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Merged and fixed conflicts, names still need changing accordingly

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Ricardo 2013-06-05 14:22:16 +01:00
commit b3eeacd956
55 changed files with 912 additions and 927 deletions
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6
GPy/core/__init__.py
View file

@ -1,9 +1,9 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from GP import GP
from sparse_GP import sparse_GP
from FITC import FITC
from model import *
from parameterised import *
import priors
from GPy.core.gp import GP
from GPy.core.sparse_gp import SparseGP
from FITC import FITC

14
GPy/core/GP.py → GPy/core/gp.py
View file

@ -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.D * self.Ki)
self.dL_dK = 0.5 * (tdot(alpha) - self.input_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.D * self.Ki)
self.dL_dK = 0.5 * (tmp - self.input_dim * self.Ki)
def _get_params(self):
return np.hstack((self.kern._get_params_transformed(), self.likelihood._get_params()))
@ -89,7 +89,7 @@ class GP(GPBase):
model for a new variable Y* = v_tilde/tau_tilde, with a covariance
matrix K* = K + diag(1./tau_tilde) plus a normalization term.
"""
return -0.5 * self.D * self.K_logdet + self._model_fit_term() + self.likelihood.Z
return -0.5 * self.input_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z
def _log_likelihood_gradients(self):
@ -117,7 +117,7 @@ class GP(GPBase):
var = Kxx - np.sum(np.multiply(KiKx, Kx), 0)
var = var[:, None]
if stop:
debug_this
debug_this # @UndefinedVariable
return mu, var
def predict(self, Xnew, which_parts='all', full_cov=False):
@ -131,12 +131,12 @@ class GP(GPBase):
:type which_parts: ('all', list of bools)
:param full_cov: whether to return the folll covariance matrix, or just the diagonal
:type full_cov: bool
:rtype: posterior mean, a Numpy array, Nnew x self.D
:rtype: posterior mean, a Numpy array, Nnew x self.input_dim
:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.D
:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 1, the return shape is Nnew x Nnew.
If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
This is to allow for different normalizations of the output dimensions.
"""

16
GPy/core/gp_base.py
View file

@ -18,15 +18,15 @@ class GPBase(model.model):
self.kern = kernel
self.likelihood = likelihood
assert self.X.shape[0] == self.likelihood.data.shape[0]
self.N, self.D = self.likelihood.data.shape
self.N, self.output_dim = self.likelihood.data.shape
if normalize_X:
self._Xmean = X.mean(0)[None, :]
self._Xstd = X.std(0)[None, :]
self.X = (X.copy() - self._Xmean) / self._Xstd
else:
self._Xmean = np.zeros((1,self.input_dim))
self._Xstd = np.ones((1,self.input_dim))
self._Xmean = np.zeros((1, self.input_dim))
self._Xstd = np.ones((1, self.input_dim))
model.model.__init__(self)
@ -70,7 +70,7 @@ class GPBase(model.model):
else:
m, v = self._raw_predict(Xnew, which_parts=which_parts, full_cov=True)
Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None,], axes=ax)
gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
for i in range(samples):
ax.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
ax.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
@ -108,19 +108,19 @@ class GPBase(model.model):
if self.X.shape[1] == 1:
Xu = self.X * self._Xstd + self._Xmean # NOTE self.X are the normalized values now
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)
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)
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)
ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
elif self.X.shape[1] == 2: # FIXME
elif self.X.shape[1] == 2: # FIXME
resolution = resolution or 50
Xnew, xx, yy, 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)

2
GPy/core/model.py
View file

@ -23,7 +23,7 @@ class model(parameterised):
self.priors = None
self.optimization_runs = []
self.sampling_runs = []
self.preferred_optimizer = 'tnc'
self.preferred_optimizer = 'scg'
#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"

2
GPy/core/parameterised.py
View file

@ -85,7 +85,7 @@ class parameterised(object):
else:
return self._get_params()[matches]
else:
raise AttributeError, "no parameter matches %s" % name
raise AttributeError, "no parameter matches %s" % regexp
def __setitem__(self, name, val):
"""

6
GPy/core/priors.py
View file

@ -99,9 +99,9 @@ class MultivariateGaussian:
assert len(self.var.shape) == 2
assert self.var.shape[0] == self.var.shape[1]
assert self.var.shape[0] == self.mu.size
self.D = self.mu.size
self.input_dim = self.mu.size
self.inv, self.hld = pdinv(self.var)
self.constant = -0.5 * self.D * np.log(2 * np.pi) - self.hld
self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld
def summary(self):
raise NotImplementedError
@ -121,7 +121,7 @@ class MultivariateGaussian:
return np.random.multivariate_normal(self.mu, self.var, n)
def plot(self):
if self.D == 2:
if self.input_dim == 2:
rvs = self.rvs(200)
pb.plot(rvs[:, 0], rvs[:, 1], 'kx', mew=1.5)
xmin, xmax = pb.xlim()

46
GPy/core/sparse_GP.py → GPy/core/sparse_gp.py
View file

@ -8,7 +8,7 @@ from scipy import linalg
from ..likelihoods import Gaussian
from gp_base import GPBase
class sparse_GP(GPBase):
class SparseGP(GPBase):
"""
Variational sparse GP model
@ -21,9 +21,9 @@ class sparse_GP(GPBase):
:param X_variance: The uncertainty in the measurements of X (Gaussian variance)
:type X_variance: np.ndarray (N x input_dim) | None
:param Z: inducing inputs (optional, see note)
:type Z: np.ndarray (M x input_dim) | None
:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
:type M: int
: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)
:type num_inducing: int
:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
:type normalize_(X|Y): bool
"""
@ -32,7 +32,7 @@ class sparse_GP(GPBase):
GPBase.__init__(self, X, likelihood, kernel, normalize_X=normalize_X)
self.Z = Z
self.M = Z.shape[0]
self.num_inducing = Z.shape[0]
self.likelihood = likelihood
if X_variance is None:
@ -85,7 +85,7 @@ class sparse_GP(GPBase):
# factor B
self.B = np.eye(self.M) + self.A
self.B = np.eye(self.num_inducing) + self.A
self.LB = jitchol(self.B)
# TODO: make a switch for either first compute psi1V, or VV.T
@ -99,16 +99,16 @@ class sparse_GP(GPBase):
# Compute dL_dKmm
tmp = tdot(self._LBi_Lmi_psi1V)
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.input_dim * np.eye(self.num_inducing) + tmp)
tmp = -0.5 * self.DBi_plus_BiPBi
tmp += -0.5 * self.B * self.D
tmp += self.D * np.eye(self.M)
tmp += -0.5 * self.B * self.input_dim
tmp += self.input_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.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
self.dL_dpsi0 = -0.5 * self.input_dim * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - self.DBi_plus_BiPBi)
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.input_dim * np.eye(self.num_inducing) - self.DBi_plus_BiPBi)
if self.likelihood.is_heteroscedastic:
if self.has_uncertain_inputs:
@ -135,24 +135,24 @@ class sparse_GP(GPBase):
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
# likelihood is not heterscedatic
self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
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 += 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.D * 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.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
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.likelihood.V * self.likelihood.Y)
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.D * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
A = -0.5 * self.N * self.input_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 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))
C = -self.input_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.M * self.input_dim].reshape(self.M, self.input_dim)
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._compute_kernel_matrices()
@ -221,7 +221,7 @@ class sparse_GP(GPBase):
Bi, _ = linalg.lapack.flapack.dpotri(self.LB, lower=0) # WTH? this lower switch should be 1, but that doesn't work!
symmetrify(Bi)
Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.M) - Bi)
Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.num_inducing) - Bi)
if X_variance_new is None:
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
@ -259,12 +259,12 @@ class sparse_GP(GPBase):
:type which_parts: ('all', list of bools)
:param full_cov: whether to return the folll covariance matrix, or just the diagonal
:type full_cov: bool
:rtype: posterior mean, a Numpy array, Nnew x self.D
:rtype: posterior mean, a Numpy array, Nnew x self.input_dim
:rtype: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.D
:rtype: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
If full_cov and self.D > 1, the return shape of var is Nnew x Nnew x self.D. If self.D == 1, the return shape is Nnew x Nnew.
If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
This is to allow for different normalizations of the output dimensions.
"""

