting tied_indices to an empty list."""
@ -145,7 +143,7 @@ class parameterised(object):
else:
return np.nonzero([regexp.match(name) for name in names])[0]
def Nparam_transformed(self):
def num_params_transformed(self):
removed = 0
for tie in self.tied_indices:
removed += tie.size - 1
@ -159,18 +157,18 @@ class parameterised(object):
"""Unconstrain matching parameters. does not untie parameters"""
matches = self.grep_param_names(regexp)
#tranformed contraints:
# tranformed contraints:
for match in matches:
self.constrained_indices = [i[i<>match] for i in self.constrained_indices]
self.constrained_indices = [i[i <> match] for i in self.constrained_indices]
#remove empty constraints
tmp = zip(*[(i,t) for i,t in zip(self.constrained_indices,self.constraints) if len(i)])
# remove empty constraints
tmp = zip(*[(i, t) for i, t in zip(self.constrained_indices, self.constraints) if len(i)])
if tmp:
self.constrained_indices, self.constraints = zip(*[(i,t) for i,t in zip(self.constrained_indices,self.constraints) if len(i)])
self.constrained_indices, self.constraints = zip(*[(i, t) for i, t in zip(self.constrained_indices, self.constraints) if len(i)])
self.constrained_indices, self.constraints = list(self.constrained_indices), list(self.constraints)
# fixed:
self.fixed_values = [np.delete(values, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices,values in zip(self.fixed_indices,self.fixed_values)]
self.fixed_values = [np.delete(values, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices, values in zip(self.fixed_indices, self.fixed_values)]
self.fixed_indices = [np.delete(indices, np.nonzero(np.sum(indices[:, None] == matches[None, :], 1))[0]) for indices in self.fixed_indices]
# remove empty elements
@ -189,7 +187,7 @@ class parameterised(object):
""" Set positive constraints. """
self.constrain(regexp, transformations.logexp())
def constrain_bounded(self, regexp,lower, upper):
def constrain_bounded(self, regexp, lower, upper):
""" Set bounded constraints. """
self.constrain(regexp, transformations.logistic(lower, upper))
@ -199,8 +197,8 @@ class parameterised(object):
else:
return np.empty(shape=(0,))
def constrain(self,regexp,transform):
assert isinstance(transform,transformations.transformation)
def constrain(self, regexp, transform):
assert isinstance(transform, transformations.transformation)
matches = self.grep_param_names(regexp)
overlap = set(matches).intersection(set(self.all_constrained_indices()))
@ -251,7 +249,7 @@ class parameterised(object):
def _get_params_transformed(self):
"""use self._get_params to get the 'true' parameters of the model, which are then tied, constrained and fixed"""
x = self._get_params()
[np.put(x,i,t.finv(x[i])) for i,t in zip(self.constrained_indices,self.constraints)]
[np.put(x, i, t.finv(x[i])) for i, t in zip(self.constrained_indices, self.constraints)]
to_remove = self.fixed_indices + [t[1:] for t in self.tied_indices]
if len(to_remove):
@ -263,7 +261,7 @@ class parameterised(object):
""" takes the vector x, which is then modified (by untying, reparameterising or inserting fixed values), and then call self._set_params"""
self._set_params(self._untransform_params(x))
def _untransform_params(self,x):
def _untransform_params(self, x):
"""
The transformation required for _set_params_transformed.
@ -290,9 +288,9 @@ class parameterised(object):
[np.put(xx, i, v) for i, v in zip(self.fixed_indices, self.fixed_values)]
[np.put(xx, i, v) for i, v in [(t[1:], xx[t[0]]) for t in self.tied_indices] ]
[np.put(xx,i,t.f(xx[i])) for i,t in zip(self.constrained_indices, self.constraints)]
if hasattr(self,'debug'):
stop
[np.put(xx, i, t.f(xx[i])) for i, t in zip(self.constrained_indices, self.constraints)]
if hasattr(self, 'debug'):
stop # @UndefinedVariable
return xx
@ -316,7 +314,7 @@ class parameterised(object):
remove = np.hstack((remove, np.hstack(self.fixed_indices)))
# add markers to show that some variables are constrained
for i,t in zip(self.constrained_indices,self.constraints):
for i, t in zip(self.constrained_indices, self.constraints):
for ii in i:
n[ii] = n[ii] + t.__str__()
@ -333,10 +331,10 @@ class parameterised(object):
if not N:
return "This object has no free parameters."
header = ['Name', 'Value', 'Constraints', 'Ties']
values = self._get_params() # map(str,self._get_params())
values = self._get_params() # map(str,self._get_params())
# sort out the constraints
constraints = [''] * len(names)
for i,t in zip(self.constrained_indices,self.constraints):
for i, t in zip(self.constrained_indices, self.constraints):
for ii in i:
constraints[ii] = t.__str__()
for i in self.fixed_indices:
@ -354,7 +352,7 @@ class parameterised(object):
max_constraint = max([len(constraints[i]) for i in range(len(constraints))] + [len(header[2])])
max_ties = max([len(ties[i]) for i in range(len(ties))] + [len(header[3])])
cols = np.array([max_names, max_values, max_constraint, max_ties]) + 4
columns = cols.sum()
# columns = cols.sum()
header_string = ["{h:^{col}}".format(h=header[i], col=cols[i]) for i in range(len(cols))]
header_string = map(lambda x: '|'.join(x), [header_string])

36
GPy/core/sparse_gp.py
View file

@ -13,13 +13,13 @@ class SparseGP(GPBase):
Variational sparse GP model
:param X: inputs
:type X: np.ndarray (N x input_dim)
:type X: np.ndarray (num_data x input_dim)
:param likelihood: a likelihood instance, containing the observed data
:type likelihood: GPy.likelihood.(Gaussian | EP | Laplace)
:param kernel : the kernel (covariance function). See link kernels
:type kernel: a GPy.kern.kern instance
:param X_variance: The uncertainty in the measurements of X (Gaussian variance)
:type X_variance: np.ndarray (N x input_dim) | None
:type X_variance: np.ndarray (num_data x input_dim) | None
:param Z: inducing inputs (optional, see note)
:type Z: np.ndarray (num_inducing x input_dim) | None
:param num_inducing : Number of inducing points (optional, default 10. Ignored if Z is not None)
@ -69,7 +69,7 @@ class SparseGP(GPBase):
# The rather complex computations of self.A
if self.has_uncertain_inputs:
if self.likelihood.is_heteroscedastic:
psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.num_data, 1, 1))).sum(0)
else:
psi2_beta = self.psi2.sum(0) * self.likelihood.precision
evals, evecs = linalg.eigh(psi2_beta)
@ -77,7 +77,7 @@ class SparseGP(GPBase):
tmp = evecs * np.sqrt(clipped_evals)
else:
if self.likelihood.is_heteroscedastic:
tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.num_data)))
else:
tmp = self.psi1 * (np.sqrt(self.likelihood.precision))
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
@ -99,28 +99,28 @@ class SparseGP(GPBase):
# Compute dL_dKmm
tmp = tdot(self._LBi_Lmi_psi1V)
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.input_dim * np.eye(self.num_inducing) + tmp)
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.output_dim * np.eye(self.num_inducing) + tmp)
tmp = -0.5 * self.DBi_plus_BiPBi
tmp += -0.5 * self.B * self.input_dim
tmp += self.input_dim * np.eye(self.num_inducing)
tmp += -0.5 * self.B * self.output_dim
tmp += self.output_dim * np.eye(self.num_inducing)
self.dL_dKmm = backsub_both_sides(self.Lm, tmp)
# Compute dL_dpsi # FIXME: this is untested for the heterscedastic + uncertain inputs case
self.dL_dpsi0 = -0.5 * self.input_dim * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
self.dL_dpsi0 = -0.5 * self.output_dim * (self.likelihood.precision * np.ones([self.num_data, 1])).flatten()
self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.input_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi)
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.output_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi)
if self.likelihood.is_heteroscedastic:
if self.has_uncertain_inputs:
self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
else:
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, self.psi1 * self.likelihood.precision.reshape(1, self.N))
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, self.psi1 * self.likelihood.precision.reshape(1, self.num_data))
self.dL_dpsi2 = None
else:
dL_dpsi2 = self.likelihood.precision * dL_dpsi2_beta
if self.has_uncertain_inputs:
# repeat for each of the N psi_2 matrices
self.dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], self.N, axis=0)
self.dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], self.num_data, axis=0)
else:
# subsume back into psi1 (==Kmn)
self.dL_dpsi1 += 2.*np.dot(dL_dpsi2, self.psi1)
@ -135,26 +135,26 @@ class SparseGP(GPBase):
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
# likelihood is not heterscedatic
self.partial_for_likelihood = -0.5 * self.N * self.input_dim * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
self.partial_for_likelihood += 0.5 * self.input_dim * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
self.partial_for_likelihood = -0.5 * self.num_data * self.output_dim * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
self.partial_for_likelihood += 0.5 * self.output_dim * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V)))
def log_likelihood(self):
""" Compute the (lower bound on the) log marginal likelihood """
if self.likelihood.is_heteroscedastic:
A = -0.5 * self.N * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
else:
A = -0.5 * self.N * self.output_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
A = -0.5 * self.num_data * self.output_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
C = -self.output_dim * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.num_inducing * np.log(sf2))
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
return A + B + C + D + self.likelihood.Z
def _set_params(self, p):
self.Z = p[:self.num_inducing * self.output_dim].reshape(self.num_inducing, self.input_dim)
self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.Nparam])
self.likelihood._set_params(p[self.Z.size + self.kern.Nparam:])
self.Z = p[:self.num_inducing * self.input_dim].reshape(self.num_inducing, self.input_dim)
self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.num_params])
self.likelihood._set_params(p[self.Z.size + self.kern.num_params:])
self._compute_kernel_matrices()
self._computations()

42
GPy/examples/dimensionality_reduction.py
View file

@ -12,7 +12,7 @@ default_seed = np.random.seed(123344)
def BGPLVM(seed=default_seed):
N = 10
M = 3
num_inducing = 3
Q = 2
D = 4
# generate GPLVM-like data
@ -26,7 +26,7 @@ def BGPLVM(seed=default_seed):
# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
# k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001)
m = GPy.models.BayesianGPLVM(Y, Q, kernel=k, M=M)
m = GPy.models.BayesianGPLVM(Y, Q, kernel=k, num_inducing=num_inducing)
m.constrain_positive('(rbf|bias|noise|white|S)')
# m.constrain_fixed('S', 1)
@ -62,7 +62,7 @@ def GPLVM_oil_100(optimize=True):
m.plot_latent(labels=m.data_labels)
return m
def swiss_roll(optimize=True, N=1000, M=15, Q=4, sigma=.2, plot=False):
def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False):
from GPy.util.datasets import swiss_roll_generated
from GPy.core.transformations import logexp_clipped
@ -100,11 +100,11 @@ def swiss_roll(optimize=True, N=1000, M=15, Q=4, sigma=.2, plot=False):
S = (var * np.ones_like(X) + np.clip(np.random.randn(N, Q) * var ** 2,
- (1 - var),
(1 - var))) + .001
Z = np.random.permutation(X)[:M]
Z = np.random.permutation(X)[:num_inducing]
kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
m = BayesianGPLVM(Y, Q, X=X, X_variance=S, M=M, Z=Z, kernel=kernel)
m = BayesianGPLVM(Y, Q, X=X, X_variance=S, num_inducing=num_inducing, Z=Z, kernel=kernel)
m.data_colors = c
m.data_t = t
@ -117,7 +117,7 @@ def swiss_roll(optimize=True, N=1000, M=15, Q=4, sigma=.2, plot=False):
m.optimize('scg', messages=1)
return m
def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k):
def BGPLVM_oil(optimize=True, N=100, Q=5, num_inducing=25, max_f_eval=4e3, plot=False, **k):
np.random.seed(0)
data = GPy.util.datasets.oil()
from GPy.core.transformations import logexp_clipped
@ -128,7 +128,7 @@ def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k)
Yn = Y - Y.mean(0)
Yn /= Yn.std(0)
m = GPy.models.BayesianGPLVM(Yn, Q, kernel=kernel, M=M, **k)
m = GPy.models.BayesianGPLVM(Yn, Q, kernel=kernel, num_inducing=num_inducing, **k)
m.data_labels = data['Y'][:N].argmax(axis=1)
# m.constrain('variance|leng', logexp_clipped())
@ -167,7 +167,7 @@ def oil_100():
def _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim=False):
def _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim=False):
x = np.linspace(0, 4 * np.pi, N)[:, None]
s1 = np.vectorize(lambda x: np.sin(x))
s2 = np.vectorize(lambda x: np.cos(x))
@ -227,13 +227,13 @@ def bgplvm_simulation_matlab_compare():
Y = sim_data['Y']
S = sim_data['S']
mu = sim_data['mu']
M, [_, Q] = 3, mu.shape
num_inducing, [_, Q] = 3, mu.shape
from GPy.models import mrd
from GPy import kern
reload(mrd); reload(kern)
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
m = BayesianGPLVM(Y, Q, init="PCA", M=M, kernel=k,
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k,
# X=mu,
# X_variance=S,
_debug=False)
@ -247,8 +247,8 @@ def bgplvm_simulation(optimize='scg',
plot=True,
max_f_eval=2e4):
# from GPy.core.transformations import logexp_clipped
D1, D2, D3, N, M, Q = 15, 8, 8, 100, 3, 5
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot)
D1, D2, D3, N, num_inducing, Q = 15, 8, 8, 100, 3, 5
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot)
from GPy.models import mrd
from GPy import kern
@ -258,7 +258,7 @@ def bgplvm_simulation(optimize='scg',
Y = Ylist[0]
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) # + kern.bias(Q)
m = BayesianGPLVM(Y, Q, init="PCA", M=M, kernel=k, _debug=True)
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k, _debug=True)
# m.constrain('variance|noise', logexp_clipped())
m.ensure_default_constraints()
m['noise'] = Y.var() / 100.
@ -275,8 +275,8 @@ def bgplvm_simulation(optimize='scg',
return m
def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
D1, D2, D3, N, M, Q = 150, 200, 400, 500, 3, 7
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim)
D1, D2, D3, N, num_inducing, Q = 150, 200, 400, 500, 3, 7
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
from GPy.models import mrd
from GPy import kern
@ -284,7 +284,7 @@ def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
reload(mrd); reload(kern)
k = kern.linear(Q, [.05] * Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
m = mrd.MRD(Ylist, input_dim=Q, M=M, kernels=k, initx="", initz='permute', **kw)
m = mrd.MRD(Ylist, input_dim=Q, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw)
for i, Y in enumerate(Ylist):
m['{}_noise'.format(i + 1)] = Y.var() / 100.
@ -312,7 +312,7 @@ def brendan_faces():
Yn /= Yn.std()
m = GPy.models.GPLVM(Yn, Q)
# m = GPy.models.BayesianGPLVM(Yn, Q, M=100)
# m = GPy.models.BayesianGPLVM(Yn, Q, num_inducing=100)
# optimize
m.constrain('rbf|noise|white', GPy.core.transformations.logexp_clipped())
@ -376,16 +376,16 @@ def cmu_mocap(subject='35', motion=['01'], in_place=True):
# X /= X.std(axis=0)
#
# Q = 10
# M = 30
# num_inducing = 30
#
# kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
# m = GPy.models.BayesianGPLVM(X, Q, kernel=kernel, M=M)
# m = GPy.models.BayesianGPLVM(X, Q, kernel=kernel, num_inducing=num_inducing)
# # m.scale_factor = 100.0
# m.constrain_positive('(white|noise|bias|X_variance|rbf_variance|rbf_length)')
# from sklearn import cluster
# km = cluster.KMeans(M, verbose=10)
# km = cluster.KMeans(num_inducing, verbose=10)
# Z = km.fit(m.X).cluster_centers_
# # Z = GPy.util.misc.kmm_init(m.X, M)
# # Z = GPy.util.misc.kmm_init(m.X, num_inducing)
# m.set('iip', Z)
# m.set('bias', 1e-4)
# # optimize

42
GPy/examples/regression.py
View file

@ -10,16 +10,16 @@ import numpy as np
import GPy
def toy_rbf_1d(max_nb_eval_optim=100):
def toy_rbf_1d(optimizer='tnc', max_nb_eval_optim=100):
"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
data = GPy.util.datasets.toy_rbf_1d()
# create simple GP model
# create simple GP Model
m = GPy.models.GPRegression(data['X'],data['Y'])
# optimize
m.ensure_default_constraints()
m.optimize(max_f_eval=max_nb_eval_optim)
m.optimize(optimizer, max_f_eval=max_nb_eval_optim)
# plot
m.plot()
print(m)
@ -29,7 +29,7 @@ def rogers_girolami_olympics(optim_iters=100):
"""Run a standard Gaussian process regression on the Rogers and Girolami olympics data."""
data = GPy.util.datasets.rogers_girolami_olympics()
# create simple GP model
# create simple GP Model
m = GPy.models.GPRegression(data['X'],data['Y'])
#set the lengthscale to be something sensible (defaults to 1)
@ -48,7 +48,7 @@ def toy_rbf_1d_50(optim_iters=100):
"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
data = GPy.util.datasets.toy_rbf_1d_50()
# create simple GP model
# create simple GP Model
m = GPy.models.GPRegression(data['X'],data['Y'])
# optimize
@ -64,7 +64,7 @@ def silhouette(optim_iters=100):
"""Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper."""
data = GPy.util.datasets.silhouette()
# create simple GP model
# create simple GP Model
m = GPy.models.GPRegression(data['X'],data['Y'])
# optimize
@ -151,8 +151,8 @@ def coregionalisation_sparse(optim_iters=100):
Y2 = -np.sin(X2) + np.random.randn(*X2.shape)*0.05
Y = np.vstack((Y1,Y2))
M = 40
Z = np.hstack((np.random.rand(M,1)*8,np.random.randint(0,2,M)[:,None]))
num_inducing = 40
Z = np.hstack((np.random.rand(num_inducing,1)*8,np.random.randint(0,2,num_inducing)[:,None]))
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.Coregionalise(2,2)
@ -244,24 +244,24 @@ def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf):
lls = []
total_var = np.var(data['Y'])
kernel = kernel_call(1, variance=1., lengthscale=1.)
model = GPy.models.GPRegression(data['X'], data['Y'], kernel=kernel)
Model = GPy.models.GPRegression(data['X'], data['Y'], kernel=kernel)
for log_SNR in log_SNRs:
SNR = 10.**log_SNR
noise_var = total_var/(1.+SNR)
signal_var = total_var - noise_var
model.kern['.*variance'] = signal_var
model['noise_variance'] = noise_var
Model.kern['.*variance'] = signal_var
Model['noise_variance'] = noise_var
length_scale_lls = []
for length_scale in length_scales:
model['.*lengthscale'] = length_scale
length_scale_lls.append(model.log_likelihood())
Model['.*lengthscale'] = length_scale
length_scale_lls.append(Model.log_likelihood())
lls.append(length_scale_lls)
return np.array(lls)
def sparse_GP_regression_1D(N = 400, M = 5, optim_iters=100):
def sparse_GP_regression_1D(N = 400, num_inducing = 5, optim_iters=100):
"""Run a 1D example of a sparse GP regression."""
# sample inputs and outputs
X = np.random.uniform(-3.,3.,(N,1))
@ -270,8 +270,8 @@ def sparse_GP_regression_1D(N = 400, M = 5, optim_iters=100):
rbf = GPy.kern.rbf(1)
noise = GPy.kern.white(1)
kernel = rbf + noise
# create simple GP model
m = GPy.models.SparseGPRegression(X, Y, kernel, M=M)
# create simple GP Model
m = GPy.models.SparseGPRegression(X, Y, kernel, num_inducing=num_inducing)
m.ensure_default_constraints()
@ -280,7 +280,7 @@ def sparse_GP_regression_1D(N = 400, M = 5, optim_iters=100):
m.plot()
return m
def sparse_GP_regression_2D(N = 400, M = 50, optim_iters=100):
def sparse_GP_regression_2D(N = 400, num_inducing = 50, optim_iters=100):
"""Run a 2D example of a sparse GP regression."""
X = np.random.uniform(-3.,3.,(N,2))
Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(N,1)*0.05
@ -290,8 +290,8 @@ def sparse_GP_regression_2D(N = 400, M = 50, optim_iters=100):
noise = GPy.kern.white(2)
kernel = rbf + noise
# create simple GP model
m = GPy.models.SparseGPRegression(X,Y,kernel, M = M)
# create simple GP Model
m = GPy.models.SparseGPRegression(X,Y,kernel, num_inducing = num_inducing)
# contrain all parameters to be positive (but not inducing inputs)
m.ensure_default_constraints()
@ -318,7 +318,7 @@ def uncertain_inputs_sparse_regression(optim_iters=100):
k = GPy.kern.rbf(1) + GPy.kern.white(1)
# create simple GP model - no input uncertainty on this one
# create simple GP Model - no input uncertainty on this one
m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z)
m.ensure_default_constraints()
m.optimize('scg', messages=1, max_f_eval=optim_iters)
@ -326,7 +326,7 @@ def uncertain_inputs_sparse_regression(optim_iters=100):
axes[0].set_title('no input uncertainty')
#the same model with uncertainty
#the same Model with uncertainty
m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z, X_variance=S)
m.ensure_default_constraints()
m.optimize('scg', messages=1, max_f_eval=optim_iters)