22
GPy/examples/dimensionality_reduction.py
View file

@ -5,9 +5,9 @@ import numpy as np
from matplotlib import pyplot as plt
import GPy
from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
from GPy.util.datasets import swiss_roll_generated
from GPy.core.transformations import logexp
from GPy.models.bayesian_gplvm import BayesianGPLVM
default_seed = np.random.seed(123344)
@ -20,14 +20,14 @@ def BGPLVM(seed=default_seed):
X = np.random.rand(N, Q)
k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N), K, D).T
Y = np.random.multivariate_normal(np.zeros(N), K, Q).T
k = GPy.kern.rbf(Q, ARD=True) + GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True) + GPy.kern.white(Q)
# k = GPy.kern.rbf(Q) + GPy.kern.rbf(Q) + GPy.kern.white(Q)
# 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.Bayesian_GPLVM(Y, Q, kernel=k, M=M)
m = GPy.models.BayesianGPLVM(Y, Q, kernel=k, M=M)
m.constrain_positive('(rbf|bias|noise|white|S)')
# m.constrain_fixed('S', 1)
@ -105,7 +105,7 @@ def swiss_roll(optimize=True, N=1000, M=15, Q=4, sigma=.2, plot=False):
kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
m = Bayesian_GPLVM(Y, Q, X=X, X_variance=S, M=M, Z=Z, kernel=kernel)
m = BayesianGPLVM(Y, Q, X=X, X_variance=S, M=M, Z=Z, kernel=kernel)
m.data_colors = c
m.data_t = t
@ -129,7 +129,7 @@ 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.Bayesian_GPLVM(Yn, Q, kernel=kernel, M=M, **k)
m = GPy.models.BayesianGPLVM(Yn, Q, kernel=kernel, M=M, **k)
m.data_labels = data['Y'][:N].argmax(axis=1)
# m.constrain('variance|leng', logexp_clipped())
@ -234,7 +234,7 @@ def bgplvm_simulation_matlab_compare():
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 = Bayesian_GPLVM(Y, Q, init="PCA", M=M, kernel=k,
m = BayesianGPLVM(Y, Q, init="PCA", M=M, kernel=k,
# X=mu,
# X_variance=S,
_debug=False)
@ -259,7 +259,7 @@ 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 = Bayesian_GPLVM(Y, Q, init="PCA", M=M, kernel=k, _debug=True)
m = BayesianGPLVM(Y, Q, init="PCA", M=M, kernel=k, _debug=True)
# m.constrain('variance|noise', logexp_clipped())
m.ensure_default_constraints()
m['noise'] = Y.var() / 100.
@ -285,7 +285,7 @@ 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, Q=Q, M=M, kernels=k, initx="", initz='permute', **kw)
m = mrd.MRD(Ylist, input_dim=Q, M=M, kernels=k, initx="", initz='permute', **kw)
for i, Y in enumerate(Ylist):
m['{}_noise'.format(i + 1)] = Y.var() / 100.
@ -297,7 +297,7 @@ def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
if optimize:
print "Optimizing Model:"
m.optimize('scg', messages=1, max_iters=5e4, max_f_eval=5e4)
m.optimize('scg', messages=1, max_iters=5e4, max_f_eval=5e4, gtol=.05)
if plot:
m.plot_X_1d("MRD Latent Space 1D")
m.plot_scales("MRD Scales")
@ -313,7 +313,7 @@ def brendan_faces():
Yn /= Yn.std()
m = GPy.models.GPLVM(Yn, Q)
# m = GPy.models.Bayesian_GPLVM(Yn, Q, M=100)
# m = GPy.models.BayesianGPLVM(Yn, Q, M=100)
# optimize
m.constrain('rbf|noise|white', GPy.core.transformations.logexp_clipped())
@ -380,7 +380,7 @@ def cmu_mocap(subject='35', motion=['01'], in_place=True):
# M = 30
#
# kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
# m = GPy.models.Bayesian_GPLVM(X, Q, kernel=kernel, M=M)
# m = GPy.models.BayesianGPLVM(X, Q, kernel=kernel, M=M)
# # m.scale_factor = 100.0
# m.constrain_positive('(white|noise|bias|X_variance|rbf_variance|rbf_length)')
# from sklearn import cluster

85
GPy/examples/regression.py
View file

@ -10,16 +10,16 @@ import numpy as np
import GPy
def toy_rbf_1d(optim_iters=100):
def toy_rbf_1d(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
m = GPy.models.GP_regression(data['X'],data['Y'])
m = GPy.models.GPRegression(data['X'],data['Y'])
# optimize
m.ensure_default_constraints()
m.optimize(max_f_eval=optim_iters)
m.optimize(max_f_eval=max_nb_eval_optim)
# plot
m.plot()
print(m)
@ -30,7 +30,7 @@ def rogers_girolami_olympics(optim_iters=100):
data = GPy.util.datasets.rogers_girolami_olympics()
# create simple GP model
m = GPy.models.GP_regression(data['X'],data['Y'])
m = GPy.models.GPRegression(data['X'],data['Y'])
#set the lengthscale to be something sensible (defaults to 1)
m['rbf_lengthscale'] = 10
@ -49,7 +49,7 @@ def toy_rbf_1d_50(optim_iters=100):
data = GPy.util.datasets.toy_rbf_1d_50()
# create simple GP model
m = GPy.models.GP_regression(data['X'],data['Y'])
m = GPy.models.GPRegression(data['X'],data['Y'])
# optimize
m.ensure_default_constraints()
@ -65,7 +65,7 @@ def silhouette(optim_iters=100):
data = GPy.util.datasets.silhouette()
# create simple GP model
m = GPy.models.GP_regression(data['X'],data['Y'])
m = GPy.models.GPRegression(data['X'],data['Y'])
# optimize
m.ensure_default_constraints()
@ -87,9 +87,9 @@ def coregionalisation_toy2(optim_iters=100):
Y = np.vstack((Y1,Y2))
k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
k2 = GPy.kern.coregionalise(2,1)
k2 = GPy.kern.Coregionalise(2,1)
k = k1.prod(k2,tensor=True)
m = GPy.models.GP_regression(X,Y,kernel=k)
m = GPy.models.GPRegression(X,Y,kernel=k)
m.constrain_fixed('.*rbf_var',1.)
#m.constrain_positive('.*kappa')
m.ensure_default_constraints()
@ -119,9 +119,9 @@ def coregionalisation_toy(optim_iters=100):
Y = np.vstack((Y1,Y2))
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.coregionalise(2,2)
k2 = GPy.kern.Coregionalise(2,2)
k = k1.prod(k2,tensor=True)
m = GPy.models.GP_regression(X,Y,kernel=k)
m = GPy.models.GPRegression(X,Y,kernel=k)
m.constrain_fixed('.*rbf_var',1.)
#m.constrain_positive('kappa')
m.ensure_default_constraints()
@ -155,10 +155,10 @@ def coregionalisation_sparse(optim_iters=100):
Z = np.hstack((np.random.rand(M,1)*8,np.random.randint(0,2,M)[:,None]))
k1 = GPy.kern.rbf(1)
k2 = GPy.kern.coregionalise(2,2)
k2 = GPy.kern.Coregionalise(2,2)
k = k1.prod(k2,tensor=True) + GPy.kern.white(2,0.001)
m = GPy.models.sparse_GP_regression(X,Y,kernel=k,Z=Z)
m = GPy.models.SparseGPRegression(X,Y,kernel=k,Z=Z)
m.scale_factor = 10000.
m.constrain_fixed('.*rbf_var',1.)
#m.constrain_positive('kappa')
@ -181,7 +181,7 @@ def coregionalisation_sparse(optim_iters=100):
return m
def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000, optim_iters=100):
def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000, optim_iters=300):
"""Show an example of a multimodal error surface for Gaussian process regression. Gene 939 has bimodal behaviour where the noisey mode is higher."""
# Contour over a range of length scales and signal/noise ratios.
@ -197,7 +197,7 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
data['Y'] = data['Y'] - np.mean(data['Y'])
lls = GPy.examples.regression._contour_data(data, length_scales, log_SNRs, GPy.kern.rbf)
pb.contour(length_scales, log_SNRs, np.exp(lls), 20)
pb.contour(length_scales, log_SNRs, np.exp(lls), 20, cmap=pb.cm.jet)
ax = pb.gca()
pb.xlabel('length scale')
pb.ylabel('log_10 SNR')
@ -211,18 +211,20 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
optim_point_y = np.empty(2)
np.random.seed(seed=seed)
for i in range(0, model_restarts):
kern = GPy.kern.rbf(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.)) + GPy.kern.white(1,variance=np.random.exponential(1.))
#kern = GPy.kern.rbf(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.))
kern = GPy.kern.rbf(1, variance=np.random.uniform(1e-3,1), lengthscale=np.random.uniform(5,50))
m = GPy.models.GP_regression(data['X'],data['Y'], kernel=kern)
optim_point_x[0] = m.get('rbf_lengthscale')
optim_point_y[0] = np.log10(m.get('rbf_variance')) - np.log10(m.get('white_variance'));
m = GPy.models.GPRegression(data['X'],data['Y'], kernel=kern)
m['noise_variance'] = np.random.uniform(1e-3,1)
optim_point_x[0] = m['rbf_lengthscale']
optim_point_y[0] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
# optimize
m.ensure_default_constraints()
m.optimize(xtol=1e-6, ftol=1e-6, max_f_eval=optim_iters)
m.optimize('scg', xtol=1e-6, ftol=1e-6, max_f_eval=optim_iters)
optim_point_x[1] = m.get('rbf_lengthscale')
optim_point_y[1] = np.log10(m.get('rbf_variance')) - np.log10(m.get('white_variance'));
optim_point_x[1] = m['rbf_lengthscale']
optim_point_y[1] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
pb.arrow(optim_point_x[0], optim_point_y[0], optim_point_x[1]-optim_point_x[0], optim_point_y[1]-optim_point_y[0], label=str(i), head_length=1, head_width=0.5, fc='k', ec='k')
models.append(m)
@ -231,39 +233,32 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
ax.set_ylim(ylim)
return (models, lls)
def _contour_data(data, length_scales, log_SNRs, signal_kernel_call=GPy.kern.rbf):
def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf):
"""Evaluate the GP objective function for a given data set for a range of signal to noise ratios and a range of lengthscales.
:data_set: A data set from the utils.datasets director.
:length_scales: a list of length scales to explore for the contour plot.
:log_SNRs: a list of base 10 logarithm signal to noise ratios to explore for the contour plot.
:signal_kernel: a kernel to use for the 'signal' portion of the data."""
:kernel: a kernel to use for the 'signal' portion of the data."""
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)
for log_SNR in log_SNRs:
SNR = 10**log_SNR
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
length_scale_lls = []
for length_scale in length_scales:
noise_var = 1.
signal_var = SNR
noise_var = noise_var/(noise_var + signal_var)*total_var
signal_var = signal_var/(noise_var + signal_var)*total_var
signal_kernel = signal_kernel_call(1, variance=signal_var, lengthscale=length_scale)
noise_kernel = GPy.kern.white(1, variance=noise_var)
kernel = signal_kernel + noise_kernel
K = kernel.K(data['X'])
total_var = (np.dot(np.dot(data['Y'].T,GPy.util.linalg.pdinv(K)[0]), data['Y'])/data['Y'].shape[0])[0,0]
noise_var *= total_var
signal_var *= total_var
kernel = signal_kernel_call(1, variance=signal_var, lengthscale=length_scale) + GPy.kern.white(1, variance=noise_var)
model = GPy.models.GP_regression(data['X'], data['Y'], kernel=kernel)
model.constrain_positive('')
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):
@ -276,7 +271,7 @@ def sparse_GP_regression_1D(N = 400, M = 5, optim_iters=100):
noise = GPy.kern.white(1)
kernel = rbf + noise
# create simple GP model
m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
m = GPy.models.SparseGPRegression(X, Y, kernel, M=M)
m.ensure_default_constraints()
@ -296,7 +291,7 @@ def sparse_GP_regression_2D(N = 400, M = 50, optim_iters=100):
kernel = rbf + noise
# create simple GP model
m = GPy.models.sparse_GP_regression(X,Y,kernel, M = M)
m = GPy.models.SparseGPRegression(X,Y,kernel, M = M)
# contrain all parameters to be positive (but not inducing inputs)
m.ensure_default_constraints()
@ -325,7 +320,7 @@ 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
m = GPy.models.sparse_GP_regression(X, Y, kernel=k, Z=Z)
m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z)
m.ensure_default_constraints()
m.optimize('scg', messages=1, max_f_eval=optim_iters)
m.plot(ax=axes[0])
@ -333,7 +328,7 @@ def uncertain_inputs_sparse_regression(optim_iters=100):
#the same model with uncertainty
m = GPy.models.sparse_GP_regression(X, Y, kernel=k, Z=Z, X_variance=S)
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)
m.plot(ax=axes[1])