2
GPy/examples/tutorials.py
View file

@ -33,7 +33,7 @@ def tuto_GP_regression():
m.optimize()
m.optimize_restarts(Nrestarts = 10)
m.optimize_restarts(num_restarts = 10)
###########################
# 2-dimensional example #

178
GPy/inference/sgd.py
View file

@ -11,17 +11,17 @@ class opt_SGD(Optimizer):
Optimize using stochastic gradient descent.
*** Parameters ***
model: reference to the model object
Model: reference to the Model object
iterations: number of iterations
learning_rate: learning rate
momentum: momentum
"""
def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, learning_rate_adaptation=None, actual_iter=None, schedule=None, **kwargs):
def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, Model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, learning_rate_adaptation=None, actual_iter=None, schedule=None, **kwargs):
self.opt_name = "Stochastic Gradient Descent"
self.model = model
self.Model = Model
self.iterations = iterations
self.momentum = momentum
self.learning_rate = learning_rate
@ -42,17 +42,17 @@ class opt_SGD(Optimizer):
self.learning_rate_0 = self.learning_rate.mean()
self.schedule = schedule
# if len([p for p in self.model.kern.parts if p.name == 'bias']) == 1:
# if len([p for p in self.Model.kern.parts if p.name == 'bias']) == 1:
# self.param_traces.append(('bias',[]))
# if len([p for p in self.model.kern.parts if p.name == 'linear']) == 1:
# if len([p for p in self.Model.kern.parts if p.name == 'linear']) == 1:
# self.param_traces.append(('linear',[]))
# if len([p for p in self.model.kern.parts if p.name == 'rbf']) == 1:
# if len([p for p in self.Model.kern.parts if p.name == 'rbf']) == 1:
# self.param_traces.append(('rbf_var',[]))
self.param_traces = dict(self.param_traces)
self.fopt_trace = []
num_params = len(self.model._get_params())
num_params = len(self.Model._get_params())
if isinstance(self.learning_rate, float):
self.learning_rate = np.ones((num_params,)) * self.learning_rate
@ -84,7 +84,7 @@ class opt_SGD(Optimizer):
return (np.isnan(data).sum(axis=1) == 0)
def check_for_missing(self, data):
if sp.sparse.issparse(self.model.likelihood.Y):
if sp.sparse.issparse(self.Model.likelihood.Y):
return True
else:
return np.isnan(data).sum() > 0
@ -107,32 +107,32 @@ class opt_SGD(Optimizer):
def shift_constraints(self, j):
constrained_indices = copy.deepcopy(self.model.constrained_indices)
constrained_indices = copy.deepcopy(self.Model.constrained_indices)
for c, constraint in enumerate(constrained_indices):
mask = (np.ones_like(constrained_indices[c]) == 1)
for i in range(len(constrained_indices[c])):
pos = np.where(j == constrained_indices[c][i])[0]
if len(pos) == 1:
self.model.constrained_indices[c][i] = pos
self.Model.constrained_indices[c][i] = pos
else:
mask[i] = False
self.model.constrained_indices[c] = self.model.constrained_indices[c][mask]
self.Model.constrained_indices[c] = self.Model.constrained_indices[c][mask]
return constrained_indices
# back them up
# bounded_i = copy.deepcopy(self.model.constrained_bounded_indices)
# bounded_l = copy.deepcopy(self.model.constrained_bounded_lowers)
# bounded_u = copy.deepcopy(self.model.constrained_bounded_uppers)
# bounded_i = copy.deepcopy(self.Model.constrained_bounded_indices)
# bounded_l = copy.deepcopy(self.Model.constrained_bounded_lowers)
# bounded_u = copy.deepcopy(self.Model.constrained_bounded_uppers)
# for b in range(len(bounded_i)): # for each group of constraints
# for bc in range(len(bounded_i[b])):
# pos = np.where(j == bounded_i[b][bc])[0]
# if len(pos) == 1:
# pos2 = np.where(self.model.constrained_bounded_indices[b] == bounded_i[b][bc])[0][0]
# self.model.constrained_bounded_indices[b][pos2] = pos[0]
# pos2 = np.where(self.Model.constrained_bounded_indices[b] == bounded_i[b][bc])[0][0]
# self.Model.constrained_bounded_indices[b][pos2] = pos[0]
# else:
# if len(self.model.constrained_bounded_indices[b]) == 1:
# if len(self.Model.constrained_bounded_indices[b]) == 1:
# # if it's the last index to be removed
# # the logic here is just a mess. If we remove the last one, then all the
# # b-indices change and we have to iterate through everything to find our
@ -140,35 +140,35 @@ class opt_SGD(Optimizer):
# raise NotImplementedError
# else: # just remove it from the indices
# mask = self.model.constrained_bounded_indices[b] != bc
# self.model.constrained_bounded_indices[b] = self.model.constrained_bounded_indices[b][mask]
# mask = self.Model.constrained_bounded_indices[b] != bc
# self.Model.constrained_bounded_indices[b] = self.Model.constrained_bounded_indices[b][mask]
# # here we shif the positive constraints. We cycle through each positive
# # constraint
# positive = self.model.constrained_positive_indices.copy()
# positive = self.Model.constrained_positive_indices.copy()
# mask = (np.ones_like(positive) == 1)
# for p in range(len(positive)):
# # we now check whether the constrained index appears in the j vector
# # (the vector of the "active" indices)
# pos = np.where(j == self.model.constrained_positive_indices[p])[0]
# pos = np.where(j == self.Model.constrained_positive_indices[p])[0]
# if len(pos) == 1:
# self.model.constrained_positive_indices[p] = pos
# self.Model.constrained_positive_indices[p] = pos
# else:
# mask[p] = False
# self.model.constrained_positive_indices = self.model.constrained_positive_indices[mask]
# self.Model.constrained_positive_indices = self.Model.constrained_positive_indices[mask]
# return (bounded_i, bounded_l, bounded_u), positive
def restore_constraints(self, c):#b, p):
# self.model.constrained_bounded_indices = b[0]
# self.model.constrained_bounded_lowers = b[1]
# self.model.constrained_bounded_uppers = b[2]
# self.model.constrained_positive_indices = p
self.model.constrained_indices = c
# self.Model.constrained_bounded_indices = b[0]
# self.Model.constrained_bounded_lowers = b[1]
# self.Model.constrained_bounded_uppers = b[2]
# self.Model.constrained_positive_indices = p
self.Model.constrained_indices = c
def get_param_shapes(self, N = None, input_dim = None):
model_name = self.model.__class__.__name__
model_name = self.Model.__class__.__name__
if model_name == 'GPLVM':
return [(N, input_dim)]
if model_name == 'Bayesian_GPLVM':
@ -179,37 +179,37 @@ class opt_SGD(Optimizer):
def step_with_missing_data(self, f_fp, X, step, shapes):
N, input_dim = X.shape
if not sp.sparse.issparse(self.model.likelihood.Y):
Y = self.model.likelihood.Y
samples = self.non_null_samples(self.model.likelihood.Y)
self.model.N = samples.sum()
if not sp.sparse.issparse(self.Model.likelihood.Y):
Y = self.Model.likelihood.Y
samples = self.non_null_samples(self.Model.likelihood.Y)
self.Model.N = samples.sum()
Y = Y[samples]
else:
samples = self.model.likelihood.Y.nonzero()[0]
self.model.N = len(samples)
Y = np.asarray(self.model.likelihood.Y[samples].todense(), dtype = np.float64)
samples = self.Model.likelihood.Y.nonzero()[0]
self.Model.N = len(samples)
Y = np.asarray(self.Model.likelihood.Y[samples].todense(), dtype = np.float64)
if self.model.N == 0 or Y.std() == 0.0:
return 0, step, self.model.N
if self.Model.N == 0 or Y.std() == 0.0:
return 0, step, self.Model.N
self.model.likelihood._offset = Y.mean()
self.model.likelihood._scale = Y.std()
self.model.likelihood.set_data(Y)
# self.model.likelihood.V = self.model.likelihood.Y*self.model.likelihood.precision
self.Model.likelihood._offset = Y.mean()
self.Model.likelihood._scale = Y.std()
self.Model.likelihood.set_data(Y)
# self.Model.likelihood.V = self.Model.likelihood.Y*self.Model.likelihood.precision
sigma = self.model.likelihood._variance
self.model.likelihood._variance = None # invalidate cache
self.model.likelihood._set_params(sigma)
sigma = self.Model.likelihood._variance
self.Model.likelihood._variance = None # invalidate cache
self.Model.likelihood._set_params(sigma)
j = self.subset_parameter_vector(self.x_opt, samples, shapes)
self.model.X = X[samples]
self.Model.X = X[samples]
model_name = self.model.__class__.__name__
model_name = self.Model.__class__.__name__
if model_name == 'Bayesian_GPLVM':
self.model.likelihood.YYT = np.dot(self.model.likelihood.Y, self.model.likelihood.Y.T)
self.model.likelihood.trYYT = np.trace(self.model.likelihood.YYT)
self.Model.likelihood.YYT = np.dot(self.Model.likelihood.Y, self.Model.likelihood.Y.T)
self.Model.likelihood.trYYT = np.trace(self.Model.likelihood.YYT)
ci = self.shift_constraints(j)
f, fp = f_fp(self.x_opt[j])
@ -218,18 +218,18 @@ class opt_SGD(Optimizer):
self.x_opt[j] -= step[j]
self.restore_constraints(ci)
self.model.grads[j] = fp
self.Model.grads[j] = fp
# restore likelihood _offset and _scale, otherwise when we call set_data(y) on
# the next feature, it will get normalized with the mean and std of this one.
self.model.likelihood._offset = 0
self.model.likelihood._scale = 1
self.Model.likelihood._offset = 0
self.Model.likelihood._scale = 1
return f, step, self.model.N
return f, step, self.Model.N
def adapt_learning_rate(self, t, D):
if self.learning_rate_adaptation == 'adagrad':
if t > 0:
g_k = self.model.grads
g_k = self.Model.grads
self.s_k += np.square(g_k)
t0 = 100.0
self.learning_rate = 0.1/(t0 + np.sqrt(self.s_k))
@ -245,8 +245,8 @@ class opt_SGD(Optimizer):
elif self.learning_rate_adaptation == 'semi_pesky':
if self.model.__class__.__name__ == 'Bayesian_GPLVM':
g_t = self.model.grads
if self.Model.__class__.__name__ == 'Bayesian_GPLVM':
g_t = self.Model.grads
if t == 0:
self.hbar_t = 0.0
self.tau_t = 100.0
@ -259,28 +259,28 @@ class opt_SGD(Optimizer):
def opt(self, f_fp=None, f=None, fp=None):
self.x_opt = self.model._get_params_transformed()
self.x_opt = self.Model._get_params_transformed()
self.grads = []
X, Y = self.model.X.copy(), self.model.likelihood.Y.copy()
X, Y = self.Model.X.copy(), self.Model.likelihood.Y.copy()
self.model.likelihood.YYT = 0
self.model.likelihood.trYYT = 0
self.model.likelihood._offset = 0.0
self.model.likelihood._scale = 1.0
self.Model.likelihood.YYT = 0
self.Model.likelihood.trYYT = 0
self.Model.likelihood._offset = 0.0
self.Model.likelihood._scale = 1.0
N, input_dim = self.model.X.shape
D = self.model.likelihood.Y.shape[1]
num_params = self.model._get_params()
N, input_dim = self.Model.X.shape
D = self.Model.likelihood.Y.shape[1]
num_params = self.Model._get_params()
self.trace = []
missing_data = self.check_for_missing(self.model.likelihood.Y)
missing_data = self.check_for_missing(self.Model.likelihood.Y)
step = np.zeros_like(num_params)
for it in range(self.iterations):
if self.actual_iter != None:
it = self.actual_iter
self.model.grads = np.zeros_like(self.x_opt) # TODO this is ugly
self.Model.grads = np.zeros_like(self.x_opt) # TODO this is ugly
if it == 0 or self.self_paced is False:
features = np.random.permutation(Y.shape[1])
@ -292,29 +292,29 @@ class opt_SGD(Optimizer):
NLL = []
import pylab as plt
for count, j in enumerate(features):
self.model.input_dim = len(j)
self.model.likelihood.input_dim = len(j)
self.model.likelihood.set_data(Y[:, j])
# self.model.likelihood.V = self.model.likelihood.Y*self.model.likelihood.precision
self.Model.input_dim = len(j)
self.Model.likelihood.input_dim = len(j)
self.Model.likelihood.set_data(Y[:, j])
# self.Model.likelihood.V = self.Model.likelihood.Y*self.Model.likelihood.precision
sigma = self.model.likelihood._variance
self.model.likelihood._variance = None # invalidate cache
self.model.likelihood._set_params(sigma)
sigma = self.Model.likelihood._variance
self.Model.likelihood._variance = None # invalidate cache
self.Model.likelihood._set_params(sigma)
if missing_data:
shapes = self.get_param_shapes(N, input_dim)
f, step, Nj = self.step_with_missing_data(f_fp, X, step, shapes)
else:
self.model.likelihood.YYT = np.dot(self.model.likelihood.Y, self.model.likelihood.Y.T)
self.model.likelihood.trYYT = np.trace(self.model.likelihood.YYT)
self.Model.likelihood.YYT = np.dot(self.Model.likelihood.Y, self.Model.likelihood.Y.T)
self.Model.likelihood.trYYT = np.trace(self.Model.likelihood.YYT)
Nj = N
f, fp = f_fp(self.x_opt)
self.model.grads = fp.copy()
self.Model.grads = fp.copy()
step = self.momentum * step + self.learning_rate * fp
self.x_opt -= step
if self.messages == 2:
noise = self.model.likelihood._variance
noise = self.Model.likelihood._variance
status = "evaluating {feature: 5d}/{tot: 5d} \t f: {f: 2.3f} \t non-missing: {nm: 4d}\t noise: {noise: 2.4f}\r".format(feature = count, tot = len(features), f = f, nm = Nj, noise = noise)
sys.stdout.write(status)
sys.stdout.flush()
@ -328,19 +328,19 @@ class opt_SGD(Optimizer):
# plt.plot(self.param_traces['noise'])
# for k in self.param_traces.keys():
# self.param_traces[k].append(self.model.get(k)[0])
self.grads.append(self.model.grads.tolist())
# self.param_traces[k].append(self.Model.get(k)[0])
self.grads.append(self.Model.grads.tolist())
# should really be a sum(), but earlier samples in the iteration will have a very crappy ll
self.f_opt = np.mean(NLL)
self.model.N = N
self.model.X = X
self.model.input_dim = D
self.model.likelihood.N = N
self.model.likelihood.input_dim = D
self.model.likelihood.Y = Y
sigma = self.model.likelihood._variance
self.model.likelihood._variance = None # invalidate cache
self.model.likelihood._set_params(sigma)
self.Model.N = N
self.Model.X = X
self.Model.input_dim = D
self.Model.likelihood.N = N
self.Model.likelihood.input_dim = D
self.Model.likelihood.Y = Y
sigma = self.Model.likelihood._variance
self.Model.likelihood._variance = None # invalidate cache
self.Model.likelihood._set_params(sigma)
self.trace.append(self.f_opt)
if self.iteration_file is not None:

6
GPy/kern/Brownian.py
View file

@ -2,14 +2,14 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
def theta(x):
"""Heavisdie step function"""
return np.where(x>=0.,1.,0.)
class Brownian(kernpart):
class Brownian(Kernpart):
"""
Brownian Motion kernel.
@ -21,7 +21,7 @@ class Brownian(kernpart):
def __init__(self,input_dim,variance=1.):
self.input_dim = input_dim
assert self.input_dim==1, "Brownian motion in 1D only"
self.Nparam = 1.
self.num_params = 1.
self.name = 'Brownian'
self._set_params(np.array([variance]).flatten())