8
GPy/examples/tutorials.py
View file

@ -19,7 +19,7 @@ def tuto_GP_regression():
kernel = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
m = GPy.models.GP_regression(X,Y,kernel)
m = GPy.models.GPRegression(X, Y, kernel)
print m
m.plot()
@ -47,7 +47,7 @@ def tuto_GP_regression():
ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2)
# create simple GP model
m = GPy.models.GP_regression(X,Y,ker)
m = GPy.models.GPRegression(X, Y, ker)
# contrain all parameters to be positive
m.constrain_positive('')
@ -145,7 +145,7 @@ def tuto_kernel_overview():
Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:])
# Create GP regression model
m = GPy.models.GP_regression(X,Y,Kanova)
m = GPy.models.GPRegression(X, Y, Kanova)
pb.figure(figsize=(5,5))
m.plot()
@ -196,5 +196,5 @@ def model_interaction():
X = np.random.randn(20,1)
Y = np.sin(X) + np.random.randn(*X.shape)*0.01 + 5.
k = GPy.kern.rbf(1) + GPy.kern.bias(1)
return GPy.models.GP_regression(X,Y,kernel=k)
return GPy.models.GPRegression(X, Y, kernel=k)

38
GPy/inference/optimization.py
View file

@ -1,18 +1,16 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import pdb
import pylab as pb
import datetime as dt
from scipy import optimize
import numpy as np
try:
import rasmussens_minimize as rasm
rasm_available = True
except ImportError:
rasm_available = False
from SCG import SCG
from scg import SCG
class Optimizer():
"""
@ -51,9 +49,9 @@ class Optimizer():
start = dt.datetime.now()
self.opt(**kwargs)
end = dt.datetime.now()
self.time = str(end-start)
self.time = str(end - start)
def opt(self, f_fp = None, f = None, fp = None):
def opt(self, f_fp=None, f=None, fp=None):
raise NotImplementedError, "this needs to be implemented to use the optimizer class"
def plot(self):
@ -78,7 +76,7 @@ class opt_tnc(Optimizer):
Optimizer.__init__(self, *args, **kwargs)
self.opt_name = "TNC (Scipy implementation)"
def opt(self, f_fp = None, f = None, fp = None):
def opt(self, f_fp=None, f=None, fp=None):
"""
Run the TNC optimizer
@ -96,8 +94,8 @@ class opt_tnc(Optimizer):
if self.gtol is not None:
opt_dict['pgtol'] = self.gtol
opt_result = optimize.fmin_tnc(f_fp, self.x_init, messages = self.messages,
maxfun = self.max_f_eval, **opt_dict)
opt_result = optimize.fmin_tnc(f_fp, self.x_init, messages=self.messages,
maxfun=self.max_f_eval, **opt_dict)
self.x_opt = opt_result[0]
self.f_opt = f_fp(self.x_opt)[0]
self.funct_eval = opt_result[1]
@ -108,7 +106,7 @@ class opt_lbfgsb(Optimizer):
Optimizer.__init__(self, *args, **kwargs)
self.opt_name = "L-BFGS-B (Scipy implementation)"
def opt(self, f_fp = None, f = None, fp = None):
def opt(self, f_fp=None, f=None, fp=None):
"""
Run the optimizer
@ -130,8 +128,8 @@ class opt_lbfgsb(Optimizer):
if self.gtol is not None:
opt_dict['pgtol'] = self.gtol
opt_result = optimize.fmin_l_bfgs_b(f_fp, self.x_init, iprint = iprint,
maxfun = self.max_f_eval, **opt_dict)
opt_result = optimize.fmin_l_bfgs_b(f_fp, self.x_init, iprint=iprint,
maxfun=self.max_f_eval, **opt_dict)
self.x_opt = opt_result[0]
self.f_opt = f_fp(self.x_opt)[0]
self.funct_eval = opt_result[2]['funcalls']
@ -142,12 +140,12 @@ class opt_simplex(Optimizer):
Optimizer.__init__(self, *args, **kwargs)
self.opt_name = "Nelder-Mead simplex routine (via Scipy)"
def opt(self, f_fp = None, f = None, fp = None):
def opt(self, f_fp=None, f=None, fp=None):
"""
The simplex optimizer does not require gradients.
"""
statuses = ['Converged', 'Maximum number of function evaluations made','Maximum number of iterations reached']
statuses = ['Converged', 'Maximum number of function evaluations made', 'Maximum number of iterations reached']
opt_dict = {}
if self.xtol is not None:
@ -157,8 +155,8 @@ class opt_simplex(Optimizer):
if self.gtol is not None:
print "WARNING: simplex doesn't have an gtol arg, so I'm going to ignore it"
opt_result = optimize.fmin(f, self.x_init, (), disp = self.messages,
maxfun = self.max_f_eval, full_output=True, **opt_dict)
opt_result = optimize.fmin(f, self.x_init, (), disp=self.messages,
maxfun=self.max_f_eval, full_output=True, **opt_dict)
self.x_opt = opt_result[0]
self.f_opt = opt_result[1]
@ -172,7 +170,7 @@ class opt_rasm(Optimizer):
Optimizer.__init__(self, *args, **kwargs)
self.opt_name = "Rasmussen's Conjugate Gradient"
def opt(self, f_fp = None, f = None, fp = None):
def opt(self, f_fp=None, f=None, fp=None):
"""
Run Rasmussen's Conjugate Gradient optimizer
"""
@ -189,8 +187,8 @@ class opt_rasm(Optimizer):
if self.gtol is not None:
print "WARNING: minimize doesn't have an gtol arg, so I'm going to ignore it"
opt_result = rasm.minimize(self.x_init, f_fp, (), messages = self.messages,
maxnumfuneval = self.max_f_eval)
opt_result = rasm.minimize(self.x_init, f_fp, (), messages=self.messages,
maxnumfuneval=self.max_f_eval)
self.x_opt = opt_result[0]
self.f_opt = opt_result[1][-1]
self.funct_eval = opt_result[2]
@ -203,7 +201,7 @@ class opt_SCG(Optimizer):
Optimizer.__init__(self, *args, **kwargs)
self.opt_name = "Scaled Conjugate Gradients"
def opt(self, f_fp = None, f = None, fp = None):
def opt(self, f_fp=None, f=None, fp=None):
assert not f is None
assert not fp is None
opt_result = SCG(f, fp, self.x_init, display=self.messages,
@ -218,7 +216,7 @@ class opt_SCG(Optimizer):
self.status = opt_result[3]
def get_optimizer(f_min):
from SGD import opt_SGD
from sgd import opt_SGD
optimizers = {'fmin_tnc': opt_tnc,
'simplex': opt_simplex,

0
GPy/inference/SCG.py → GPy/inference/scg.py
View file

8
GPy/inference/SGD.py → GPy/inference/sgd.py
View file

@ -292,8 +292,8 @@ class opt_SGD(Optimizer):
NLL = []
import pylab as plt
for count, j in enumerate(features):
self.model.D = len(j)
self.model.likelihood.D = len(j)
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
@ -334,9 +334,9 @@ class opt_SGD(Optimizer):
self.f_opt = np.mean(NLL)
self.model.N = N
self.model.X = X
self.model.D = D
self.model.input_dim = D
self.model.likelihood.N = N
self.model.likelihood.D = D
self.model.likelihood.input_dim = D
self.model.likelihood.Y = Y
sigma = self.model.likelihood._variance
self.model.likelihood._variance = None # invalidate cache

10
GPy/kern/Brownian.py
View file

@ -13,14 +13,14 @@ class Brownian(kernpart):
"""
Brownian Motion kernel.
:param D: the number of input dimensions
:type D: int
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance:
:type variance: float
"""
def __init__(self,D,variance=1.):
self.D = D
assert self.D==1, "Brownian motion in 1D only"
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.name = 'Brownian'
self._set_params(np.array([variance]).flatten())

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, independent_outputs
try:
from constructors import rbf_sympy, sympykern # these depend on sympy
except:

8
GPy/kern/bias.py
View file

@ -7,14 +7,14 @@ import numpy as np
import hashlib
class bias(kernpart):
def __init__(self,D,variance=1.):
def __init__(self,input_dim,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.Nparam = 1
self.name = 'bias'
self._set_params(np.array([variance]).flatten())

60
GPy/kern/constructors.py
View file

@ -21,7 +21,7 @@ from periodic_Matern32 import periodic_Matern32 as periodic_Matern32part
from periodic_Matern52 import periodic_Matern52 as periodic_Matern52part
from prod import prod as prodpart
from symmetric import symmetric as symmetric_part
from coregionalise import coregionalise as coregionalise_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
@ -33,8 +33,8 @@ def rbf(D,variance=1., lengthscale=None,ARD=False):
"""
Construct an RBF kernel
:param D: dimensionality of the kernel, obligatory
:type D: int
:param input_dim: dimensionality of the kernel, obligatory
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -51,7 +51,7 @@ def linear(D,variances=None,ARD=False):
Arguments
---------
D (int), obligatory
input_dimD (int), obligatory
variances (np.ndarray)
ARD (boolean)
"""
@ -64,7 +64,7 @@ def white(D,variance=1.):
Arguments
---------
D (int), obligatory
input_dimD (int), obligatory
variance (float)
"""
part = whitepart(D,variance)
@ -74,8 +74,8 @@ def exponential(D,variance=1., lengthscale=None, ARD=False):
"""
Construct an exponential kernel
:param D: dimensionality of the kernel, obligatory
:type D: int
:param input_dim: dimensionality of the kernel, obligatory
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -90,8 +90,8 @@ def Matern32(D,variance=1., lengthscale=None, ARD=False):
"""
Construct a Matern 3/2 kernel.
:param D: dimensionality of the kernel, obligatory
:type D: int
:param input_dim: dimensionality of the kernel, obligatory
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -106,8 +106,8 @@ def Matern52(D,variance=1., lengthscale=None, ARD=False):
"""
Construct a Matern 5/2 kernel.
:param D: dimensionality of the kernel, obligatory
:type D: int
:param input_dim: dimensionality of the kernel, obligatory
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -124,7 +124,7 @@ def bias(D,variance=1.):
Arguments
---------
D (int), obligatory
input_dim (int), obligatory
variance (float)
"""
part = biaspart(D,variance)
@ -133,7 +133,7 @@ def bias(D,variance=1.):
def finite_dimensional(D,F,G,variances=1.,weights=None):
"""
Construct a finite dimensional kernel.
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
variances : np.ndarray with shape (n,)
@ -145,8 +145,8 @@ def spline(D,variance=1.):
"""
Construct a spline kernel.
:param D: Dimensionality of the kernel
:type D: int
:param input_dim: Dimensionality of the kernel
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
"""
@ -157,8 +157,8 @@ def Brownian(D,variance=1.):
"""
Construct a Brownian motion kernel.
:param D: Dimensionality of the kernel
:type D: int
:param input_dim: Dimensionality of the kernel
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
"""
@ -204,8 +204,8 @@ def periodic_exponential(D=1,variance=1., lengthscale=None, period=2*np.pi,n_fre
"""
Construct an periodic exponential kernel
:param D: dimensionality, only defined for D=1
:type D: int
:param input_dim: dimensionality, only defined for input_dim=1
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -222,8 +222,8 @@ def periodic_Matern32(D,variance=1., lengthscale=None, period=2*np.pi,n_freq=10,
"""
Construct a periodic Matern 3/2 kernel.
:param D: dimensionality, only defined for D=1
:type D: int
:param input_dim: dimensionality, only defined for input_dim=1
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -240,8 +240,8 @@ def periodic_Matern52(D,variance=1., lengthscale=None, period=2*np.pi,n_freq=10,
"""
Construct a periodic Matern 5/2 kernel.
:param D: dimensionality, only defined for D=1
:type D: int
:param input_dim: dimensionality, only defined for input_dim=1
:type input_dim: int
:param variance: the variance of the kernel
:type variance: float
:param lengthscale: the lengthscale of the kernel
@ -256,14 +256,14 @@ def periodic_Matern52(D,variance=1., lengthscale=None, period=2*np.pi,n_freq=10,
def prod(k1,k2,tensor=False):
"""
Construct a product kernel over D from two kernels over D
Construct a product kernel over input_dim from two kernels over input_dim
:param k1, k2: the kernels to multiply
:type k1, k2: kernpart
:rtype: kernel object
"""
part = prodpart(k1,k2,tensor)
return kern(part.D, [part])
return kern(part.input_dim, [part])
def symmetric(k):
"""
@ -273,7 +273,7 @@ def symmetric(k):
k_.parts = [symmetric_part(p) for p in k.parts]
return k_
def coregionalise(Nout,R=1, W=None, kappa=None):
def Coregionalise(Nout,R=1, W=None, kappa=None):
p = coregionalise_part(Nout,R,W,kappa)
return kern(1,[p])
@ -282,8 +282,8 @@ def rational_quadratic(D,variance=1., lengthscale=1., power=1.):
"""
Construct rational quadratic kernel.
:param D: the number of input dimensions
:type D: int (D=1 is the only value currently supported)
:param input_dim: the number of input dimensions
:type input_dim: int (input_dim=1 is the only value currently supported)
:param variance: the variance :math:`\sigma^2`
:type variance: float
:param lengthscale: the lengthscale :math:`\ell`
@ -300,7 +300,7 @@ def fixed(D, K, variance=1.):
Arguments
---------
D (int), obligatory
input_dim (int), obligatory
K (np.array), obligatory
variance (float)
"""
@ -321,6 +321,6 @@ def independent_outputs(k):
for sl in k.input_slices:
assert (sl.start is None) and (sl.stop is None), "cannot adjust input slices! (TODO)"
parts = [independent_output_part(p) for p in k.parts]
return kern(k.D+1,parts)
return kern(k.input_dim+1,parts)