98
GPy/kern/Matern32.py
View file

@ -2,13 +2,11 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
from ..util.linalg import pdinv,mdot
from scipy import integrate
class Matern32(kernpart):
class Matern32(Kernpart):
"""
Matern 3/2 kernel:
@ -28,11 +26,11 @@ class Matern32(kernpart):
"""
def __init__(self,input_dim,variance=1.,lengthscale=None,ARD=False):
def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False):
self.input_dim = input_dim
self.ARD = ARD
if ARD == False:
self.Nparam = 2
self.num_params = 2
self.name = 'Mat32'
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
@ -40,76 +38,76 @@ class Matern32(kernpart):
else:
lengthscale = np.ones(1)
else:
self.Nparam = self.input_dim + 1
self.num_params = self.input_dim + 1
self.name = 'Mat32'
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == self.input_dim, "bad number of lengthscales"
else:
lengthscale = np.ones(self.input_dim)
self._set_params(np.hstack((variance,lengthscale.flatten())))
self._set_params(np.hstack((variance, lengthscale.flatten())))
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale))
return np.hstack((self.variance, self.lengthscale))
def _set_params(self,x):
def _set_params(self, x):
"""set the value of the parameters."""
assert x.size == self.Nparam
assert x.size == self.num_params
self.variance = x[0]
self.lengthscale = x[1:]
def _get_param_names(self):
"""return parameter names."""
if self.Nparam == 2:
return ['variance','lengthscale']
if self.num_params == 2:
return ['variance', 'lengthscale']
else:
return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)]
return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)]
def K(self,X,X2,target):
def K(self, X, X2, target):
"""Compute the covariance matrix between X and X2."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
np.add(self.variance*(1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist), target,target)
dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))
np.add(self.variance * (1 + np.sqrt(3.) * dist) * np.exp(-np.sqrt(3.) * dist), target, target)
def Kdiag(self,X,target):
def Kdiag(self, X, target):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
np.add(target, self.variance, target)
def dK_dtheta(self,dL_dK,X,X2,target):
def dK_dtheta(self, dL_dK, X, X2, target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
dvar = (1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist)
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscale**3
#dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[0] += np.sum(dvar*dL_dK)
dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))
dvar = (1 + np.sqrt(3.) * dist) * np.exp(-np.sqrt(3.) * dist)
invdist = 1. / np.where(dist != 0., dist, np.inf)
dist2M = np.square(X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 3
# dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[0] += np.sum(dvar * dL_dK)
if self.ARD == True:
dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
#dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None]
target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0)
dl = (self.variance * 3 * dist * np.exp(-np.sqrt(3.) * dist))[:, :, np.newaxis] * dist2M * invdist[:, :, np.newaxis]
# dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None]
target[1:] += (dl * dL_dK[:, :, None]).sum(0).sum(0)
else:
dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist)) * dist2M.sum(-1)*invdist
#dl = self.variance*dvar*dist2M.sum(-1)*invdist
target[1] += np.sum(dl*dL_dK)
dl = (self.variance * 3 * dist * np.exp(-np.sqrt(3.) * dist)) * dist2M.sum(-1) * invdist
# dl = self.variance*dvar*dist2M.sum(-1)*invdist
target[1] += np.sum(dl * dL_dK)
def dKdiag_dtheta(self,dL_dKdiag,X,target):
def dKdiag_dtheta(self, dL_dKdiag, X, target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
target[0] += np.sum(dL_dKdiag)
def dK_dX(self,dL_dK,X,X2,target):
def dK_dX(self, dL_dK, X, X2, target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
dK_dX = - np.transpose(3*self.variance*dist*np.exp(-np.sqrt(3)*dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*dL_dK.T[:,:,None],0)
dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None]
ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
dK_dX = -np.transpose(3 * self.variance * dist * np.exp(-np.sqrt(3) * dist) * ddist_dX, (1, 0, 2))
target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)
def dKdiag_dX(self,dL_dKdiag,X,target):
def dKdiag_dX(self, dL_dKdiag, X, target):
pass
def Gram_matrix(self,F,F1,F2,lower,upper):
def Gram_matrix(self, F, F1, F2, lower, upper):
"""
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1.
@ -123,15 +121,15 @@ class Matern32(kernpart):
:type lower,upper: floats
"""
assert self.input_dim == 1
def L(x,i):
return(3./self.lengthscale**2*F[i](x) + 2*np.sqrt(3)/self.lengthscale*F1[i](x) + F2[i](x))
def L(x, i):
return(3. / self.lengthscale ** 2 * F[i](x) + 2 * np.sqrt(3) / self.lengthscale * F1[i](x) + F2[i](x))
n = F.shape[0]
G = np.zeros((n,n))
G = np.zeros((n, n))
for i in range(n):
for j in range(i,n):
G[i,j] = G[j,i] = integrate.quad(lambda x : L(x,i)*L(x,j),lower,upper)[0]
Flower = np.array([f(lower) for f in F])[:,None]
F1lower = np.array([f(lower) for f in F1])[:,None]
#print "OLD \n", np.dot(F1lower,F1lower.T), "\n \n"
#return(G)
return(self.lengthscale**3/(12.*np.sqrt(3)*self.variance) * G + 1./self.variance*np.dot(Flower,Flower.T) + self.lengthscale**2/(3.*self.variance)*np.dot(F1lower,F1lower.T))
for j in range(i, n):
G[i, j] = G[j, i] = integrate.quad(lambda x : L(x, i) * L(x, j), lower, upper)[0]
Flower = np.array([f(lower) for f in F])[:, None]
F1lower = np.array([f(lower) for f in F1])[:, None]
# print "OLD \n", np.dot(F1lower,F1lower.T), "\n \n"
# return(G)
return(self.lengthscale ** 3 / (12.*np.sqrt(3) * self.variance) * G + 1. / self.variance * np.dot(Flower, Flower.T) + self.lengthscale ** 2 / (3.*self.variance) * np.dot(F1lower, F1lower.T))

12
GPy/kern/Matern52.py
View file

@ -2,12 +2,12 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
from scipy import integrate
class Matern52(kernpart):
class Matern52(Kernpart):
"""
Matern 5/2 kernel:
@ -30,7 +30,7 @@ class Matern52(kernpart):
self.input_dim = input_dim
self.ARD = ARD
if ARD == False:
self.Nparam = 2
self.num_params = 2
self.name = 'Mat52'
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
@ -38,7 +38,7 @@ class Matern52(kernpart):
else:
lengthscale = np.ones(1)
else:
self.Nparam = self.input_dim + 1
self.num_params = self.input_dim + 1
self.name = 'Mat52'
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
@ -53,13 +53,13 @@ class Matern52(kernpart):
def _set_params(self,x):
"""set the value of the parameters."""
assert x.size == self.Nparam
assert x.size == self.num_params
self.variance = x[0]
self.lengthscale = x[1:]
def _get_param_names(self):
"""return parameter names."""
if self.Nparam == 2:
if self.num_params == 2:
return ['variance','lengthscale']
else:
return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)]

2
GPy/kern/__init__.py
View file

@ -2,7 +2,7 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, periodic_exponential, periodic_Matern32, periodic_Matern52, prod, symmetric, Coregionalise, rational_quadratic, fixed, rbfcos, independent_outputs
from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, periodic_exponential, periodic_Matern32, periodic_Matern52, prod, symmetric, Coregionalise, rational_quadratic, Fixed, rbfcos, IndependentOutputs
try:
from constructors import rbf_sympy, sympykern # these depend on sympy
except:

6
GPy/kern/bias.py
View file

@ -2,11 +2,11 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
class bias(kernpart):
class bias(Kernpart):
def __init__(self,input_dim,variance=1.):
"""
:param input_dim: the number of input dimensions
@ -15,7 +15,7 @@ class bias(kernpart):
:type variance: float
"""
self.input_dim = input_dim
self.Nparam = 1
self.num_params = 1
self.name = 'bias'
self._set_params(np.array([variance]).flatten())

10
GPy/kern/constructors.py
View file

@ -12,7 +12,7 @@ from exponential import exponential as exponentialpart
from Matern32 import Matern32 as Matern32part
from Matern52 import Matern52 as Matern52part
from bias import bias as biaspart
from fixed import fixed as fixedpart
from fixed import Fixed as fixedpart
from finite_dimensional import finite_dimensional as finite_dimensionalpart
from spline import spline as splinepart
from Brownian import Brownian as Brownianpart
@ -24,7 +24,7 @@ from symmetric import symmetric as symmetric_part
from coregionalise import Coregionalise as coregionalise_part
from rational_quadratic import rational_quadratic as rational_quadraticpart
from rbfcos import rbfcos as rbfcospart
from independent_outputs import independent_outputs as independent_output_part
from independent_outputs import IndependentOutputs as independent_output_part
#TODO these s=constructors are not as clean as we'd like. Tidy the code up
#using meta-classes to make the objects construct properly wthout them.
@ -294,9 +294,9 @@ def rational_quadratic(D,variance=1., lengthscale=1., power=1.):
part = rational_quadraticpart(D,variance, lengthscale, power)
return kern(D, [part])
def fixed(D, K, variance=1.):
def Fixed(D, K, variance=1.):
"""
Construct a fixed effect kernel.
Construct a Fixed effect kernel.
Arguments
---------
@ -314,7 +314,7 @@ def rbfcos(D,variance=1.,frequencies=None,bandwidths=None,ARD=False):
part = rbfcospart(D,variance,frequencies,bandwidths,ARD)
return kern(D,[part])
def independent_outputs(k):
def IndependentOutputs(k):
"""
Construct a kernel with independent outputs from an existing kernel
"""

24
GPy/kern/coregionalise.py
View file

@ -1,13 +1,13 @@
# Copyright (c) 2012, James Hensman and Ricardo Andrade
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot, pdinv
import pdb
from scipy import weave
class Coregionalise(kernpart):
class Coregionalise(Kernpart):
"""
Kernel for Intrinsic Corregionalization Models
"""
@ -26,14 +26,14 @@ class Coregionalise(kernpart):
else:
assert kappa.shape==(self.Nout,)
self.kappa = kappa
self.Nparam = self.Nout*(self.R + 1)
self.num_params = self.Nout*(self.R + 1)
self._set_params(np.hstack([self.W.flatten(),self.kappa]))
def _get_params(self):
return np.hstack([self.W.flatten(),self.kappa])
def _set_params(self,x):
assert x.size == self.Nparam
assert x.size == self.num_params
self.kappa = x[-self.Nout:]
self.W = x[:-self.Nout].reshape(self.Nout,self.R)
self.B = np.dot(self.W,self.W.T) + np.diag(self.kappa)
@ -69,14 +69,14 @@ class Coregionalise(kernpart):
else:
index2 = np.asarray(index2,dtype=np.int)
code="""
for(int i=0;i<M; i++){
for(int i=0;i<num_inducing; i++){
for(int j=0; j<N; j++){
target[i+j*M] += B[Nout*index[j]+index2[i]];
target[i+j*num_inducing] += B[Nout*index[j]+index2[i]];
}
}
"""
N,M,B,Nout = index.size,index2.size, self.B, self.Nout
weave.inline(code,['target','index','index2','N','M','B','Nout'])
N,num_inducing,B,Nout = index.size,index2.size, self.B, self.Nout
weave.inline(code,['target','index','index2','N','num_inducing','B','Nout'])
def Kdiag(self,index,target):
@ -91,14 +91,14 @@ class Coregionalise(kernpart):
index2 = np.asarray(index2,dtype=np.int)
code="""
for(int i=0; i<M; i++){
for(int i=0; i<num_inducing; i++){
for(int j=0; j<N; j++){
dL_dK_small[index[j] + Nout*index2[i]] += dL_dK[i+j*M];
dL_dK_small[index[j] + Nout*index2[i]] += dL_dK[i+j*num_inducing];
}
}
"""
N, M, Nout = index.size, index2.size, self.Nout
weave.inline(code, ['N','M','Nout','dL_dK','dL_dK_small','index','index2'])
N, num_inducing, Nout = index.size, index2.size, self.Nout
weave.inline(code, ['N','num_inducing','Nout','dL_dK','dL_dK_small','index','index2'])
dkappa = np.diag(dL_dK_small)
dL_dK_small += dL_dK_small.T

101
GPy/kern/exponential.py
View file

@ -2,21 +2,20 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
from scipy import integrate
class exponential(kernpart):
class exponential(Kernpart):
"""
Exponential kernel (aka Ornstein-Uhlenbeck or Matern 1/2)
.. math::
k(r) = \sigma^2 \exp(- r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^D \\frac{(x_i-y_i)^2}{\ell_i^2} }
k(r) = \sigma^2 \exp(- r) \ \ \ \ \ \\text{ where } r = \sqrt{\sum_{i=1}^input_dim \\frac{(x_i-y_i)^2}{\ell_i^2} }
:param D: the number of input dimensions
:type D: int
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance: the variance :math:`\sigma^2`
:type variance: float
:param lengthscale: the vector of lengthscale :math:`\ell_i`
@ -26,11 +25,11 @@ class exponential(kernpart):
:rtype: kernel object
"""
def __init__(self,D,variance=1.,lengthscale=None,ARD=False):
self.D = D
def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False):
self.input_dim = input_dim
self.ARD = ARD
if ARD == False:
self.Nparam = 2
self.num_params = 2
self.name = 'exp'
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
@ -38,76 +37,76 @@ class exponential(kernpart):
else:
lengthscale = np.ones(1)
else:
self.Nparam = self.D + 1
self.num_params = self.input_dim + 1
self.name = 'exp'
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == self.D, "bad number of lengthscales"
assert lengthscale.size == self.input_dim, "bad number of lengthscales"
else:
lengthscale = np.ones(self.D)
self._set_params(np.hstack((variance,lengthscale.flatten())))
lengthscale = np.ones(self.input_dim)
self._set_params(np.hstack((variance, lengthscale.flatten())))
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale))
return np.hstack((self.variance, self.lengthscale))
def _set_params(self,x):
def _set_params(self, x):
"""set the value of the parameters."""
assert x.size == self.Nparam
assert x.size == self.num_params
self.variance = x[0]
self.lengthscale = x[1:]
def _get_param_names(self):
"""return parameter names."""
if self.Nparam == 2:
return ['variance','lengthscale']
if self.num_params == 2:
return ['variance', 'lengthscale']
else:
return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)]
return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)]
def K(self,X,X2,target):
def K(self, X, X2, target):
"""Compute the covariance matrix between X and X2."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
np.add(self.variance*np.exp(-dist), target,target)
dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))
np.add(self.variance * np.exp(-dist), target, target)
def Kdiag(self,X,target):
def Kdiag(self, X, target):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
np.add(target, self.variance, target)
def dK_dtheta(self,dL_dK,X,X2,target):
def dK_dtheta(self, dL_dK, X, X2, target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscale**3
dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))
invdist = 1. / np.where(dist != 0., dist, np.inf)
dist2M = np.square(X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 3
dvar = np.exp(-dist)
target[0] += np.sum(dvar*dL_dK)
target[0] += np.sum(dvar * dL_dK)
if self.ARD == True:
dl = self.variance*dvar[:,:,None]*dist2M*invdist[:,:,None]
target[1:] += (dl*dL_dK[:,:,None]).sum(0).sum(0)
dl = self.variance * dvar[:, :, None] * dist2M * invdist[:, :, None]
target[1:] += (dl * dL_dK[:, :, None]).sum(0).sum(0)
else:
dl = self.variance*dvar*dist2M.sum(-1)*invdist
target[1] += np.sum(dl*dL_dK)
dl = self.variance * dvar * dist2M.sum(-1) * invdist
target[1] += np.sum(dl * dL_dK)
def dKdiag_dtheta(self,dL_dKdiag,X,target):
def dKdiag_dtheta(self, dL_dKdiag, X, target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
#NB: derivative of diagonal elements wrt lengthscale is 0
# NB: derivative of diagonal elements wrt lengthscale is 0
target[0] += np.sum(dL_dKdiag)
def dK_dX(self,dL_dK,X,X2,target):
def dK_dX(self, dL_dK, X, X2, target):
"""derivative of the covariance matrix with respect to X."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscale),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscale**2/np.where(dist!=0.,dist,np.inf)
dK_dX = - np.transpose(self.variance*np.exp(-dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*dL_dK.T[:,:,None],0)
dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None]
ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
dK_dX = -np.transpose(self.variance * np.exp(-dist) * ddist_dX, (1, 0, 2))
target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)
def dKdiag_dX(self,dL_dKdiag,X,target):
def dKdiag_dX(self, dL_dKdiag, X, target):
pass
def Gram_matrix(self,F,F1,lower,upper):
def Gram_matrix(self, F, F1, lower, upper):
"""
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to D=1.
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1.
:param F: vector of functions
:type F: np.array
@ -116,13 +115,13 @@ class exponential(kernpart):
:param lower,upper: boundaries of the input domain
:type lower,upper: floats
"""
assert self.D == 1
def L(x,i):
return(1./self.lengthscale*F[i](x) + F1[i](x))
assert self.input_dim == 1
def L(x, i):
return(1. / self.lengthscale * F[i](x) + F1[i](x))
n = F.shape[0]
G = np.zeros((n,n))
G = np.zeros((n, n))
for i in range(n):
for j in range(i,n):
G[i,j] = G[j,i] = integrate.quad(lambda x : L(x,i)*L(x,j),lower,upper)[0]
Flower = np.array([f(lower) for f in F])[:,None]
return(self.lengthscale/2./self.variance * G + 1./self.variance * np.dot(Flower,Flower.T))
for j in range(i, n):
G[i, j] = G[j, i] = integrate.quad(lambda x : L(x, i) * L(x, j), lower, upper)[0]
Flower = np.array([f(lower) for f in F])[:, None]
return(self.lengthscale / 2. / self.variance * G + 1. / self.variance * np.dot(Flower, Flower.T))

16
GPy/kern/finite_dimensional.py
View file

@ -2,21 +2,21 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
from ..util.linalg import pdinv,mdot
class finite_dimensional(kernpart):
def __init__(self, D, F, G, variance=1., weights=None):
class finite_dimensional(Kernpart):
def __init__(self, input_dim, F, G, variance=1., weights=None):
"""
Argumnents
----------
D: int - the number of input dimensions
input_dim: int - the number of input dimensions
F: np.array of functions with shape (n,) - the n basis functions
G: np.array with shape (n,n) - the Gram matrix associated to F
weights : np.ndarray with shape (n,)
"""
self.D = D
self.input_dim = input_dim
self.F = F
self.G = G
self.G_1 ,L,Li,logdet = pdinv(G)
@ -25,14 +25,14 @@ class finite_dimensional(kernpart):
assert weights.shape==(self.n,)
else:
weights = np.ones(self.n)
self.Nparam = self.n + 1
self.num_params = self.n + 1
self.name = 'finite_dim'
self._set_params(np.hstack((variance,weights)))
def _get_params(self):
return np.hstack((self.variance,self.weights))
def _set_params(self,x):
assert x.size == (self.Nparam)
assert x.size == (self.num_params)
self.variance = x[0]
self.weights = x[1:]
def _get_param_names(self):
@ -48,7 +48,7 @@ class finite_dimensional(kernpart):
product = self.variance * mdot(FX,np.diag(np.sqrt(self.weights)),self.G_1,np.diag(np.sqrt(self.weights)),FX2.T)
np.add(product,target,target)
def Kdiag(self,X,target):
product = np.diag(self.K(X,X2))
product = np.diag(self.K(X, X))
np.add(target,product,target)
def dK_dtheta(self,X,X2,target):
"""Return shape is NxMx(Ntheta)"""

29
GPy/kern/fixed.py
View file

@ -1,42 +1,41 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
class fixed(kernpart):
def __init__(self,D,K,variance=1.):
class Fixed(Kernpart):
def __init__(self, input_dim, K, variance=1.):
"""
:param D: the number of input dimensions
:type D: int
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
"""
self.D = D
self.input_dim = input_dim
self.fixed_K = K
self.Nparam = 1
self.name = 'fixed'
self.num_params = 1
self.name = 'Fixed'
self._set_params(np.array([variance]).flatten())
def _get_params(self):
return self.variance
def _set_params(self,x):
assert x.shape==(1,)
def _set_params(self, x):
assert x.shape == (1,)
self.variance = x
def _get_param_names(self):
return ['variance']
def K(self,X,X2,target):
def K(self, X, X2, target):
target += self.variance * self.fixed_K
def dK_dtheta(self,partial,X,X2,target):
def dK_dtheta(self, partial, X, X2, target):
target += (partial * self.fixed_K).sum()
def dK_dX(self, partial,X, X2, target):
def dK_dX(self, partial, X, X2, target):
pass
def dKdiag_dX(self,partial,X,target):
def dKdiag_dX(self, partial, X, target):
pass

8
GPy/kern/independent_outputs.py
View file

@ -2,7 +2,7 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
def index_to_slices(index):
@ -31,7 +31,7 @@ def index_to_slices(index):
[ret[ind_i].append(slice(*indexes_i)) for ind_i,indexes_i in zip(ind[switchpoints[:-1]],zip(switchpoints,switchpoints[1:]))]
return ret
class independent_outputs(kernpart):
class IndependentOutputs(Kernpart):
"""
A kernel part shich can reopresent several independent functions.
this kernel 'switches off' parts of the matrix where the output indexes are different.
@ -41,8 +41,8 @@ class independent_outputs(kernpart):
"""
def __init__(self,k):
self.D = k.D + 1
self.Nparam = k.Nparam
self.input_dim = k.input_dim + 1
self.num_params = k.num_params
self.name = 'iops('+ k.name + ')'
self.k = k

83
GPy/kern/kern.py
View file

@ -4,30 +4,29 @@
import numpy as np
import pylab as pb
from ..core.parameterised import parameterised
from kernpart import kernpart
from ..core.parameterised import Parameterised
from kernpart import Kernpart
import itertools
from prod import prod
from ..util.linalg import symmetrify
class kern(parameterised):
class kern(Parameterised):
def __init__(self, input_dim, parts=[], input_slices=None):
"""
This is the main kernel class for GPy. It handles multiple (additive) kernel functions, and keeps track of variaous things like which parameters live where.
The technical code for kernels is divided into _parts_ (see e.g. rbf.py). This obnject contains a list of parts, which are computed additively. For multiplication, special _prod_ parts are used.
:param input_dim: The dimensioality of the kernel's input space
:param input_dim: The dimensionality of the kernel's input space
:type input_dim: int
:param parts: the 'parts' (PD functions) of the kernel
:type parts: list of kernpart objects
:type parts: list of Kernpart objects
:param input_slices: the slices on the inputs which apply to each kernel
:type input_slices: list of slice objects, or list of bools
"""
self.parts = parts
self.Nparts = len(parts)
self.Nparam = sum([p.Nparam for p in self.parts])
self.num_params = sum([p.num_params for p in self.parts])
self.input_dim = input_dim
@ -39,11 +38,11 @@ class kern(parameterised):
self.input_slices = [sl if type(sl) is slice else slice(None) for sl in input_slices]
for p in self.parts:
assert isinstance(p, kernpart), "bad kernel part"
assert isinstance(p, Kernpart), "bad kernel part"
self.compute_param_slices()
parameterised.__init__(self)
Parameterised.__init__(self)
def plot_ARD(self, fignum=None, ax=None):
@ -80,8 +79,8 @@ class kern(parameterised):
self.param_slices = []
count = 0
for p in self.parts:
self.param_slices.append(slice(count, count + p.Nparam))
count += p.Nparam
self.param_slices.append(slice(count, count + p.num_params))
count += p.num_params
def __add__(self, other):
"""
@ -104,21 +103,21 @@ class kern(parameterised):
newkern = kern(D, self.parts + other.parts, self_input_slices + other_input_slices)
# transfer constraints:
newkern.constrained_indices = self.constrained_indices + [x + self.Nparam for x in other.constrained_indices]
newkern.constrained_indices = self.constrained_indices + [x + self.num_params for x in other.constrained_indices]
newkern.constraints = self.constraints + other.constraints
newkern.fixed_indices = self.fixed_indices + [self.Nparam + x for x in other.fixed_indices]
newkern.fixed_indices = self.fixed_indices + [self.num_params + x for x in other.fixed_indices]
newkern.fixed_values = self.fixed_values + other.fixed_values
newkern.constraints = self.constraints + other.constraints
newkern.tied_indices = self.tied_indices + [self.Nparam + x for x in other.tied_indices]
newkern.tied_indices = self.tied_indices + [self.num_params + x for x in other.tied_indices]
else:
assert self.input_dim == other.input_dim
newkern = kern(self.input_dim, self.parts + other.parts, self.input_slices + other.input_slices)
# transfer constraints:
newkern.constrained_indices = self.constrained_indices + [i + self.Nparam for i in other.constrained_indices]
newkern.constrained_indices = self.constrained_indices + [i + self.num_params for i in other.constrained_indices]
newkern.constraints = self.constraints + other.constraints
newkern.fixed_indices = self.fixed_indices + [self.Nparam + x for x in other.fixed_indices]
newkern.fixed_indices = self.fixed_indices + [self.num_params + x for x in other.fixed_indices]
newkern.fixed_values = self.fixed_values + other.fixed_values
newkern.tied_indices = self.tied_indices + [self.Nparam + x for x in other.tied_indices]
newkern.tied_indices = self.tied_indices + [self.num_params + x for x in other.tied_indices]
return newkern
def __mul__(self, other):
@ -158,13 +157,13 @@ class kern(parameterised):
K1_param = []
n = 0
for k1 in K1.parts:
K1_param += [range(n, n + k1.Nparam)]
n += k1.Nparam
K1_param += [range(n, n + k1.num_params)]
n += k1.num_params
n = 0
K2_param = []
for k2 in K2.parts:
K2_param += [range(K1.Nparam + n, K1.Nparam + n + k2.Nparam)]
n += k2.Nparam
K2_param += [range(K1.num_params + n, K1.num_params + n + k2.num_params)]
n += k2.num_params
index_param = []
for p1 in K1_param:
for p2 in K2_param:
@ -172,12 +171,12 @@ class kern(parameterised):
index_param = np.array(index_param)
# Get the ties and constrains of the kernels before the multiplication
prev_ties = K1.tied_indices + [arr + K1.Nparam for arr in K2.tied_indices]
prev_ties = K1.tied_indices + [arr + K1.num_params for arr in K2.tied_indices]
prev_constr_ind = [K1.constrained_indices] + [K1.Nparam + i for i in K2.constrained_indices]
prev_constr_ind = [K1.constrained_indices] + [K1.num_params + i for i in K2.constrained_indices]
prev_constr = K1.constraints + K2.constraints
# prev_constr_fix = K1.fixed_indices + [arr + K1.Nparam for arr in K2.fixed_indices]
# prev_constr_fix = K1.fixed_indices + [arr + K1.num_params for arr in K2.fixed_indices]
# prev_constr_fix_values = K1.fixed_values + K2.fixed_values
# follow the previous ties
@ -186,7 +185,7 @@ class kern(parameterised):
index_param[np.where(index_param == j)[0]] = arr[0]
# ties and constrains
for i in range(K1.Nparam + K2.Nparam):
for i in range(K1.num_params + K2.num_params):
index = np.where(index_param == i)[0]
if index.size > 1:
self.tie_params(index)
@ -223,14 +222,14 @@ class kern(parameterised):
def dK_dtheta(self, dL_dK, X, X2=None):
"""
:param dL_dK: An array of dL_dK derivaties, dL_dK
:type dL_dK: Np.ndarray (N x M)
:type dL_dK: Np.ndarray (N x num_inducing)
:param X: Observed data inputs
:type X: np.ndarray (N x input_dim)
:param X2: Observed dara inputs (optional, defaults to X)
:type X2: np.ndarray (M x input_dim)
:type X2: np.ndarray (num_inducing x input_dim)
"""
assert X.shape[1] == self.input_dim
target = np.zeros(self.Nparam)
target = np.zeros(self.num_params)
if X2 is None:
[p.dK_dtheta(dL_dK, X[:, i_s], None, target[ps]) for p, i_s, ps, in zip(self.parts, self.input_slices, self.param_slices)]
else:
@ -259,7 +258,7 @@ class kern(parameterised):
def dKdiag_dtheta(self, dL_dKdiag, X):
assert X.shape[1] == self.input_dim
assert dL_dKdiag.size == X.shape[0]
target = np.zeros(self.Nparam)
target = np.zeros(self.num_params)
[p.dKdiag_dtheta(dL_dKdiag, X[:, i_s], target[ps]) for p, i_s, ps in zip(self.parts, self.input_slices, self.param_slices)]
return self._transform_gradients(target)
@ -275,7 +274,7 @@ class kern(parameterised):
return target
def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S):
target = np.zeros(self.Nparam)
target = np.zeros(self.num_params)
[p.dpsi0_dtheta(dL_dpsi0, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self.parts, self.param_slices, self.input_slices)]
return self._transform_gradients(target)
@ -290,7 +289,7 @@ class kern(parameterised):
return target
def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S):
target = np.zeros((self.Nparam))
target = np.zeros((self.num_params))
[p.dpsi1_dtheta(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self.parts, self.param_slices, self.input_slices)]
return self._transform_gradients(target)
@ -300,16 +299,16 @@ class kern(parameterised):
return target
def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S):
"""return shapes are N,M,input_dim"""
"""return shapes are N,num_inducing,input_dim"""
target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
[p.dpsi1_dmuS(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
return target_mu, target_S
def psi2(self, Z, mu, S):
"""
:param Z: np.ndarray of inducing inputs (M x input_dim)
:param Z: np.ndarray of inducing inputs (num_inducing x input_dim)
:param mu, S: np.ndarrays of means and variances (each N x input_dim)
:returns psi2: np.ndarray (N,M,M)
:returns psi2: np.ndarray (N,num_inducing,num_inducing)
"""
target = np.zeros((mu.shape[0], Z.shape[0], Z.shape[0]))
[p.psi2(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self.parts, self.input_slices)]
@ -327,13 +326,13 @@ class kern(parameterised):
p2.psi1(Z, mu, S, tmp2)
prod = np.multiply(tmp1, tmp2)
crossterms += prod[:,:,None] + prod[:, None, :]
crossterms += prod[:, :, None] + prod[:, None, :]
target += crossterms
return target
def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
target = np.zeros(self.Nparam)
target = np.zeros(self.num_params)
[p.dpsi2_dtheta(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, i_s, ps in zip(self.parts, self.input_slices, self.param_slices)]
# compute the "cross" terms
@ -345,14 +344,14 @@ class kern(parameterised):
tmp = np.zeros((mu.shape[0], Z.shape[0]))
p1.psi1(Z, mu, S, tmp)
p2.dpsi1_dtheta((tmp[:,None,:]*dL_dpsi2).sum(1)*2., Z, mu, S, target[ps2])
p2.dpsi1_dtheta((tmp[:, None, :] * dL_dpsi2).sum(1) * 2., Z, mu, S, target[ps2])
return self._transform_gradients(target)
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S):
target = np.zeros_like(Z)
[p.dpsi2_dZ(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
#target *= 2
# target *= 2
# compute the "cross" terms
# TODO: we need input_slices here.
@ -362,7 +361,7 @@ class kern(parameterised):
tmp = np.zeros((mu.shape[0], Z.shape[0]))
p1.psi1(Z, mu, S, tmp)
tmp2 = np.zeros_like(target)
p2.dpsi1_dZ((tmp[:,None,:]*dL_dpsi2).sum(1).T, Z, mu, S, tmp2)
p2.dpsi1_dZ((tmp[:, None, :] * dL_dpsi2).sum(1).T, Z, mu, S, tmp2)
target += tmp2
return target * 2
@ -379,7 +378,7 @@ class kern(parameterised):
tmp = np.zeros((mu.shape[0], Z.shape[0]))
p1.psi1(Z, mu, S, tmp)
p2.dpsi1_dmuS((tmp[:,None,:]*dL_dpsi2).sum(1).T*2., Z, mu, S, target_mu, target_S)
p2.dpsi1_dmuS((tmp[:, None, :] * dL_dpsi2).sum(1).T * 2., Z, mu, S, target_mu, target_S)
return target_mu, target_S
@ -430,7 +429,7 @@ class kern(parameterised):
Xnew = np.vstack((xx.flatten(), yy.flatten())).T
Kx = self.K(Xnew, x, which_parts)
Kx = Kx.reshape(resolution, resolution).T
pb.contour(xg, yg, Kx, vmin=Kx.min(), vmax=Kx.max(), cmap=pb.cm.jet, *args, **kwargs)
pb.contour(xg, yg, Kx, vmin=Kx.min(), vmax=Kx.max(), cmap=pb.cm.jet, *args, **kwargs) # @UndefinedVariable
pb.xlim(xmin[0], xmax[0])
pb.ylim(xmin[1], xmax[1])
pb.xlabel("x1")

4
GPy/kern/kernpart.py
View file

@ -2,7 +2,7 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
class kernpart(object):
class Kernpart(object):
def __init__(self,input_dim):
"""
The base class for a kernpart: a positive definite function which forms part of a kernel
@ -13,7 +13,7 @@ class kernpart(object):
Do not instantiate.
"""
self.input_dim = input_dim
self.Nparam = 1
self.num_params = 1
self.name = 'unnamed'
def _get_params(self):

34
GPy/kern/linear.py
View file

@ -2,12 +2,12 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
from ..util.linalg import tdot
from scipy import weave
class linear(kernpart):
class linear(Kernpart):
"""
Linear kernel
@ -28,7 +28,7 @@ class linear(kernpart):
self.input_dim = input_dim
self.ARD = ARD
if ARD == False:
self.Nparam = 1
self.num_params = 1
self.name = 'linear'
if variances is not None:
variances = np.asarray(variances)
@ -37,7 +37,7 @@ class linear(kernpart):
variances = np.ones(1)
self._Xcache, self._X2cache = np.empty(shape=(2,))
else:
self.Nparam = self.input_dim
self.num_params = self.input_dim
self.name = 'linear'
if variances is not None:
variances = np.asarray(variances)
@ -54,12 +54,12 @@ class linear(kernpart):
return self.variances
def _set_params(self, x):
assert x.size == (self.Nparam)
assert x.size == (self.num_params)
self.variances = x
self.variances2 = np.square(self.variances)
def _get_param_names(self):
if self.Nparam == 1:
if self.num_params == 1:
return ['variance']
else:
return ['variance_%i' % i for i in range(self.variances.size)]
@ -138,7 +138,7 @@ class linear(kernpart):
def psi2(self, Z, mu, S, target):
"""
returns N,M,M matrix
returns N,num_inducing,num_inducing matrix
"""
self._psi_computations(Z, mu, S)
# psi2_old = self.ZZ * np.square(self.variances) * self.mu2_S[:, None, None, :]
@ -168,7 +168,7 @@ class linear(kernpart):
target += tmp.sum()
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S):
"""Think N,M,M,input_dim """
"""Think N,num_inducing,num_inducing,input_dim """
self._psi_computations(Z, mu, S)
AZZA = self.ZA.T[:, None, :, None] * self.ZA[None, :, None, :]
AZZA = AZZA + AZZA.swapaxes(1, 2)
@ -184,7 +184,7 @@ class linear(kernpart):
double factor,tmp;
#pragma omp parallel for private(m,mm,q,qq,factor,tmp)
for(n=0;n<N;n++){
for(m=0;m<M;m++){
for(m=0;m<num_inducing;m++){
for(mm=0;mm<=m;mm++){
//add in a factor of 2 for the off-diagonal terms (and then count them only once)
if(m==mm)
@ -215,9 +215,9 @@ class linear(kernpart):
'extra_compile_args': ['-fopenmp -O3'], #-march=native'],
'extra_link_args' : ['-lgomp']}
N,M,input_dim = mu.shape[0],Z.shape[0],mu.shape[1]
N,num_inducing,input_dim = mu.shape[0],Z.shape[0],mu.shape[1]
weave.inline(code, support_code=support_code, libraries=['gomp'],
arg_names=['N','M','input_dim','mu','AZZA','AZZA_2','target_mu','target_S','dL_dpsi2'],
arg_names=['N','num_inducing','input_dim','mu','AZZA','AZZA_2','target_mu','target_S','dL_dpsi2'],
type_converters=weave.converters.blitz,**weave_options)
@ -231,9 +231,9 @@ class linear(kernpart):
code="""
int n,m,mm,q;
#pragma omp parallel for private(n,mm,q)
for(m=0;m<M;m++){
for(m=0;m<num_inducing;m++){
for(q=0;q<input_dim;q++){
for(mm=0;mm<M;mm++){
for(mm=0;mm<num_inducing;mm++){
for(n=0;n<N;n++){
target(m,q) += dL_dpsi2(n,m,mm)*AZA(n,mm,q);
}
@ -249,9 +249,9 @@ class linear(kernpart):
'extra_compile_args': ['-fopenmp -O3'], #-march=native'],
'extra_link_args' : ['-lgomp']}
N,M,input_dim = mu.shape[0],Z.shape[0],mu.shape[1]
N,num_inducing,input_dim = mu.shape[0],Z.shape[0],mu.shape[1]
weave.inline(code, support_code=support_code, libraries=['gomp'],
arg_names=['N','M','input_dim','AZA','target','dL_dpsi2'],
arg_names=['N','num_inducing','input_dim','AZA','target','dL_dpsi2'],
type_converters=weave.converters.blitz,**weave_options)
@ -278,7 +278,7 @@ class linear(kernpart):
muS_changed = not (np.array_equal(mu, self._mu) and np.array_equal(S, self._S))
if Zv_changed:
# Z has changed, compute Z specific stuff
# self.ZZ = Z[:,None,:]*Z[None,:,:] # M,M,input_dim
# self.ZZ = Z[:,None,:]*Z[None,:,:] # num_inducing,num_inducing,input_dim
# self.ZZ = np.empty((Z.shape[0], Z.shape[0], Z.shape[1]), order='F')
# [tdot(Z[:, i:i + 1], self.ZZ[:, :, i].T) for i in xrange(Z.shape[1])]
self.ZA = Z * self.variances
@ -291,5 +291,5 @@ class linear(kernpart):
self.inner[:, diag_indices[0], diag_indices[1]] += S
self._mu, self._S = mu.copy(), S.copy()
if Zv_changed or muS_changed:
self.ZAinner = np.dot(self.ZA, self.inner).swapaxes(0, 1) # NOTE: self.ZAinner \in [M x N x input_dim]!
self.ZAinner = np.dot(self.ZA, self.inner).swapaxes(0, 1) # NOTE: self.ZAinner \in [num_inducing x N x input_dim]!
self._psi2 = np.dot(self.ZAinner, self.ZA.T)

14
GPy/kern/periodic_Matern32.py
View file

@ -2,12 +2,12 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot, pdinv
from GPy.util.linalg import mdot
from GPy.util.decorators import silence_errors
class periodic_Matern32(kernpart):
class periodic_Matern32(Kernpart):
"""
Kernel of the periodic subspace (up to a given frequency) of a Matern 3/2 RKHS. Only defined for input_dim=1.
@ -25,7 +25,7 @@ class periodic_Matern32(kernpart):
"""
def __init__(self,input_dim=1,variance=1.,lengthscale=None,period=2*np.pi,n_freq=10,lower=0.,upper=4*np.pi):
def __init__(self, input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
assert input_dim==1, "Periodic kernels are only defined for input_dim=1"
self.name = 'periodic_Mat32'
self.input_dim = input_dim
@ -35,7 +35,7 @@ class periodic_Matern32(kernpart):
else:
lengthscale = np.ones(1)
self.lower,self.upper = lower, upper
self.Nparam = 3
self.num_params = 3
self.n_freq = n_freq
self.n_basis = 2*n_freq
self._set_params(np.hstack((variance,lengthscale,period)))
@ -64,7 +64,7 @@ class periodic_Matern32(kernpart):
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale,self.period))
def _set_params(self,x):
"""set the value of the parameters."""
assert x.size==3
@ -113,7 +113,7 @@ class periodic_Matern32(kernpart):
@silence_errors
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is NxMxNparam)"""
"""derivative of the covariance matrix with respect to the parameters (shape is Nxnum_inducingxNparam)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)

14
GPy/kern/periodic_Matern52.py
View file

@ -2,12 +2,12 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot, pdinv
from GPy.util.linalg import mdot
from GPy.util.decorators import silence_errors
class periodic_Matern52(kernpart):
class periodic_Matern52(Kernpart):
"""
Kernel of the periodic subspace (up to a given frequency) of a Matern 5/2 RKHS. Only defined for input_dim=1.
@ -35,7 +35,7 @@ class periodic_Matern52(kernpart):
else:
lengthscale = np.ones(1)
self.lower,self.upper = lower, upper
self.Nparam = 3
self.num_params = 3
self.n_freq = n_freq
self.n_basis = 2*n_freq
self._set_params(np.hstack((variance,lengthscale,period)))
@ -64,7 +64,7 @@ class periodic_Matern52(kernpart):
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale,self.period))
def _set_params(self,x):
"""set the value of the parameters."""
assert x.size==3
@ -115,7 +115,7 @@ class periodic_Matern52(kernpart):
@silence_errors
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is NxMxNparam)"""
"""derivative of the covariance matrix with respect to the parameters (shape is Nxnum_inducingxNparam)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)
@ -209,7 +209,7 @@ class periodic_Matern52(kernpart):
F2lower = np.array(self._cos(self.basis_alpha*self.basis_omega**2,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None]
#dK_dvar
dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T)
dK_dvar = 1. / self.variance * mdot(FX, self.Gi, FX.T)
#dK_dlen
da_dlen = [-3*self.a[0]/self.lengthscale, -2*self.a[1]/self.lengthscale, -self.a[2]/self.lengthscale, 0.]