4
GPy/kern/coregionalise.py
View file

@ -7,12 +7,12 @@ from GPy.util.linalg import mdot, pdinv
import pdb
from scipy import weave
class coregionalise(kernpart):
class Coregionalise(kernpart):
"""
Kernel for Intrinsic Corregionalization Models
"""
def __init__(self,Nout,R=1, W=None, kappa=None):
self.D = 1
self.input_dim = 1
self.name = 'coregion'
self.Nout = Nout
self.R = R

44
GPy/kern/kern.py
View file

@ -11,14 +11,14 @@ from prod import prod
from ..util.linalg import symmetrify
class kern(parameterised):
def __init__(self, D, parts=[], input_slices=None):
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 D: The dimensioality of the kernel's input space
:type D: int
:param input_dim: The dimensioality 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
:param input_slices: the slices on the inputs which apply to each kernel
@ -29,7 +29,7 @@ class kern(parameterised):
self.Nparts = len(parts)
self.Nparam = sum([p.Nparam for p in self.parts])
self.D = D
self.input_dim = input_dim
# deal with input_slices
if input_slices is None:
@ -96,10 +96,10 @@ class kern(parameterised):
:type other: GPy.kern
"""
if tensor:
D = self.D + other.D
self_input_slices = [slice(*sl.indices(self.D)) for sl in self.input_slices]
other_input_indices = [sl.indices(other.D) for sl in other.input_slices]
other_input_slices = [slice(i[0] + self.D, i[1] + self.D, i[2]) for i in other_input_indices]
D = self.input_dim + other.input_dim
self_input_slices = [slice(*sl.indices(self.input_dim)) for sl in self.input_slices]
other_input_indices = [sl.indices(other.input_dim) for sl in other.input_slices]
other_input_slices = [slice(i[0] + self.input_dim, i[1] + self.input_dim, i[2]) for i in other_input_indices]
newkern = kern(D, self.parts + other.parts, self_input_slices + other_input_slices)
@ -111,8 +111,8 @@ class kern(parameterised):
newkern.constraints = self.constraints + other.constraints
newkern.tied_indices = self.tied_indices + [self.Nparam + x for x in other.tied_indices]
else:
assert self.D == other.D
newkern = kern(self.D, self.parts + other.parts, self.input_slices + other.input_slices)
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.constraints = self.constraints + other.constraints
@ -138,16 +138,16 @@ class kern(parameterised):
slices = []
for sl1, sl2 in itertools.product(K1.input_slices, K2.input_slices):
s1, s2 = [False] * K1.D, [False] * K2.D
s1, s2 = [False] * K1.input_dim, [False] * K2.input_dim
s1[sl1], s2[sl2] = [True], [True]
slices += [s1 + s2]
newkernparts = [prod(k1, k2, tensor) for k1, k2 in itertools.product(K1.parts, K2.parts)]
if tensor:
newkern = kern(K1.D + K2.D, newkernparts, slices)
newkern = kern(K1.input_dim + K2.input_dim, newkernparts, slices)
else:
newkern = kern(K1.D, newkernparts, slices)
newkern = kern(K1.input_dim, newkernparts, slices)
newkern._follow_constrains(K1, K2)
return newkern
@ -211,7 +211,7 @@ class kern(parameterised):
def K(self, X, X2=None, which_parts='all'):
if which_parts == 'all':
which_parts = [True] * self.Nparts
assert X.shape[1] == self.D
assert X.shape[1] == self.input_dim
if X2 is None:
target = np.zeros((X.shape[0], X.shape[0]))
[p.K(X[:, i_s], None, target=target) for p, i_s, part_i_used in zip(self.parts, self.input_slices, which_parts) if part_i_used]
@ -225,11 +225,11 @@ class kern(parameterised):
:param dL_dK: An array of dL_dK derivaties, dL_dK
:type dL_dK: Np.ndarray (N x M)
:param X: Observed data inputs
:type X: np.ndarray (N x D)
:type X: np.ndarray (N x input_dim)
:param X2: Observed dara inputs (optional, defaults to X)
:type X2: np.ndarray (M x D)
:type X2: np.ndarray (M x input_dim)
"""
assert X.shape[1] == self.D
assert X.shape[1] == self.input_dim
target = np.zeros(self.Nparam)
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)]
@ -251,20 +251,20 @@ class kern(parameterised):
def Kdiag(self, X, which_parts='all'):
if which_parts == 'all':
which_parts = [True] * self.Nparts
assert X.shape[1] == self.D
assert X.shape[1] == self.input_dim
target = np.zeros(X.shape[0])
[p.Kdiag(X[:, i_s], target=target) for p, i_s, part_on in zip(self.parts, self.input_slices, which_parts) if part_on]
return target
def dKdiag_dtheta(self, dL_dKdiag, X):
assert X.shape[1] == self.D
assert X.shape[1] == self.input_dim
assert dL_dKdiag.size == X.shape[0]
target = np.zeros(self.Nparam)
[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)
def dKdiag_dX(self, dL_dKdiag, X):
assert X.shape[1] == self.D
assert X.shape[1] == self.input_dim
target = np.zeros_like(X)
[p.dKdiag_dX(dL_dKdiag, X[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
return target
@ -386,7 +386,7 @@ class kern(parameterised):
def plot(self, x=None, plot_limits=None, which_parts='all', resolution=None, *args, **kwargs):
if which_parts == 'all':
which_parts = [True] * self.Nparts
if self.D == 1:
if self.input_dim == 1:
if x is None:
x = np.zeros((1, 1))
else:
@ -408,7 +408,7 @@ class kern(parameterised):
pb.xlabel("x")
pb.ylabel("k(x,%0.1f)" % x)
elif self.D == 2:
elif self.input_dim == 2:
if x is None:
x = np.zeros((1, 2))
else:

8
GPy/kern/kernpart.py
View file

@ -3,16 +3,16 @@
class kernpart(object):
def __init__(self,D):
def __init__(self,input_dim):
"""
The base class for a kernpart: a positive definite function which forms part of a kernel
:param D: the number of input dimensions to the function
:type D: int
:param input_dim: the number of input dimensions to the function
:type input_dim: int
Do not instantiate.
"""
self.D = D
self.input_dim = input_dim
self.Nparam = 1
self.name = 'unnamed'