14
GPy/kern/periodic_exponential.py
View file

@ -2,12 +2,12 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
from GPy.util.linalg import mdot, pdinv
from GPy.util.linalg import mdot
from GPy.util.decorators import silence_errors
class periodic_exponential(kernpart):
class periodic_exponential(Kernpart):
"""
Kernel of the periodic subspace (up to a given frequency) of a exponential (Matern 1/2) RKHS. Only defined for input_dim=1.
@ -25,7 +25,7 @@ class periodic_exponential(kernpart):
"""
def __init__(self,input_dim=1,variance=1.,lengthscale=None,period=2*np.pi,n_freq=10,lower=0.,upper=4*np.pi):
def __init__(self, input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
assert input_dim==1, "Periodic kernels are only defined for input_dim=1"
self.name = 'periodic_exp'
self.input_dim = input_dim
@ -35,7 +35,7 @@ class periodic_exponential(kernpart):
else:
lengthscale = np.ones(1)
self.lower,self.upper = lower, upper
self.Nparam = 3
self.num_params = 3
self.n_freq = n_freq
self.n_basis = 2*n_freq
self._set_params(np.hstack((variance,lengthscale,period)))
@ -64,7 +64,7 @@ class periodic_exponential(kernpart):
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscale,self.period))
def _set_params(self,x):
"""set the value of the parameters."""
assert x.size==3
@ -111,7 +111,7 @@ class periodic_exponential(kernpart):
@silence_errors
def dK_dtheta(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters (shape is NxMxNparam)"""
"""derivative of the covariance matrix with respect to the parameters (shape is Nxnum_inducingxNparam)"""
if X2 is None: X2 = X
FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
FX2 = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X2)

24
GPy/kern/prod.py
View file

@ -1,23 +1,23 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
class prod(kernpart):
class prod(Kernpart):
"""
Computes the product of 2 kernels
:param k1, k2: the kernels to multiply
:type k1, k2: kernpart
:type k1, k2: Kernpart
:param tensor: The kernels are either multiply as functions defined on the same input space (default) or on the product of the input spaces
:type tensor: Boolean
:rtype: kernel object
"""
def __init__(self,k1,k2,tensor=False):
self.Nparam = k1.Nparam + k2.Nparam
self.num_params = k1.num_params + k2.num_params
self.name = k1.name + '<times>' + k2.name
self.k1 = k1
self.k2 = k2
@ -40,8 +40,8 @@ class prod(kernpart):
def _set_params(self,x):
"""set the value of the parameters."""
self.k1._set_params(x[:self.k1.Nparam])
self.k2._set_params(x[self.k1.Nparam:])
self.k1._set_params(x[:self.k1.num_params])
self.k2._set_params(x[self.k1.num_params:])
def _get_param_names(self):
"""return parameter names."""
@ -55,11 +55,11 @@ class prod(kernpart):
"""derivative of the covariance matrix with respect to the parameters."""
self._K_computations(X,X2)
if X2 is None:
self.k1.dK_dtheta(dL_dK*self._K2, X[:,self.slice1], None, target[:self.k1.Nparam])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.slice2], None, target[self.k1.Nparam:])
self.k1.dK_dtheta(dL_dK*self._K2, X[:,self.slice1], None, target[:self.k1.num_params])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.slice2], None, target[self.k1.num_params:])
else:
self.k1.dK_dtheta(dL_dK*self._K2, X[:,self.slice1], X2[:,self.slice1], target[:self.k1.Nparam])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.slice2], X2[:,self.slice2], target[self.k1.Nparam:])
self.k1.dK_dtheta(dL_dK*self._K2, X[:,self.slice1], X2[:,self.slice1], target[:self.k1.num_params])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.slice2], X2[:,self.slice2], target[self.k1.num_params:])
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
@ -74,8 +74,8 @@ class prod(kernpart):
K2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,self.slice1],K1)
self.k2.Kdiag(X[:,self.slice2],K2)
self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,self.slice1],target[:self.k1.Nparam])
self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.slice2],target[self.k1.Nparam:])
self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,self.slice1],target[:self.k1.num_params])
self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.slice2],target[self.k1.num_params:])
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""

24
GPy/kern/prod_orthogonal.py
View file

@ -1,23 +1,23 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
#from scipy import integrate # This may not be necessary (Nicolas, 20th Feb)
class prod_orthogonal(kernpart):
class prod_orthogonal(Kernpart):
"""
Computes the product of 2 kernels
:param k1, k2: the kernels to multiply
:type k1, k2: kernpart
:type k1, k2: Kernpart
:rtype: kernel object
"""
def __init__(self,k1,k2):
self.input_dim = k1.input_dim + k2.input_dim
self.Nparam = k1.Nparam + k2.Nparam
self.num_params = k1.num_params + k2.num_params
self.name = k1.name + '<times>' + k2.name
self.k1 = k1
self.k2 = k2
@ -30,8 +30,8 @@ class prod_orthogonal(kernpart):
def _set_params(self,x):
"""set the value of the parameters."""
self.k1._set_params(x[:self.k1.Nparam])
self.k2._set_params(x[self.k1.Nparam:])
self.k1._set_params(x[:self.k1.num_params])
self.k2._set_params(x[self.k1.num_params:])
def _get_param_names(self):
"""return parameter names."""
@ -45,11 +45,11 @@ class prod_orthogonal(kernpart):
"""derivative of the covariance matrix with respect to the parameters."""
self._K_computations(X,X2)
if X2 is None:
self.k1.dK_dtheta(dL_dK*self._K2, X[:,:self.k1.input_dim], None, target[:self.k1.Nparam])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.k1.input_dim:], None, target[self.k1.Nparam:])
self.k1.dK_dtheta(dL_dK*self._K2, X[:,:self.k1.input_dim], None, target[:self.k1.num_params])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.k1.input_dim:], None, target[self.k1.num_params:])
else:
self.k1.dK_dtheta(dL_dK*self._K2, X[:,:self.k1.input_dim], X2[:,:self.k1.input_dim], target[:self.k1.Nparam])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.k1.input_dim:], X2[:,self.k1.input_dim:], target[self.k1.Nparam:])
self.k1.dK_dtheta(dL_dK*self._K2, X[:,:self.k1.input_dim], X2[:,:self.k1.input_dim], target[:self.k1.num_params])
self.k2.dK_dtheta(dL_dK*self._K1, X[:,self.k1.input_dim:], X2[:,self.k1.input_dim:], target[self.k1.num_params:])
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
@ -64,8 +64,8 @@ class prod_orthogonal(kernpart):
K2 = np.zeros(X.shape[0])
self.k1.Kdiag(X[:,:self.k1.input_dim],K1)
self.k2.Kdiag(X[:,self.k1.input_dim:],K2)
self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,:self.k1.input_dim],target[:self.k1.Nparam])
self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.k1.input_dim:],target[self.k1.Nparam:])
self.k1.dKdiag_dtheta(dL_dKdiag*K2,X[:,:self.k1.input_dim],target[:self.k1.num_params])
self.k2.dKdiag_dtheta(dL_dKdiag*K1,X[:,self.k1.input_dim:],target[self.k1.num_params:])
def dK_dX(self,dL_dK,X,X2,target):
"""derivative of the covariance matrix with respect to X."""

8
GPy/kern/rational_quadratic.py
View file

@ -2,10 +2,10 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
class rational_quadratic(kernpart):
class rational_quadratic(Kernpart):
"""
rational quadratic kernel
@ -21,13 +21,13 @@ class rational_quadratic(kernpart):
:type lengthscale: float
:param power: the power :math:`\\alpha`
:type power: float
:rtype: kernpart object
:rtype: Kernpart object
"""
def __init__(self,input_dim,variance=1.,lengthscale=1.,power=1.):
assert input_dim == 1, "For this kernel we assume input_dim=1"
self.input_dim = input_dim
self.Nparam = 3
self.num_params = 3
self.name = 'rat_quad'
self.variance = variance
self.lengthscale = lengthscale

87
GPy/kern/rbf.py
View file

@ -2,13 +2,13 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
from scipy import weave
from ..util.linalg import tdot
class rbf(kernpart):
class rbf(Kernpart):
"""
Radial Basis Function kernel, aka squared-exponential, exponentiated quadratic or Gaussian kernel:
@ -36,14 +36,14 @@ class rbf(kernpart):
self.name = 'rbf'
self.ARD = ARD
if not ARD:
self.Nparam = 2
self.num_params = 2
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == 1, "Only one lengthscale needed for non-ARD kernel"
else:
lengthscale = np.ones(1)
else:
self.Nparam = self.input_dim + 1
self.num_params = self.input_dim + 1
if lengthscale is not None:
lengthscale = np.asarray(lengthscale)
assert lengthscale.size == self.input_dim, "bad number of lengthscales"
@ -67,7 +67,7 @@ class rbf(kernpart):
return np.hstack((self.variance, self.lengthscale))
def _set_params(self, x):
assert x.size == (self.Nparam)
assert x.size == (self.num_params)
self.variance = x[0]
self.lengthscale = x[1:]
self.lengthscale2 = np.square(self.lengthscale)
@ -76,7 +76,7 @@ class rbf(kernpart):
self._Z, self._mu, self._S = np.empty(shape=(3, 1)) # cached versions of Z,mu,S
def _get_param_names(self):
if self.Nparam == 2:
if self.num_params == 2:
return ['variance', 'lengthscale']
else:
return ['variance'] + ['lengthscale_%i' % i for i in range(self.lengthscale.size)]
@ -110,7 +110,7 @@ class rbf(kernpart):
target(q+1) += var_len3(q)*tmp;
}
"""
N, M, input_dim = X.shape[0], X.shape[0], self.input_dim
N, num_inducing, input_dim = X.shape[0], X.shape[0], self.input_dim
else:
code = """
int q,i,j;
@ -118,16 +118,16 @@ class rbf(kernpart):
for(q=0; q<input_dim; q++){
tmp = 0;
for(i=0; i<N; i++){
for(j=0; j<M; j++){
for(j=0; j<num_inducing; j++){
tmp += (X(i,q)-X2(j,q))*(X(i,q)-X2(j,q))*dvardLdK(i,j);
}
}
target(q+1) += var_len3(q)*tmp;
}
"""
N, M, input_dim = X.shape[0], X2.shape[0], self.input_dim
N, num_inducing, input_dim = X.shape[0], X2.shape[0], self.input_dim
# [np.add(target[1+q:2+q],var_len3[q]*np.sum(dvardLdK*np.square(X[:,q][:,None]-X2[:,q][None,:])),target[1+q:2+q]) for q in range(self.input_dim)]
weave.inline(code, arg_names=['N', 'M', 'input_dim', 'X', 'X2', 'target', 'dvardLdK', 'var_len3'],
weave.inline(code, arg_names=['N','num_inducing','input_dim','X','X2','target','dvardLdK','var_len3'],
type_converters=weave.converters.blitz, **self.weave_options)
else:
target[1] += (self.variance / self.lengthscale) * np.sum(self._K_dvar * self._K_dist2 * dL_dK)
@ -191,7 +191,7 @@ class rbf(kernpart):
target += self._psi2
def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S, target):
"""Shape N,M,M,Ntheta"""
"""Shape N,num_inducing,num_inducing,Ntheta"""
self._psi_computations(Z, mu, S)
d_var = 2.*self._psi2 / self.variance
d_length = 2.*self._psi2[:, :, :, None] * (self._psi2_Zdist_sq * self._psi2_denom + self._psi2_mudist_sq + S[:, None, None, :] / self.lengthscale2) / (self.lengthscale * self._psi2_denom)
@ -205,19 +205,18 @@ class rbf(kernpart):
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S, target):
self._psi_computations(Z, mu, S)
term1 = self._psi2_Zdist / self.lengthscale2 # M, M, input_dim
term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, M, M, input_dim
term1 = self._psi2_Zdist / self.lengthscale2 # num_inducing, num_inducing, input_dim
term2 = self._psi2_mudist / self._psi2_denom / self.lengthscale2 # N, num_inducing, num_inducing, input_dim
dZ = self._psi2[:, :, :, None] * (term1[None] + term2)
target += (dL_dpsi2[:, :, :, None] * dZ).sum(0).sum(0)
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S, target_mu, target_S):
"""Think N,M,M,input_dim """
"""Think N,num_inducing,num_inducing,input_dim """
self._psi_computations(Z, mu, S)
tmp = self._psi2[:, :, :, None] / self.lengthscale2 / self._psi2_denom
target_mu += -2.*(dL_dpsi2[:, :, :, None] * tmp * self._psi2_mudist).sum(1).sum(1)
target_S += (dL_dpsi2[:, :, :, None] * tmp * (2.*self._psi2_mudist_sq - 1)).sum(1).sum(1)
#---------------------------------------#
# Precomputations #
#---------------------------------------#
@ -241,41 +240,41 @@ class rbf(kernpart):
def _psi_computations(self, Z, mu, S):
# here are the "statistics" for psi1 and psi2
if not np.array_equal(Z, self._Z):
# Z has changed, compute Z specific stuff
self._psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,input_dim
self._psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,input_dim
self._psi2_Zdist_sq = np.square(self._psi2_Zdist / self.lengthscale) # M,M,input_dim
#Z has changed, compute Z specific stuff
self._psi2_Zhat = 0.5*(Z[:,None,:] +Z[None,:,:]) # num_inducing,num_inducing,input_dim
self._psi2_Zdist = 0.5*(Z[:,None,:]-Z[None,:,:]) # num_inducing,num_inducing,input_dim
self._psi2_Zdist_sq = np.square(self._psi2_Zdist/self.lengthscale) # num_inducing,num_inducing,input_dim
self._Z = Z
if not (np.array_equal(Z, self._Z) and np.array_equal(mu, self._mu) and np.array_equal(S, self._S)):
# something's changed. recompute EVERYTHING
#something's changed. recompute EVERYTHING
# psi1
self._psi1_denom = S[:, None, :] / self.lengthscale2 + 1.
self._psi1_dist = Z[None, :, :] - mu[:, None, :]
self._psi1_dist_sq = np.square(self._psi1_dist) / self.lengthscale2 / self._psi1_denom
self._psi1_exponent = -0.5 * np.sum(self._psi1_dist_sq + np.log(self._psi1_denom), -1)
self._psi1 = self.variance * np.exp(self._psi1_exponent)
#psi1
self._psi1_denom = S[:,None,:]/self.lengthscale2 + 1.
self._psi1_dist = Z[None,:,:]-mu[:,None,:]
self._psi1_dist_sq = np.square(self._psi1_dist)/self.lengthscale2/self._psi1_denom
self._psi1_exponent = -0.5*np.sum(self._psi1_dist_sq+np.log(self._psi1_denom),-1)
self._psi1 = self.variance*np.exp(self._psi1_exponent)
# psi2
self._psi2_denom = 2.*S[:, None, None, :] / self.lengthscale2 + 1. # N,M,M,input_dim
self._psi2_mudist, self._psi2_mudist_sq, self._psi2_exponent, _ = self.weave_psi2(mu, self._psi2_Zhat)
# self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,M,M,input_dim
# self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
# self._psi2_exponent = np.sum(-self._psi2_Zdist_sq -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,M,M
self._psi2 = np.square(self.variance) * np.exp(self._psi2_exponent) # N,M,M
#psi2
self._psi2_denom = 2.*S[:,None,None,:]/self.lengthscale2+1. # N,num_inducing,num_inducing,input_dim
self._psi2_mudist, self._psi2_mudist_sq, self._psi2_exponent, _ = self.weave_psi2(mu,self._psi2_Zhat)
#self._psi2_mudist = mu[:,None,None,:]-self._psi2_Zhat #N,num_inducing,num_inducing,input_dim
#self._psi2_mudist_sq = np.square(self._psi2_mudist)/(self.lengthscale2*self._psi2_denom)
#self._psi2_exponent = np.sum(-self._psi2_Zdist_sq -self._psi2_mudist_sq -0.5*np.log(self._psi2_denom),-1) #N,num_inducing,num_inducing
self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,num_inducing,num_inducing
# store matrices for caching
self._Z, self._mu, self._S = Z, mu, S
#store matrices for caching
self._Z, self._mu, self._S = Z, mu,S
def weave_psi2(self, mu, Zhat):
N, input_dim = mu.shape
M = Zhat.shape[0]
def weave_psi2(self,mu,Zhat):
N,input_dim = mu.shape
num_inducing = Zhat.shape[0]
mudist = np.empty((N, M, M, input_dim))
mudist_sq = np.empty((N, M, M, input_dim))
psi2_exponent = np.zeros((N, M, M))
psi2 = np.empty((N, M, M))
mudist = np.empty((N,num_inducing,num_inducing,input_dim))
mudist_sq = np.empty((N,num_inducing,num_inducing,input_dim))
psi2_exponent = np.zeros((N,num_inducing,num_inducing))
psi2 = np.empty((N,num_inducing,num_inducing))
psi2_Zdist_sq = self._psi2_Zdist_sq
_psi2_denom = self._psi2_denom.squeeze().reshape(N, self.input_dim)
@ -290,7 +289,7 @@ class rbf(kernpart):
#pragma omp parallel for private(tmp)
for (int n=0; n<N; n++){
for (int m=0; m<M; m++){
for (int m=0; m<num_inducing; m++){
for (int mm=0; mm<(m+1); mm++){
for (int q=0; q<input_dim; q++){
//compute mudist
@ -325,7 +324,7 @@ class rbf(kernpart):
#include <math.h>
"""
weave.inline(code, support_code=support_code, libraries=['gomp'],
arg_names=['N', 'M', 'input_dim', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'lengthscale2', '_psi2_denom', 'psi2_Zdist_sq', 'psi2_exponent', 'half_log_psi2_denom', 'psi2', 'variance_sq'],
arg_names=['N','num_inducing','input_dim','mu','Zhat','mudist_sq','mudist','lengthscale2','_psi2_denom','psi2_Zdist_sq','psi2_exponent','half_log_psi2_denom','psi2','variance_sq'],
type_converters=weave.converters.blitz, **self.weave_options)
return mudist, mudist_sq, psi2_exponent, psi2

16
GPy/kern/rbfcos.py
View file

@ -3,10 +3,10 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
class rbfcos(kernpart):
class rbfcos(Kernpart):
def __init__(self,input_dim,variance=1.,frequencies=None,bandwidths=None,ARD=False):
self.input_dim = input_dim
self.name = 'rbfcos'
@ -14,9 +14,9 @@ class rbfcos(kernpart):
print "Warning: the rbfcos kernel requires a lot of memory for high dimensional inputs"
self.ARD = ARD
#set the default frequencies and bandwidths, appropriate Nparam
#set the default frequencies and bandwidths, appropriate num_params
if ARD:
self.Nparam = 2*self.input_dim + 1
self.num_params = 2*self.input_dim + 1
if frequencies is not None:
frequencies = np.asarray(frequencies)
assert frequencies.size == self.input_dim, "bad number of frequencies"
@ -28,7 +28,7 @@ class rbfcos(kernpart):
else:
bandwidths = np.ones(self.input_dim)
else:
self.Nparam = 3
self.num_params = 3
if frequencies is not None:
frequencies = np.asarray(frequencies)
assert frequencies.size == 1, "Exactly one frequency needed for non-ARD kernel"
@ -51,7 +51,7 @@ class rbfcos(kernpart):
return np.hstack((self.variance,self.frequencies, self.bandwidths))
def _set_params(self,x):
assert x.size==(self.Nparam)
assert x.size==(self.num_params)
if self.ARD:
self.variance = x[0]
self.frequencies = x[1:1+self.input_dim]
@ -60,7 +60,7 @@ class rbfcos(kernpart):
self.variance, self.frequencies, self.bandwidths = x
def _get_param_names(self):
if self.Nparam == 3:
if self.num_params == 3:
return ['variance','frequency','bandwidth']
else:
return ['variance']+['frequency_%i'%i for i in range(self.input_dim)]+['bandwidth_%i'%i for i in range(self.input_dim)]
@ -106,7 +106,7 @@ class rbfcos(kernpart):
self._dist2 = np.square(self._dist)
#ensure the next section is computed:
self._params = np.empty(self.Nparam)
self._params = np.empty(self.num_params)
if not np.all(self._params == self._get_params()):
self._params == self._get_params().copy()

6
GPy/kern/spline.py
View file

@ -2,14 +2,14 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
import hashlib
def theta(x):
"""Heaviside step function"""
return np.where(x>=0.,1.,0.)
class spline(kernpart):
class spline(Kernpart):
"""
Spline kernel
@ -23,7 +23,7 @@ class spline(kernpart):
def __init__(self,input_dim,variance=1.,lengthscale=1.):
self.input_dim = input_dim
assert self.input_dim==1
self.Nparam = 1
self.num_params = 1
self.name = 'spline'
self._set_params(np.squeeze(variance))

10
GPy/kern/symmetric.py
View file

@ -1,18 +1,18 @@
# Copyright (c) 2012 James Hensman
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
class symmetric(kernpart):
class symmetric(Kernpart):
"""
Symmetrical kernels
:param k: the kernel to symmetrify
:type k: kernpart
:type k: Kernpart
:param transform: the transform to use in symmetrification (allows symmetry on specified axes)
:type transform: A numpy array (input_dim x input_dim) specifiying the transform
:rtype: kernpart
:rtype: Kernpart
"""
def __init__(self,k,transform=None):
@ -21,7 +21,7 @@ class symmetric(kernpart):
assert transform.shape == (k.input_dim, k.input_dim)
self.transform = transform
self.input_dim = k.input_dim
self.Nparam = k.Nparam
self.num_params = k.num_params
self.name = k.name + '_symm'
self.k = k
self._set_params(k._get_params())

34
GPy/kern/sympykern.py
View file

@ -9,9 +9,9 @@ import sys
current_dir = os.path.dirname(os.path.abspath(os.path.dirname(__file__)))
import tempfile
import pdb
from kernpart import kernpart
from kernpart import Kernpart
class spkern(kernpart):
class spkern(Kernpart):
"""
A kernel object, where all the hard work in done by sympy.
@ -38,12 +38,12 @@ class spkern(kernpart):
self.input_dim = len(self._sp_x)
assert self.input_dim == input_dim
self._sp_theta = sorted([e for e in sp_vars if not (e.name[0]=='x' or e.name[0]=='z')],key=lambda e:e.name)
self.Nparam = len(self._sp_theta)
self.num_params = len(self._sp_theta)
#deal with param
if param is None:
param = np.ones(self.Nparam)
assert param.size==self.Nparam
param = np.ones(self.num_params)
assert param.size==self.num_params
self._set_params(param)
#Differentiate!
@ -115,19 +115,19 @@ class spkern(kernpart):
#Here's some code to do the looping for K
arglist = ", ".join(["X[i*input_dim+%s]"%x.name[1:] for x in self._sp_x]\
+ ["Z[j*input_dim+%s]"%z.name[1:] for z in self._sp_z]\
+ ["param[%i]"%i for i in range(self.Nparam)])
+ ["param[%i]"%i for i in range(self.num_params)])
self._K_code =\
"""
int i;
int j;
int N = target_array->dimensions[0];
int M = target_array->dimensions[1];
int num_inducing = target_array->dimensions[1];
int input_dim = X_array->dimensions[1];
//#pragma omp parallel for private(j)
for (i=0;i<N;i++){
for (j=0;j<M;j++){
target[i*M+j] = k(%s);
for (j=0;j<num_inducing;j++){
target[i*num_inducing+j] = k(%s);
}
}
%s
@ -149,17 +149,17 @@ class spkern(kernpart):
"""%(diag_arglist,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
#here's some code to compute gradients
funclist = '\n'.join([' '*16 + 'target[%i] += partial[i*M+j]*dk_d%s(%s);'%(i,theta.name,arglist) for i,theta in enumerate(self._sp_theta)])
funclist = '\n'.join([' '*16 + 'target[%i] += partial[i*num_inducing+j]*dk_d%s(%s);'%(i,theta.name,arglist) for i,theta in enumerate(self._sp_theta)])
self._dK_dtheta_code =\
"""
int i;
int j;
int N = partial_array->dimensions[0];
int M = partial_array->dimensions[1];
int num_inducing = partial_array->dimensions[1];
int input_dim = X_array->dimensions[1];
//#pragma omp parallel for private(j)
for (i=0;i<N;i++){
for (j=0;j<M;j++){
for (j=0;j<num_inducing;j++){
%s
}
}
@ -169,7 +169,7 @@ class spkern(kernpart):
#here's some code to compute gradients for Kdiag TODO: thius is yucky.
diag_funclist = re.sub('Z','X',funclist,count=0)
diag_funclist = re.sub('j','i',diag_funclist)
diag_funclist = re.sub('partial\[i\*M\+i\]','partial[i]',diag_funclist)
diag_funclist = re.sub('partial\[i\*num_inducing\+i\]','partial[i]',diag_funclist)
self._dKdiag_dtheta_code =\
"""
int i;
@ -182,17 +182,17 @@ class spkern(kernpart):
"""%(diag_funclist,"/*"+str(self._sp_k)+"*/") #adding a string representation forces recompile when needed
#Here's some code to do gradients wrt x
gradient_funcs = "\n".join(["target[i*input_dim+%i] += partial[i*M+j]*dk_dx%i(%s);"%(q,q,arglist) for q in range(self.input_dim)])
gradient_funcs = "\n".join(["target[i*input_dim+%i] += partial[i*num_inducing+j]*dk_dx%i(%s);"%(q,q,arglist) for q in range(self.input_dim)])
self._dK_dX_code = \
"""
int i;
int j;
int N = partial_array->dimensions[0];
int M = partial_array->dimensions[1];
int num_inducing = partial_array->dimensions[1];
int input_dim = X_array->dimensions[1];
//#pragma omp parallel for private(j)
for (i=0;i<N; i++){
for (j=0; j<M; j++){
for (j=0; j<num_inducing; j++){
%s
//if(isnan(target[i*input_dim+2])){printf("%%f\\n",dk_dx2(X[i*input_dim+0], X[i*input_dim+1], X[i*input_dim+2], Z[j*input_dim+0], Z[j*input_dim+1], Z[j*input_dim+2], param[0], param[1], param[2], param[3], param[4], param[5]));}
//if(isnan(target[i*input_dim+2])){printf("%%f,%%f,%%i,%%i\\n", X[i*input_dim+2], Z[j*input_dim+2],i,j);}
@ -208,7 +208,7 @@ class spkern(kernpart):
int i;
int j;
int N = partial_array->dimensions[0];
int M = 0;
int num_inducing = 0;
int input_dim = X_array->dimensions[1];
for (i=0;i<N; i++){
j = i;

6
GPy/kern/white.py
View file

@ -2,9 +2,9 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from kernpart import kernpart
from kernpart import Kernpart
import numpy as np
class white(kernpart):
class white(Kernpart):
"""
White noise kernel.
@ -15,7 +15,7 @@ class white(kernpart):
"""
def __init__(self,input_dim,variance=1.):
self.input_dim = input_dim
self.Nparam = 1
self.num_params = 1
self.name = 'white'
self._set_params(np.array([variance]).flatten())
self._psi1 = 0 # TODO: more elegance here

12
GPy/likelihoods/ep.py
View file

@ -139,7 +139,7 @@ class EP(likelihood):
The expectation-propagation algorithm with sparse pseudo-input.
For nomenclature see ... 2013.
"""
M = Kmm.shape[0]
num_inducing = Kmm.shape[0]
#TODO: this doesn't work with uncertain inputs!
@ -235,7 +235,7 @@ class EP(likelihood):
The expectation-propagation algorithm with sparse pseudo-input.
For nomenclature see Naish-Guzman and Holden, 2008.
"""
M = Kmm.shape[0]
num_inducing = Kmm.shape[0]
"""
Prior approximation parameters:
@ -258,7 +258,7 @@ class EP(likelihood):
mu = w + P*Gamma
"""
self.w = np.zeros(self.N)
self.Gamma = np.zeros(M)
self.Gamma = np.zeros(num_inducing)
mu = np.zeros(self.N)
P = P0.copy()
R = R0.copy()
@ -305,10 +305,10 @@ class EP(likelihood):
dtd1 = Delta_tau*Diag[i] + 1.
dii = Diag[i]
Diag[i] = dii - (Delta_tau * dii**2.)/dtd1
pi_ = P[i,:].reshape(1,M)
pi_ = P[i,:].reshape(1,num_inducing)
P[i,:] = pi_ - (Delta_tau*dii)/dtd1 * pi_
Rp_i = np.dot(R,pi_.T)
RTR = np.dot(R.T,np.dot(np.eye(M) - Delta_tau/(1.+Delta_tau*Sigma_diag[i]) * np.dot(Rp_i,Rp_i.T),R))
RTR = np.dot(R.T,np.dot(np.eye(num_inducing) - Delta_tau/(1.+Delta_tau*Sigma_diag[i]) * np.dot(Rp_i,Rp_i.T),R))
R = jitchol(RTR).T
self.w[i] += (Delta_v - Delta_tau*self.w[i])*dii/dtd1
self.Gamma += (Delta_v - Delta_tau*mu[i])*np.dot(RTR,P[i,:].T)
@ -321,7 +321,7 @@ class EP(likelihood):
Diag = Diag0 * Iplus_Dprod_i
P = Iplus_Dprod_i[:,None] * P0
safe_diag = np.where(Diag0 < self.tau_tilde, self.tau_tilde/(1.+Diag0*self.tau_tilde), (1. - Iplus_Dprod_i)/Diag0)
L = jitchol(np.eye(M) + np.dot(RPT0,safe_diag[:,None]*RPT0.T))
L = jitchol(np.eye(num_inducing) + np.dot(RPT0,safe_diag[:,None]*RPT0.T))
R,info = linalg.lapack.flapack.dtrtrs(L,R0,lower=1)
RPT = np.dot(R,P.T)
Sigma_diag = Diag + np.sum(RPT.T*RPT.T,-1)

20
GPy/models/bayesian_gplvm.py
View file

@ -23,7 +23,7 @@ class BayesianGPLVM(SparseGP, GPLVM):
:type init: 'PCA'|'random'
"""
def __init__(self, likelihood_or_Y, input_dim, X=None, X_variance=None, init='PCA', M=10,
def __init__(self, likelihood_or_Y, input_dim, X=None, X_variance=None, init='PCA', num_inducing=10,
Z=None, kernel=None, oldpsave=10, _debug=False,
**kwargs):
if type(likelihood_or_Y) is np.ndarray:
@ -39,7 +39,7 @@ class BayesianGPLVM(SparseGP, GPLVM):
X_variance = np.clip((np.ones_like(X) * 0.5) + .01 * np.random.randn(*X.shape), 0.001, 1)
if Z is None:
Z = np.random.permutation(X.copy())[:M]
Z = np.random.permutation(X.copy())[:num_inducing]
assert Z.shape[1] == X.shape[1]
if kernel is None:
@ -73,8 +73,8 @@ class BayesianGPLVM(SparseGP, GPLVM):
self._oldps.insert(0, p.copy())
def _get_param_names(self):
X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
return (X_names + S_names + SparseGP._get_param_names(self))
def _get_params(self):
@ -96,7 +96,7 @@ class BayesianGPLVM(SparseGP, GPLVM):
def _set_params(self, x, save_old=True, save_count=0):
# try:
x = self._clipped(x)
N, input_dim = self.N, self.input_dim
N, input_dim = self.num_data, self.input_dim
self.X = x[:self.X.size].reshape(N, input_dim).copy()
self.X_variance = x[(N * input_dim):(2 * N * input_dim)].reshape(N, input_dim).copy()
SparseGP._set_params(self, x[(2 * N * input_dim):])
@ -126,7 +126,7 @@ class BayesianGPLVM(SparseGP, GPLVM):
def KL_divergence(self):
var_mean = np.square(self.X).sum()
var_S = np.sum(self.X_variance - np.log(self.X_variance))
return 0.5 * (var_mean + var_S) - 0.5 * self.input_dim * self.N
return 0.5 * (var_mean + var_S) - 0.5 * self.input_dim * self.num_data
def log_likelihood(self):
ll = SparseGP.log_likelihood(self)
@ -146,11 +146,11 @@ class BayesianGPLVM(SparseGP, GPLVM):
self._savedpsiKmm.append([self.f_call, [self.Kmm, self.dL_dKmm]])
# sf2 = self.scale_factor ** 2
if self.likelihood.is_heteroscedastic:
A = -0.5 * self.N * self.input_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.V * self.likelihood.Y)
A = -0.5 * self.num_data * self.input_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.V * self.likelihood.Y)
# B = -0.5 * self.input_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A) * sf2)
B = -0.5 * self.input_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
else:
A = -0.5 * self.N * self.input_dim * (np.log(2.*np.pi) + np.log(self.likelihood._variance)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
A = -0.5 * self.num_data * self.input_dim * (np.log(2.*np.pi) + np.log(self.likelihood._variance)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
# B = -0.5 * self.input_dim * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A) * sf2)
B = -0.5 * self.input_dim * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
C = -self.input_dim * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.num_inducing * np.log(sf2))
@ -266,9 +266,9 @@ class BayesianGPLVM(SparseGP, GPLVM):
def _debug_filter_params(self, x):
start, end = 0, self.X.size,
X = x[start:end].reshape(self.N, self.input_dim)
X = x[start:end].reshape(self.num_data, self.input_dim)
start, end = end, end + self.X_variance.size
X_v = x[start:end].reshape(self.N, self.input_dim)
X_v = x[start:end].reshape(self.num_data, self.input_dim)
start, end = end, end + (self.num_inducing * self.input_dim)
Z = x[start:end].reshape(self.num_inducing, self.input_dim)
start, end = end, end + self.input_dim

6
GPy/models/fitc.py
View file

@ -52,7 +52,7 @@ class FITC(SparseGP):
else:
if self.likelihood.is_heteroscedastic:
assert self.likelihood.input_dim == 1
tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.num_data)))
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
self.A = tdot(tmp)
@ -108,7 +108,7 @@ class FITC(SparseGP):
self._dpsi1_dX_jkj = 0
self._dpsi1_dtheta_jkj = 0
for i, V_n, alpha_n, gamma_n, gamma_k in zip(range(self.N), self.V_star, alpha, gamma_2, gamma_3):
for i, V_n, alpha_n, gamma_n, gamma_k in zip(range(self.num_data), self.V_star, alpha, gamma_2, gamma_3):
K_pp_K = np.dot(Kmmipsi1[:, i:(i + 1)], Kmmipsi1[:, i:(i + 1)].T)
# Diag_dpsi1 = Diag_dA_dpsi1: yT*beta_star*y + Diag_dC_dpsi1 +Diag_dD_dpsi1
@ -155,7 +155,7 @@ class FITC(SparseGP):
def log_likelihood(self):
""" Compute the (lower bound on the) log marginal likelihood """
A = -0.5 * self.N * self.input_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y)
A = -0.5 * self.num_data * self.input_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.beta_star)) - 0.5 * np.sum(self.V_star * self.likelihood.Y)
C = -self.input_dim * (np.sum(np.log(np.diag(self.LB))))
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
return A + C + D

2
GPy/models/fitc_classification.py
View file

@ -16,7 +16,7 @@ class FITCClassification(FITC):
:param X: input observations
:param Y: observed values
:param likelihood: a GPy likelihood, defaults to binomial with probit link_function
:param likelihood: a GPy likelihood, defaults to Binomial with probit link_function
:param kernel: a GPy kernel, defaults to rbf+white
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
:type normalize_X: False|True