20
GPy/kern/linear.py
View file

@ -13,10 +13,10 @@ class linear(kernpart):
.. math::
k(x,y) = \sum_{i=1}^D \sigma^2_i x_iy_i
k(x,y) = \sum_{i=1}^input_dim \sigma^2_i x_iy_i
:param D: the number of input dimensions
:type D: int
:param input_dim: the number of input dimensions
:type input_dim: int
:param variances: the vector of variances :math:`\sigma^2_i`
:type variances: array or list of the appropriate size (or float if there is only one variance parameter)
:param ARD: Auto Relevance Determination. If equal to "False", the kernel has only one variance parameter \sigma^2, otherwise there is one variance parameter per dimension.
@ -24,8 +24,8 @@ class linear(kernpart):
:rtype: kernel object
"""
def __init__(self, D, variances=None, ARD=False):
self.D = D
def __init__(self, input_dim, variances=None, ARD=False):
self.input_dim = input_dim
self.ARD = ARD
if ARD == False:
self.Nparam = 1
@ -37,13 +37,13 @@ class linear(kernpart):
variances = np.ones(1)
self._Xcache, self._X2cache = np.empty(shape=(2,))
else:
self.Nparam = self.D
self.Nparam = self.input_dim
self.name = 'linear'
if variances is not None:
variances = np.asarray(variances)
assert variances.size == self.D, "bad number of lengthscales"
assert variances.size == self.input_dim, "bad number of lengthscales"
else:
variances = np.ones(self.D)
variances = np.ones(self.input_dim)
self._set_params(variances.flatten())
# initialize cache
@ -82,7 +82,7 @@ class linear(kernpart):
def dK_dtheta(self, dL_dK, X, X2, target):
if self.ARD:
if X2 is None:
[np.add(target[i:i + 1], np.sum(dL_dK * tdot(X[:, i:i + 1])), target[i:i + 1]) for i in range(self.D)]
[np.add(target[i:i + 1], np.sum(dL_dK * tdot(X[:, i:i + 1])), target[i:i + 1]) for i in range(self.input_dim)]
else:
product = X[:, None, :] * X2[None, :, :]
target += (dL_dK[:, :, None] * product).sum(0).sum(0)
@ -153,7 +153,7 @@ class linear(kernpart):
# psi2_real[n, m, m_prime] = np.dot(tmp, (
# self._Z[m_prime:m_prime + 1] * self.variances).T)
# mu2_S = (self._mu[:, None, :] * self._mu[:, :, None])
# mu2_S[:, np.arange(self.D), np.arange(self.D)] += self._S
# mu2_S[:, np.arange(self.input_dim), np.arange(self.input_dim)] += self._S
# psi2 = (self.ZA[None, :, None, :] * mu2_S[:, None]).sum(-1)
# psi2 = (psi2[:, :, None] * self.ZA[None, None]).sum(-1)
# psi2_tensor = np.tensordot(self.ZZ[None, :, :, :] * np.square(self.variances), self.mu2_S[:, None, None, :], ((3), (3))).squeeze().T

14
GPy/kern/prod.py
View file

@ -22,14 +22,14 @@ class prod(kernpart):
self.k1 = k1
self.k2 = k2
if tensor:
self.D = k1.D + k2.D
self.slice1 = slice(0,self.k1.D)
self.slice2 = slice(self.k1.D,self.k1.D+self.k2.D)
self.input_dim = k1.input_dim + k2.input_dim
self.slice1 = slice(0,self.k1.input_dim)
self.slice2 = slice(self.k1.input_dim,self.k1.input_dim+self.k2.input_dim)
else:
assert k1.D == k2.D, "Error: The input spaces of the kernels to sum don't have the same dimension."
self.D = k1.D
self.slice1 = slice(0,self.D)
self.slice2 = slice(0,self.D)
assert k1.input_dim == k2.input_dim, "Error: The input spaces of the kernels to sum don't have the same dimension."
self.input_dim = k1.input_dim
self.slice1 = slice(0,self.input_dim)
self.slice2 = slice(0,self.input_dim)
self._X, self._X2, self._params = np.empty(shape=(3,1))
self._set_params(np.hstack((k1._get_params(),k2._get_params())))

30
GPy/kern/rbf.py
View file

@ -18,8 +18,8 @@ class rbf(kernpart):
where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input.
: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
:param lengthscale: the vector of lengthscale of the kernel
@ -31,8 +31,8 @@ class rbf(kernpart):
.. Note: this object implements both the ARD and 'spherical' version of the function
"""
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.name = 'rbf'
self.ARD = ARD
if not ARD:
@ -43,12 +43,12 @@ class rbf(kernpart):
else:
lengthscale = np.ones(1)
else:
self.Nparam = self.D + 1
self.Nparam = self.input_dim + 1
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)
lengthscale = np.ones(self.input_dim)
self._set_params(np.hstack((variance,lengthscale.flatten())))
@ -100,7 +100,7 @@ class rbf(kernpart):
code = """
int q,i,j;
double tmp;
for(q=0; q<D; q++){
for(q=0; q<input_dim; q++){
tmp = 0;
for(i=0; i<N; i++){
for(j=0; j<i; j++){
@ -110,12 +110,12 @@ class rbf(kernpart):
target(q+1) += var_len3(q)*tmp;
}
"""
N,M,D = X.shape[0], X.shape[0], self.D
N, M, input_dim = X.shape[0], X.shape[0], self.input_dim
else:
code = """
int q,i,j;
double tmp;
for(q=0; q<D; q++){
for(q=0; q<input_dim; q++){
tmp = 0;
for(i=0; i<N; i++){
for(j=0; j<M; j++){
@ -125,9 +125,9 @@ class rbf(kernpart):
target(q+1) += var_len3(q)*tmp;
}
"""
N,M,D = X.shape[0], X2.shape[0], self.D
#[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.D)]
weave.inline(code, arg_names=['N','M','D','X','X2','target','dvardLdK','var_len3'],
N, M, 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'],
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)
@ -278,8 +278,8 @@ class rbf(kernpart):
psi2 = np.empty((N,M,M))
psi2_Zdist_sq = self._psi2_Zdist_sq
_psi2_denom = self._psi2_denom.squeeze().reshape(N,self.D)
half_log_psi2_denom = 0.5*np.log(self._psi2_denom).squeeze().reshape(N,self.D)
_psi2_denom = self._psi2_denom.squeeze().reshape(N,self.input_dim)
half_log_psi2_denom = 0.5*np.log(self._psi2_denom).squeeze().reshape(N,self.input_dim)
variance_sq = float(np.square(self.variance))
if self.ARD:
lengthscale2 = self.lengthscale2

8
GPy/kern/white.py
View file

@ -8,13 +8,13 @@ class white(kernpart):
"""
White noise kernel.
:param D: the number of input dimensions
:type D: int
:param input_dim: the number of input dimensions
:type input_dim: int
:param variance:
:type variance: float
"""
def __init__(self,D,variance=1.):
self.D = D
def __init__(self,input_dim,variance=1.):
self.input_dim = input_dim
self.Nparam = 1
self.name = 'white'
self._set_params(np.array([variance]).flatten())

4
GPy/likelihoods/__init__.py
View file

@ -1,4 +1,4 @@
from EP import EP
from Gaussian import Gaussian
from ep import EP
from gaussian import Gaussian
# TODO: from Laplace import Laplace
import likelihood_functions as functions