131
GPy/models/generalized_fitc.py
View file

@ -2,21 +2,14 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import pylab as pb
from ..util.linalg import mdot, jitchol, chol_inv, pdinv, trace_dot
from ..util.plot import gpplot
from .. import kern
from scipy import stats, linalg
<<<<<<< HEAD:GPy/models/generalized_FITC.py
from sparse_GP import sparse_GP
=======
from ..core import SparseGP
>>>>>>> 7040b26f41f382edfdca3d3f7b689b9bbfc1a54f:GPy/models/generalized_fitc.py
from scipy import linalg
from GPy.core.sparse_gp import SparseGP
from GPy.util.linalg import mdot
def backsub_both_sides(L,X):
def backsub_both_sides(L, X):
""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
tmp,_ = linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(X),lower=1,trans=1)
return linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(tmp.T),lower=1,trans=1)[0].T
tmp, _ = linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(X), lower=1, trans=1)
return linalg.lapack.flapack.dtrtrs(L, np.asfortranarray(tmp.T), lower=1, trans=1)[0].T
class GeneralizedFITC(SparseGP):
@ -45,17 +38,13 @@ class GeneralizedFITC(SparseGP):
self.num_inducing = self.Z.shape[0]
self.true_precision = likelihood.precision
<<<<<<< HEAD:GPy/models/generalized_FITC.py
sparse_GP.__init__(self, X, likelihood, kernel=kernel, Z=self.Z, X_variance=None, normalize_X=False)
=======
super(GeneralizedFITC, self).__init__(X, likelihood, kernel=kernel, Z=self.Z, X_variance=X_variance, normalize_X=normalize_X)
self._set_params(self._get_params())
>>>>>>> 7040b26f41f382edfdca3d3f7b689b9bbfc1a54f:GPy/models/generalized_fitc.py
def _set_params(self, p):
self.Z = p[:self.num_inducing*self.input_dim].reshape(self.num_inducing, self.input_dim)
self.kern._set_params(p[self.Z.size:self.Z.size+self.kern.Nparam])
self.likelihood._set_params(p[self.Z.size+self.kern.Nparam:])
self.Z = p[:self.num_inducing * self.input_dim].reshape(self.num_inducing, self.input_dim)
self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.num_params])
self.likelihood._set_params(p[self.Z.size + self.kern.num_params:])
self._compute_kernel_matrices()
self._computations()
self._FITC_computations()
@ -73,9 +62,9 @@ class GeneralizedFITC(SparseGP):
if self.has_uncertain_inputs:
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
else:
self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
self.likelihood.fit_FITC(self.Kmm, self.psi1, self.psi0)
self.true_precision = self.likelihood.precision # Save the true precision
self.likelihood.precision = self.true_precision/(1. + self.true_precision*self.Diag0[:,None]) # Add the diagonal element of the FITC approximation
self.likelihood.precision = self.true_precision / (1. + self.true_precision * self.Diag0[:, None]) # Add the diagonal element of the FITC approximation
self._set_params(self._get_params()) # update the GP
def _FITC_computations(self):
@ -87,37 +76,37 @@ class GeneralizedFITC(SparseGP):
- removes the extra terms computed in the SparseGP approximation
- computes the likelihood gradients wrt the true precision.
"""
#NOTE the true precison is now 'true_precision' not 'precision'
# NOTE the true precison is now 'true_precision' not 'precision'
if self.likelihood.is_heteroscedastic:
# Compute generalized FITC's diagonal term of the covariance
self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.num_inducing),lower=1)
Lmipsi1 = np.dot(self.Lmi,self.psi1)
self.Qnn = np.dot(Lmipsi1.T,Lmipsi1)
#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
#self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
#a = kj
self.Lmi, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.eye(self.num_inducing), lower=1)
Lmipsi1 = np.dot(self.Lmi, self.psi1)
self.Qnn = np.dot(Lmipsi1.T, Lmipsi1)
# self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
# self.Qnn = mdot(self.psi1.T,self.Kmmi,self.psi1)
# a = kj
self.Diag0 = self.psi0 - np.diag(self.Qnn)
Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.true_precision.flatten())
Iplus_Dprod_i = 1. / (1. + self.Diag0 * self.true_precision.flatten())
self.Diag = self.Diag0 * Iplus_Dprod_i
self.P = Iplus_Dprod_i[:,None] * self.psi1.T
self.RPT0 = np.dot(self.Lmi,self.psi1)
self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
self.R,info = linalg.flapack.dtrtrs(self.L,self.Lmi,lower=1)
self.RPT = np.dot(self.R,self.P.T)
self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T,self.RPT)
self.P = Iplus_Dprod_i[:, None] * self.psi1.T
self.RPT0 = np.dot(self.Lmi, self.psi1)
self.L = np.linalg.cholesky(np.eye(self.num_inducing) + np.dot(self.RPT0, ((1. - Iplus_Dprod_i) / self.Diag0)[:, None] * self.RPT0.T))
self.R, info = linalg.lapack.dtrtrs(self.L, self.Lmi, lower=1)
self.RPT = np.dot(self.R, self.P.T)
self.Sigma = np.diag(self.Diag) + np.dot(self.RPT.T, self.RPT)
self.w = self.Diag * self.likelihood.v_tilde
self.Gamma = np.dot(self.R.T, np.dot(self.RPT,self.likelihood.v_tilde))
self.mu = self.w + np.dot(self.P,self.Gamma)
self.Gamma = np.dot(self.R.T, np.dot(self.RPT, self.likelihood.v_tilde))
self.mu = self.w + np.dot(self.P, self.Gamma)
# Remove extra term from dL_dpsi1
self.dL_dpsi1 -= mdot(self.Lmi.T,Lmipsi1*self.likelihood.precision.flatten().reshape(1,self.N))
self.dL_dpsi1 -= mdot(self.Lmi.T,Lmipsi1 * self.likelihood.precision.flatten().reshape(1,self.num_data))
#self.Kmmi, Lm, Lmi, Kmm_logdet = pdinv(self.Kmm)
#self.dL_dpsi1 -= mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.N)) #dB
#self.dL_dpsi1 -= mdot(self.Kmmi,self.psi1*self.likelihood.precision.flatten().reshape(1,self.num_data)) #dB
#########333333
#self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
# self.Bi, self.LB, self.LBi, self.B_logdet = pdinv(self.B)
#########333333
@ -125,16 +114,16 @@ class GeneralizedFITC(SparseGP):
else:
raise NotImplementedError, "homoscedastic fitc not implemented"
# Remove extra term from dL_dpsi1
#self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
# self.dL_dpsi1 += -mdot(self.Kmmi,self.psi1*self.likelihood.precision) #dB
sf = self.scale_factor
sf2 = sf**2
sf2 = sf ** 2
# Remove extra term from dL_dKmm
self.dL_dKmm += 0.5 * self.input_dim * mdot(self.Lmi.T, self.A, self.Lmi)*sf2 # dB
self.dL_dKmm += 0.5 * self.input_dim * mdot(self.Lmi.T, self.A, self.Lmi) * sf2 # dB
self.dL_dpsi0 = None
#the partial derivative vector for the likelihood
# the partial derivative vector for the likelihood
if self.likelihood.Nparams == 0:
self.partial_for_likelihood = None
elif self.likelihood.is_heteroscedastic:
@ -142,7 +131,7 @@ class GeneralizedFITC(SparseGP):
else:
raise NotImplementedError, "homoscedastic derivatives not implemented"
#likelihood is not heterscedatic
#self.partial_for_likelihood = - 0.5 * self.N*self.input_dim*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
#self.partial_for_likelihood = - 0.5 * self.num_data*self.input_dim*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
#self.partial_for_likelihood += 0.5 * self.input_dim * trace_dot(self.Bi,self.A)*self.likelihood.precision
#self.partial_for_likelihood += self.likelihood.precision*(0.5*trace_dot(self.psi2_beta_scaled,self.E*sf2) - np.trace(self.Cpsi1VVpsi1))
#TODO partial derivative vector for the likelihood not implemented
@ -151,28 +140,28 @@ class GeneralizedFITC(SparseGP):
"""
Compute and return the derivative of the log marginal likelihood wrt the parameters of the kernel
"""
dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm,self.Z)
dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z)
if self.has_uncertain_inputs:
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
#NOTE in SparseGP this would include the gradient wrt psi0
dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1,self.Z,self.X)
# NOTE in SparseGP this would include the gradient wrt psi0
dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.Z, self.X)
return dL_dtheta
def log_likelihood(self):
""" Compute the (lower bound on the) log marginal likelihood """
sf2 = self.scale_factor**2
sf2 = self.scale_factor ** 2
if self.likelihood.is_heteroscedastic:
A = -0.5*self.N*self.input_dim*np.log(2.*np.pi) +0.5*np.sum(np.log(self.likelihood.precision)) -0.5*np.sum(self.V*self.likelihood.Y)
A = -0.5*self.num_data*self.input_dim*np.log(2.*np.pi) +0.5*np.sum(np.log(self.likelihood.precision)) -0.5*np.sum(self.V*self.likelihood.Y)
else:
A = -0.5*self.N*self.input_dim*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT
A = -0.5*self.num_data*self.input_dim*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT
C = -self.input_dim * (np.sum(np.log(np.diag(self.LB))) + 0.5*self.num_inducing*np.log(sf2))
#C = -0.5*self.input_dim * (self.B_logdet + self.num_inducing*np.log(sf2))
D = 0.5*np.sum(np.square(self._LBi_Lmi_psi1V))
#self.Cpsi1VVpsi1 = np.dot(self.Cpsi1V,self.psi1V.T)
#D_ = 0.5*np.trace(self.Cpsi1VVpsi1)
return A+C+D
return A + C + D
def _raw_predict(self, Xnew, which_parts, full_cov=False):
if self.likelihood.is_heteroscedastic:
@ -191,30 +180,30 @@ class GeneralizedFITC(SparseGP):
# = I - [RPT0] * (U*U.T)^-1 * [RPT0].T
# = I - V.T * V
U = np.linalg.cholesky(np.diag(self.Diag0) + self.Qnn)
V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
C = np.eye(self.num_inducing) - np.dot(V.T,V)
mu_u = np.dot(C,self.RPT0)*(1./self.Diag0[None,:])
#self.C = C
#self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
#self.mu_u = mu_u
#self.U = U
V, info = linalg.flapack.dtrtrs(U, self.RPT0.T, lower=1)
C = np.eye(self.num_inducing) - np.dot(V.T, V)
mu_u = np.dot(C, self.RPT0) * (1. / self.Diag0[None, :])
# self.C = C
# self.RPT0 = np.dot(self.R0,self.Knm.T) P0.T
# self.mu_u = mu_u
# self.U = U
# q(u|y) = N(u| R0i*mu_H,R0i*Sigma_H*R0i.T)
mu_H = np.dot(mu_u,self.mu)
mu_H = np.dot(mu_u, self.mu)
self.mu_H = mu_H
Sigma_H = C + np.dot(mu_u,np.dot(self.Sigma,mu_u.T))
Sigma_H = C + np.dot(mu_u, np.dot(self.Sigma, mu_u.T))
# q(f_star|y) = N(f_star|mu_star,sigma2_star)
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
KR0T = np.dot(Kx.T,self.Lmi.T)
mu_star = np.dot(KR0T,mu_H)
KR0T = np.dot(Kx.T, self.Lmi.T)
mu_star = np.dot(KR0T, mu_H)
if full_cov:
Kxx = self.kern.K(Xnew,which_parts=which_parts)
var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T))
Kxx = self.kern.K(Xnew, which_parts=which_parts)
var = Kxx + np.dot(KR0T, np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T))
else:
Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
Kxx_ = self.kern.K(Xnew,which_parts=which_parts) # TODO: RA, is this line needed?
var_ = Kxx_ + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T)) # TODO: RA, is this line needed?
var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.num_inducing),KR0T.T),0))[:,None]
return mu_star[:,None],var
Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
Kxx_ = self.kern.K(Xnew, which_parts=which_parts) # TODO: RA, is this line needed?
var_ = Kxx_ + np.dot(KR0T, np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T)) # TODO: RA, is this line needed?
var = (Kxx + np.sum(KR0T.T * np.dot(Sigma_H - np.eye(self.num_inducing), KR0T.T), 0))[:, None]
return mu_star[:, None], var
else:
raise NotImplementedError, "homoscedastic fitc not implemented"
"""

6
GPy/models/gplvm.py
View file

@ -6,7 +6,7 @@ import numpy as np
import pylab as pb
import sys, pdb
from .. import kern
from ..core import model
from ..core import Model
from ..util.linalg import pdinv, PCA
from ..core import GP
from ..likelihoods import Gaussian
@ -42,13 +42,13 @@ class GPLVM(GP):
return np.random.randn(Y.shape[0], input_dim)
def _get_param_names(self):
return sum([['X_%i_%i'%(n,q) for q in range(self.input_dim)] for n in range(self.N)],[]) + GP._get_param_names(self)
return sum([['X_%i_%i'%(n,q) for q in range(self.input_dim)] for n in range(self.num_data)],[]) + GP._get_param_names(self)
def _get_params(self):
return np.hstack((self.X.flatten(), GP._get_params(self)))
def _set_params(self,x):
self.X = x[:self.N*self.input_dim].reshape(self.N,self.input_dim).copy()
self.X = x[:self.num_data*self.input_dim].reshape(self.num_data,self.input_dim).copy()
GP._set_params(self, x[self.X.size:])
def _log_likelihood_gradients(self):

26
GPy/models/mrd.py
View file

@ -3,7 +3,7 @@ Created on 10 Apr 2013
@author: Max Zwiessele
'''
from GPy.core import model
from GPy.core import Model
from GPy.core import SparseGP
from GPy.util.linalg import PCA
import numpy
@ -12,7 +12,7 @@ import pylab
from GPy.kern.kern import kern
from GPy.models.bayesian_gplvm import BayesianGPLVM
class MRD(model):
class MRD(Model):
"""
Do MRD on given Datasets in Ylist.
All Ys in likelihood_list are in [N x Dn], where Dn can be different per Yn,
@ -33,7 +33,7 @@ class MRD(model):
:param X_variance:
Initial latent space variance
:param init: [cooncat|single|random]
initialization method to use:
initialization method to use:
*concat: PCA on concatenated outputs
*single: PCA on each output
*random: random
@ -44,7 +44,7 @@ class MRD(model):
:param kernels: list of kernels or kernel shared for all BGPLVMS
:type kernels: [GPy.kern.kern] | GPy.kern.kern | None (default)
"""
def __init__(self, likelihood_or_Y_list, input_dim, M=10, names=None,
def __init__(self, likelihood_or_Y_list, input_dim, num_inducing=10, names=None,
kernels=None, initx='PCA',
initz='permute', _debug=False, **kw):
if names is None:
@ -61,24 +61,24 @@ class MRD(model):
assert not ('kernel' in kw), "pass kernels through `kernels` argument"
self.input_dim = input_dim
self.num_inducing = M
self.num_inducing = num_inducing
self._debug = _debug
self._init = True
X = self._init_X(initx, likelihood_or_Y_list)
Z = self._init_Z(initz, X)
self.bgplvms = [BayesianGPLVM(l, input_dim=input_dim, kernel=k, X=X, Z=Z, M=self.num_inducing, **kw) for l, k in zip(likelihood_or_Y_list, kernels)]
self.bgplvms = [BayesianGPLVM(l, input_dim=input_dim, kernel=k, X=X, Z=Z, num_inducing=self.num_inducing, **kw) for l, k in zip(likelihood_or_Y_list, kernels)]
del self._init
self.gref = self.bgplvms[0]
nparams = numpy.array([0] + [SparseGP._get_params(g).size - g.Z.size for g in self.bgplvms])
self.nparams = nparams.cumsum()
self.N = self.gref.N
self.NQ = self.N * self.input_dim
self.num_data = self.gref.num_data
self.NQ = self.num_data * self.input_dim
self.MQ = self.num_inducing * self.input_dim
model.__init__(self) # @UndefinedVariable
Model.__init__(self) # @UndefinedVariable
self._set_params(self._get_params())
@property
@ -142,8 +142,8 @@ class MRD(model):
self._init_Z(initz, self.X)
def _get_param_names(self):
# X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
# S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
# X_names = sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
# S_names = sum([['X_variance_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
n1 = self.gref._get_param_names()
n1var = n1[:self.NQ * 2 + self.MQ]
map_names = lambda ns, name: map(lambda x: "{1}_{0}".format(*x),
@ -169,8 +169,8 @@ class MRD(model):
return params
# def _set_var_params(self, g, X, X_var, Z):
# g.X = X.reshape(self.N, self.input_dim)
# g.X_variance = X_var.reshape(self.N, self.input_dim)
# g.X = X.reshape(self.num_data, self.input_dim)
# g.X_variance = X_var.reshape(self.num_data, self.input_dim)
# g.Z = Z.reshape(self.num_inducing, self.input_dim)
#
# def _set_kern_params(self, g, p):

4
GPy/models/sparse_gp_classification.py
View file

@ -26,7 +26,7 @@ class SparseGPClassification(SparseGP):
"""
def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, M=10):
def __init__(self, X, Y=None, likelihood=None, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10):
if kernel is None:
kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1],1e-3)
@ -38,7 +38,7 @@ class SparseGPClassification(SparseGP):
raise Warning, 'likelihood.data and Y are different.'
if Z is None:
i = np.random.permutation(X.shape[0])[:M]
i = np.random.permutation(X.shape[0])[:num_inducing]
Z = X[i].copy()
else:
assert Z.shape[1]==X.shape[1]

4
GPy/models/sparse_gp_regression.py
View file

@ -26,14 +26,14 @@ class SparseGPRegression(SparseGP):
"""
def __init__(self, X, Y, kernel=None, normalize_X=False, normalize_Y=False, Z=None, M=10, X_variance=None):
def __init__(self, X, Y, kernel=None, normalize_X=False, normalize_Y=False, Z=None, num_inducing=10, X_variance=None):
# kern defaults to rbf (plus white for stability)
if kernel is None:
kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1], 1e-3)
# Z defaults to a subset of the data
if Z is None:
i = np.random.permutation(X.shape[0])[:M]
i = np.random.permutation(X.shape[0])[:num_inducing]
Z = X[i].copy()
else:
assert Z.shape[1] == X.shape[1]

8
GPy/models/sparse_gplvm.py
View file

@ -23,19 +23,19 @@ class SparseGPLVM(SparseGPRegression, GPLVM):
:type init: 'PCA'|'random'
"""
def __init__(self, Y, input_dim, kernel=None, init='PCA', M=10):
def __init__(self, Y, input_dim, kernel=None, init='PCA', num_inducing=10):
X = self.initialise_latent(init, input_dim, Y)
SparseGPRegression.__init__(self, X, Y, kernel=kernel, M=M)
SparseGPRegression.__init__(self, X, Y, kernel=kernel, num_inducing=num_inducing)
def _get_param_names(self):
return (sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.N)], [])
return (sum([['X_%i_%i' % (n, q) for q in range(self.input_dim)] for n in range(self.num_data)], [])
+ SparseGPRegression._get_param_names(self))
def _get_params(self):
return np.hstack((self.X.flatten(), SparseGPRegression._get_params(self)))
def _set_params(self, x):
self.X = x[:self.X.size].reshape(self.N, self.input_dim).copy()
self.X = x[:self.X.size].reshape(self.num_data, self.input_dim).copy()
SparseGPRegression._set_params(self, x[self.X.size:])
def log_likelihood(self):

20
GPy/testing/bgplvm_tests.py
View file

@ -8,67 +8,67 @@ from GPy.models.bayesian_gplvm import BayesianGPLVM
class BGPLVMTests(unittest.TestCase):
def test_bias_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
Y -= Y.mean(axis=0)
k = GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_linear_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
Y -= Y.mean(axis=0)
k = GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_rbf_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
Y -= Y.mean(axis=0)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_rbf_bias_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
Y -= Y.mean(axis=0)
k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
#@unittest.skip('psi2 cross terms are NotImplemented for this combination')
def test_linear_bias_kern(self):
N, M, input_dim, D = 30, 5, 4, 30
N, num_inducing, input_dim, D = 30, 5, 4, 30
X = np.random.rand(N, input_dim)
k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
Y -= Y.mean(axis=0)
k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())

40
GPy/testing/examples_tests.py
View file

@ -12,31 +12,31 @@ from nose.tools import nottest
import sys
class ExamplesTests(unittest.TestCase):
def _checkgrad(self, model):
self.assertTrue(model.checkgrad())
def _checkgrad(self, Model):
self.assertTrue(Model.checkgrad())
def _model_instance(self, model):
self.assertTrue(isinstance(model, GPy.models))
def _model_instance(self, Model):
self.assertTrue(isinstance(Model, GPy.models))
"""
def model_instance_generator(model):
def model_instance_generator(Model):
def check_model_returned(self):
self._model_instance(model)
self._model_instance(Model)
return check_model_returned
def checkgrads_generator(model):
def checkgrads_generator(Model):
def model_checkgrads(self):
self._checkgrad(model)
self._checkgrad(Model)
return model_checkgrads
"""
def model_checkgrads(model):
model.randomize()
assert model.checkgrad()
def model_checkgrads(Model):
Model.randomize()
assert Model.checkgrad()
def model_instance(model):
assert isinstance(model, GPy.core.model)
def model_instance(Model):
assert isinstance(Model, GPy.core.Model)
@nottest
def test_models():
@ -57,25 +57,25 @@ def test_models():
continue
print "Testing example: ", example[0]
# Generate model
model = example[1]()
print model
# Generate Model
Model = example[1]()
print Model
# Create tests for instance check
"""
test = model_instance_generator(model)
test = model_instance_generator(Model)
test.__name__ = 'test_instance_%s' % example[0]
setattr(ExamplesTests, test.__name__, test)
#Create tests for checkgrads check
test = checkgrads_generator(model)
test = checkgrads_generator(Model)
test.__name__ = 'test_checkgrads_%s' % example[0]
setattr(ExamplesTests, test.__name__, test)
"""
model_checkgrads.description = 'test_checkgrads_%s' % example[0]
yield model_checkgrads, model
yield model_checkgrads, Model
model_instance.description = 'test_instance_%s' % example[0]
yield model_instance, model
yield model_instance, Model
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."

6
GPy/testing/gplvm_tests.py
View file

@ -7,7 +7,7 @@ import GPy
class GPLVMTests(unittest.TestCase):
def test_bias_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
@ -19,7 +19,7 @@ class GPLVMTests(unittest.TestCase):
self.assertTrue(m.checkgrad())
def test_linear_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
@ -31,7 +31,7 @@ class GPLVMTests(unittest.TestCase):
self.assertTrue(m.checkgrad())
def test_rbf_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)

2
GPy/testing/kernel_tests.py
View file

@ -21,7 +21,7 @@ class KernelTests(unittest.TestCase):
"""
X = np.random.rand(30, 4)
K = np.dot(X, X.T)
kernel = GPy.kern.fixed(4, K)
kernel = GPy.kern.Fixed(4, K)
Y = np.ones((30,1))
m = GPy.models.GPRegression(X,Y,kernel=kernel)
self.assertTrue(m.checkgrad())

4
GPy/testing/mrd_tests.py
View file

@ -14,7 +14,7 @@ class MRDTests(unittest.TestCase):
def test_gradients(self):
num_m = 3
N, M, input_dim, D = 20, 8, 6, 20
N, num_inducing, input_dim, D = 20, 8, 6, 20
X = np.random.rand(N, input_dim)
k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim)
@ -23,7 +23,7 @@ class MRDTests(unittest.TestCase):
Ylist = [np.random.multivariate_normal(np.zeros(N), K, input_dim).T for _ in range(num_m)]
likelihood_list = [GPy.likelihoods.Gaussian(Y) for Y in Ylist]
m = GPy.models.MRD(likelihood_list, input_dim=input_dim, kernels=k, M=M)
m = GPy.models.MRD(likelihood_list, input_dim=input_dim, kernels=k, num_inducing=num_inducing)
m.ensure_default_constraints()
self.assertTrue(m.checkgrad())

28
GPy/testing/psi_stat_gradient_tests.py
View file

@ -8,10 +8,10 @@ import numpy
import GPy
import itertools
from GPy.core import model
from GPy.core import Model
class PsiStatModel(model):
def __init__(self, which, X, X_variance, Z, M, kernel):
class PsiStatModel(Model):
def __init__(self, which, X, X_variance, Z, num_inducing, kernel):
self.which = which
self.X = X
self.X_variance = X_variance
@ -64,8 +64,8 @@ class DPsiStatTest(unittest.TestCase):
def testPsi0(self):
for k in self.kernels:
m = PsiStatModel('psi0', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.num_inducing, kernel=k)
m = PsiStatModel('psi1', X=self.X, X_variance=self.X_var, Z=self.Z,
num_inducing=self.num_inducing, kernel=k)
try:
assert m.checkgrad(), "{} x psi0".format("+".join(map(lambda x: x.name, k.parts)))
except:
@ -74,33 +74,33 @@ class DPsiStatTest(unittest.TestCase):
# def testPsi1(self):
# for k in self.kernels:
# m = PsiStatModel('psi1', X=self.X, X_variance=self.X_var, Z=self.Z,
# M=self.M, kernel=k)
# num_inducing=self.num_inducing, kernel=k)
# assert m.checkgrad(), "{} x psi1".format("+".join(map(lambda x: x.name, k.parts)))
def testPsi2_lin(self):
k = self.kernels[0]
m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.num_inducing, kernel=k)
num_inducing=self.num_inducing, kernel=k)
assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts)))
def testPsi2_lin_bia(self):
k = self.kernels[3]
m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.num_inducing, kernel=k)
num_inducing=self.num_inducing, kernel=k)
assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts)))
def testPsi2_rbf(self):
k = self.kernels[1]
m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.num_inducing, kernel=k)
num_inducing=self.num_inducing, kernel=k)
assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts)))
def testPsi2_rbf_bia(self):
k = self.kernels[-1]
m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.num_inducing, kernel=k)
num_inducing=self.num_inducing, kernel=k)
assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts)))
def testPsi2_bia(self):
k = self.kernels[2]
m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.num_inducing, kernel=k)
num_inducing=self.num_inducing, kernel=k)
assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts)))
@ -122,11 +122,11 @@ if __name__ == "__main__":
numpy.random.seed(0)
input_dim = 5
N = 50
M = 10
num_inducing = 10
D = 15
X = numpy.random.randn(N, input_dim)
X_var = .5 * numpy.ones_like(X) + .1 * numpy.clip(numpy.random.randn(*X.shape), 0, 1)
Z = numpy.random.permutation(X)[:M]
Z = numpy.random.permutation(X)[:num_inducing]
Y = X.dot(numpy.random.randn(input_dim, D))
# kernel = GPy.kern.bias(input_dim)
#
@ -148,7 +148,7 @@ if __name__ == "__main__":
# m2 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z,
# num_inducing=num_inducing, kernel=GPy.kern.rbf(input_dim))
m3 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z,
M=M, kernel=GPy.kern.linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim)))
num_inducing=num_inducing, kernel=GPy.kern.linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim)))
m3.ensure_default_constraints()
# + GPy.kern.bias(input_dim))
# m4 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z,

12
GPy/testing/sparse_gplvm_tests.py
View file

@ -8,38 +8,38 @@ from GPy.models.sparse_gplvm import SparseGPLVM
class sparse_GPLVMTests(unittest.TestCase):
def test_bias_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
k = GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = SparseGPLVM(Y, input_dim, kernel=k, M=M)
m = SparseGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@unittest.skip('linear kernels do not have dKdiag_dX')
def test_linear_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
k = GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = SparseGPLVM(Y, input_dim, kernel=k, M=M)
m = SparseGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
def test_rbf_kern(self):
N, M, input_dim, D = 10, 3, 2, 4
N, num_inducing, input_dim, D = 10, 3, 2, 4
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
m = SparseGPLVM(Y, input_dim, kernel=k, M=M)
m = SparseGPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())

4
GPy/testing/unit_tests.py
View file

@ -196,9 +196,9 @@ class GradientTests(unittest.TestCase):
k = GPy.kern.rbf(1) + GPy.kern.white(1)
Y = np.hstack([np.ones(N/2),-np.ones(N/2)])[:,None]
distribution = GPy.likelihoods.likelihood_functions.binomial()
distribution = GPy.likelihoods.likelihood_functions.Binomial()
likelihood = GPy.likelihoods.EP(Y, distribution)
#likelihood = GPy.inference.likelihoods.binomial(Y)
#likelihood = GPy.inference.likelihoods.Binomial(Y)
m = GPy.models.generalized_FITC(X,likelihood,k,inducing=4)
m.constrain_positive('(var|len)')
m.approximate_likelihood()

34
GPy/util/plot_latent.py
View file

@ -2,9 +2,9 @@ import pylab as pb
import numpy as np
from .. import util
def plot_latent(model, labels=None, which_indices=None, resolution=50, ax=None, marker='o', s=40):
def plot_latent(Model, labels=None, which_indices=None, resolution=50, ax=None, marker='o', s=40):
"""
:param labels: a np.array of size model.N containing labels for the points (can be number, strings, etc)
:param labels: a np.array of size Model.N containing labels for the points (can be number, strings, etc)
:param resolution: the resolution of the grid on which to evaluate the predictive variance
"""
if ax is None:
@ -12,26 +12,26 @@ def plot_latent(model, labels=None, which_indices=None, resolution=50, ax=None,
util.plot.Tango.reset()
if labels is None:
labels = np.ones(model.N)
labels = np.ones(Model.N)
if which_indices is None:
if model.input_dim==1:
if Model.input_dim==1:
input_1 = 0
input_2 = None
if model.input_dim==2:
if Model.input_dim==2:
input_1, input_2 = 0,1
else:
try:
input_1, input_2 = np.argsort(model.input_sensitivity())[:2]
input_1, input_2 = np.argsort(Model.input_sensitivity())[:2]
except:
raise ValueError, "cannot Atomatically determine which dimensions to plot, please pass 'which_indices'"
else:
input_1, input_2 = which_indices
#first, plot the output variance as a function of the latent space
Xtest, xx,yy,xmin,xmax = util.plot.x_frame2D(model.X[:,[input_1, input_2]],resolution=resolution)
Xtest_full = np.zeros((Xtest.shape[0], model.X.shape[1]))
Xtest, xx,yy,xmin,xmax = util.plot.x_frame2D(Model.X[:,[input_1, input_2]],resolution=resolution)
Xtest_full = np.zeros((Xtest.shape[0], Model.X.shape[1]))
Xtest_full[:, :2] = Xtest
mu, var, low, up = model.predict(Xtest_full)
mu, var, low, up = Model.predict(Xtest_full)
var = var[:, :1]
ax.imshow(var.reshape(resolution, resolution).T,
extent=[xmin[0], xmax[0], xmin[1], xmax[1]], cmap=pb.cm.binary,interpolation='bilinear',origin='lower')
@ -55,12 +55,12 @@ def plot_latent(model, labels=None, which_indices=None, resolution=50, ax=None,
m = marker
index = np.nonzero(labels==ul)[0]
if model.input_dim==1:
x = model.X[index,input_1]
if Model.input_dim==1:
x = Model.X[index,input_1]
y = np.zeros(index.size)
else:
x = model.X[index,input_1]
y = model.X[index,input_2]
x = Model.X[index,input_1]
y = Model.X[index,input_2]
ax.scatter(x, y, marker=m, s=s, color=util.plot.Tango.nextMedium(), label=this_label)
ax.set_xlabel('latent dimension %i'%input_1)
@ -76,16 +76,16 @@ def plot_latent(model, labels=None, which_indices=None, resolution=50, ax=None,
return ax
def plot_latent_indices(model, which_indices=None, *args, **kwargs):
def plot_latent_indices(Model, which_indices=None, *args, **kwargs):
if which_indices is None:
try:
input_1, input_2 = np.argsort(model.input_sensitivity())[:2]
input_1, input_2 = np.argsort(Model.input_sensitivity())[:2]
except:
raise ValueError, "cannot Automatically determine which dimensions to plot, please pass 'which_indices'"
else:
input_1, input_2 = which_indices
ax = plot_latent(model, which_indices=[input_1, input_2], *args, **kwargs)
ax = plot_latent(Model, which_indices=[input_1, input_2], *args, **kwargs)
# TODO: Here test if there are inducing points...
ax.plot(model.Z[:, input_1], model.Z[:, input_2], '^w')
ax.plot(Model.Z[:, input_1], Model.Z[:, input_2], '^w')
return ax

46
GPy/util/visualize.py
View file

@ -43,16 +43,16 @@ class vector_show(data_show):
class lvm(data_show):
def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0,1]):
"""Visualize a latent variable model
def __init__(self, vals, Model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0,1]):
"""Visualize a latent variable Model
:param model: the latent variable model to visualize.
:param Model: the latent variable Model to visualize.
:param data_visualize: the object used to visualize the data which has been modelled.
:type data_visualize: visualize.data_show type.
:param latent_axes: the axes where the latent visualization should be plotted.
"""
if vals == None:
vals = model.X[0]
vals = Model.X[0]
data_show.__init__(self, vals, axes=latent_axes)
@ -68,13 +68,13 @@ class lvm(data_show):
self.cid = latent_axes[0].figure.canvas.mpl_connect('axes_enter_event', self.on_enter)
self.data_visualize = data_visualize
self.model = model
self.Model = Model
self.latent_axes = latent_axes
self.sense_axes = sense_axes
self.called = False
self.move_on = False
self.latent_index = latent_index
self.latent_dim = model.input_dim
self.latent_dim = Model.input_dim
# The red cross which shows current latent point.
self.latent_values = vals
@ -85,7 +85,7 @@ class lvm(data_show):
def modify(self, vals):
"""When latent values are modified update the latent representation and ulso update the output visualization."""
self.vals = vals.copy()
y = self.model.predict(self.vals)[0]
y = self.Model.predict(self.vals)[0]
self.data_visualize.modify(y)
self.latent_handle.set_data(self.vals[self.latent_index[0]], self.vals[self.latent_index[1]])
self.axes.figure.canvas.draw()
@ -113,15 +113,15 @@ class lvm(data_show):
# A click in the bar chart axis for selection a dimension.
if self.sense_axes != None:
self.sense_axes.cla()
self.sense_axes.bar(np.arange(self.model.input_dim),1./self.model.input_sensitivity(),color='b')
self.sense_axes.bar(np.arange(self.Model.input_dim),1./self.Model.input_sensitivity(),color='b')
if self.latent_index[1] == self.latent_index[0]:
self.sense_axes.bar(np.array(self.latent_index[0]),1./self.model.input_sensitivity()[self.latent_index[0]],color='y')
self.sense_axes.bar(np.array(self.latent_index[1]),1./self.model.input_sensitivity()[self.latent_index[1]],color='y')
self.sense_axes.bar(np.array(self.latent_index[0]),1./self.Model.input_sensitivity()[self.latent_index[0]],color='y')
self.sense_axes.bar(np.array(self.latent_index[1]),1./self.Model.input_sensitivity()[self.latent_index[1]],color='y')
else:
self.sense_axes.bar(np.array(self.latent_index[0]),1./self.model.input_sensitivity()[self.latent_index[0]],color='g')
self.sense_axes.bar(np.array(self.latent_index[1]),1./self.model.input_sensitivity()[self.latent_index[1]],color='r')
self.sense_axes.bar(np.array(self.latent_index[0]),1./self.Model.input_sensitivity()[self.latent_index[0]],color='g')
self.sense_axes.bar(np.array(self.latent_index[1]),1./self.Model.input_sensitivity()[self.latent_index[1]],color='r')
self.sense_axes.figure.canvas.draw()
@ -131,21 +131,21 @@ class lvm_subplots(lvm):
latent_axes is a np array of dimension np.ceil(input_dim/2),
one for each pair of the latent dimensions.
"""
def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None):
self.nplots = int(np.ceil(model.input_dim/2.))+1
def __init__(self, vals, Model, data_visualize, latent_axes=None, sense_axes=None):
self.nplots = int(np.ceil(Model.input_dim/2.))+1
assert len(latent_axes)==self.nplots
if vals==None:
vals = model.X[0, :]
vals = Model.X[0, :]
self.latent_values = vals
for i, axis in enumerate(latent_axes):
if i == self.nplots-1:
if self.nplots*2!=model.input_dim:
if self.nplots*2!=Model.input_dim:
latent_index = [i*2, i*2]
lvm.__init__(self, self.latent_vals, model, data_visualize, axis, sense_axes, latent_index=latent_index)
lvm.__init__(self, self.latent_vals, Model, data_visualize, axis, sense_axes, latent_index=latent_index)
else:
latent_index = [i*2, i*2+1]
lvm.__init__(self, self.latent_vals, model, data_visualize, axis, latent_index=latent_index)
lvm.__init__(self, self.latent_vals, Model, data_visualize, axis, latent_index=latent_index)
@ -158,7 +158,7 @@ class lvm_dimselect(lvm):
GPy.examples.dimensionality_reduction.BGPVLM_oil()
"""
def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0, 1]):
def __init__(self, vals, Model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0, 1]):
if latent_axes==None and sense_axes==None:
self.fig,(latent_axes,self.sense_axes) = plt.subplots(1,2)
elif sense_axes==None:
@ -167,14 +167,14 @@ class lvm_dimselect(lvm):
else:
self.sense_axes = sense_axes
lvm.__init__(self,vals,model,data_visualize,latent_axes,sense_axes,latent_index)
lvm.__init__(self,vals,Model,data_visualize,latent_axes,sense_axes,latent_index)
print "use left and right mouse butons to select dimensions"
def on_click(self, event):
if event.inaxes==self.sense_axes:
new_index = max(0,min(int(np.round(event.xdata-0.5)),self.model.input_dim-1))
new_index = max(0,min(int(np.round(event.xdata-0.5)),self.Model.input_dim-1))
if event.button == 1:
# Make it red if and y-axis (red=port=left) if it is a left button click
self.latent_index[1] = new_index
@ -185,7 +185,7 @@ class lvm_dimselect(lvm):
self.show_sensitivities()
self.latent_axes.cla()
self.model.plot_latent(which_indices=self.latent_index,
self.Model.plot_latent(which_indices=self.latent_index,
ax=self.latent_axes)
self.latent_handle = self.latent_axes.plot([0],[0],'rx',mew=2)[0]
self.modify(self.latent_values)
@ -199,7 +199,7 @@ class lvm_dimselect(lvm):
def on_leave(self,event):
latent_values = self.latent_values.copy()
y = self.model.predict(latent_values[None,:])[0]
y = self.Model.predict(latent_values[None,:])[0]
self.data_visualize.modify(y)