18
GPy/likelihoods/EP.py → GPy/likelihoods/ep.py
View file

@ -4,23 +4,23 @@ from ..util.linalg import pdinv,mdot,jitchol,chol_inv,DSYR,tdot
from likelihood import likelihood
class EP(likelihood):
def __init__(self,data,likelihood_function,epsilon=1e-3,power_ep=[1.,1.]):
def __init__(self,data,LikelihoodFunction,epsilon=1e-3,power_ep=[1.,1.]):
"""
Expectation Propagation
Arguments
---------
epsilon : Convergence criterion, maximum squared difference allowed between mean updates to stop iterations (float)
likelihood_function : a likelihood function (see likelihood_functions.py)
LikelihoodFunction : a likelihood function (see likelihood_functions.py)
"""
self.likelihood_function = likelihood_function
self.LikelihoodFunction = LikelihoodFunction
self.epsilon = epsilon
self.eta, self.delta = power_ep
self.data = data
self.N, self.D = self.data.shape
self.N, self.input_dim = self.data.shape
self.is_heteroscedastic = True
self.Nparams = 0
self._transf_data = self.likelihood_function._preprocess_values(data)
self._transf_data = self.LikelihoodFunction._preprocess_values(data)
#Initial values - Likelihood approximation parameters:
#p(y|f) = t(f|tau_tilde,v_tilde)
@ -48,7 +48,7 @@ class EP(likelihood):
def predictive_values(self,mu,var,full_cov):
if full_cov:
raise NotImplementedError, "Cannot make correlated predictions with an EP likelihood"
return self.likelihood_function.predictive_values(mu,var)
return self.LikelihoodFunction.predictive_values(mu,var)
def _get_params(self):
return np.zeros(0)
@ -110,7 +110,7 @@ class EP(likelihood):
self.tau_[i] = 1./Sigma[i,i] - self.eta*self.tau_tilde[i]
self.v_[i] = mu[i]/Sigma[i,i] - self.eta*self.v_tilde[i]
#Marginal moments
self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood_function.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.LikelihoodFunction.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
#Site parameters update
Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma[i,i])
Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma[i,i])
@ -200,7 +200,7 @@ class EP(likelihood):
self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i]
self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i]
#Marginal moments
self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood_function.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.LikelihoodFunction.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
#Site parameters update
Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])
@ -295,7 +295,7 @@ class EP(likelihood):
self.tau_[i] = 1./Sigma_diag[i] - self.eta*self.tau_tilde[i]
self.v_[i] = mu[i]/Sigma_diag[i] - self.eta*self.v_tilde[i]
#Marginal moments
self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood_function.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.LikelihoodFunction.moments_match(self._transf_data[i],self.tau_[i],self.v_[i])
#Site parameters update
Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./Sigma_diag[i])
Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - mu[i]/Sigma_diag[i])

14
GPy/likelihoods/Gaussian.py → GPy/likelihoods/gaussian.py
View file

@ -15,7 +15,7 @@ class Gaussian(likelihood):
self.is_heteroscedastic = False
self.Nparams = 1
self.Z = 0. # a correction factor which accounts for the approximation made
N, self.D = data.shape
N, self.input_dim = data.shape
# normalization
if normalize:
@ -24,8 +24,8 @@ class Gaussian(likelihood):
# Don't scale outputs which have zero variance to zero.
self._scale[np.nonzero(self._scale == 0.)] = 1.0e-3
else:
self._offset = np.zeros((1, self.D))
self._scale = np.ones((1, self.D))
self._offset = np.zeros((1, self.input_dim))
self._scale = np.ones((1, self.input_dim))
self.set_data(data)
@ -35,7 +35,7 @@ class Gaussian(likelihood):
def set_data(self, data):
self.data = data
self.N, D = data.shape
assert D == self.D
assert D == self.input_dim
self.Y = (self.data - self._offset) / self._scale
if D > self.N:
self.YYT = np.dot(self.Y, self.Y.T)
@ -52,7 +52,7 @@ class Gaussian(likelihood):
def _set_params(self, x):
x = np.float64(x)
if self._variance != x:
if np.all(self._variance != x):
if x == 0.:
self.precision = None
self.V = None
@ -68,9 +68,9 @@ class Gaussian(likelihood):
"""
mean = mu * self._scale + self._offset
if full_cov:
if self.D > 1:
if self.input_dim > 1:
raise NotImplementedError, "TODO"
# Note. for D>1, we need to re-normalise all the outputs independently.
# Note. for input_dim>1, we need to re-normalise all the outputs independently.
# This will mess up computations of diag(true_var), below.
# note that the upper, lower quantiles should be the same shape as mean
# Augment the output variance with the likelihood variance and rescale.

10
GPy/likelihoods/likelihood_functions.py
View file

@ -10,12 +10,12 @@ from ..util.plot import gpplot
from ..util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
import link_functions
class likelihood_function(object):
class LikelihoodFunction(object):
"""
Likelihood class for doing Expectation propagation
:param Y: observed output (Nx1 numpy.darray)
..Note:: Y values allowed depend on the likelihood_function used
..Note:: Y values allowed depend on the LikelihoodFunction used
"""
def __init__(self,link):
if link == self._analytical:
@ -69,7 +69,7 @@ class likelihood_function(object):
sigma2_hat = m2 - mu_hat**2 # Second central moment
return float(Z_hat), float(mu_hat), float(sigma2_hat)
class binomial(likelihood_function):
class Binomial(LikelihoodFunction):
"""
Probit likelihood
Y is expected to take values in {-1,1}
@ -82,7 +82,7 @@ class binomial(likelihood_function):
self._analytical = link_functions.probit
if not link:
link = self._analytical
super(binomial, self).__init__(link)
super(Binomial, self).__init__(link)
def _distribution(self,gp,obs):
pass
@ -134,7 +134,7 @@ class binomial(likelihood_function):
p_975 = stats.norm.cdf(norm_975/np.sqrt(1+var))
return mean[:,None], np.nan*var, p_025[:,None], p_975[:,None] # TODO: var
class Poisson(likelihood_function):
class Poisson(LikelihoodFunction):
"""
Poisson likelihood
Y is expected to take values in {0,1,2,...}

252
GPy/models/FITC.py
View file

@ -1,252 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# 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, tdot, symmetrify,pdinv
from ..util.plot import gpplot
from .. import kern
from scipy import stats, linalg
from ..core import sparse_GP
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
class FITC(sparse_GP):
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
super(FITC, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
def update_likelihood_approximation(self):
"""
Approximates a non-gaussian likelihood using Expectation Propagation
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
this function does nothing
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in sparse_GP.
The true precison is now 'true_precision' not 'precision'.
"""
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._set_params(self._get_params()) # update the GP
def _computations(self):
#factor Kmm
self.Lm = jitchol(self.Kmm)
self.Lmi,info = linalg.lapack.flapack.dtrtrs(self.Lm,np.eye(self.M),lower=1)
Lmipsi1 = np.dot(self.Lmi,self.psi1)
self.Qnn = np.dot(Lmipsi1.T,Lmipsi1).copy()
self.Diag0 = self.psi0 - np.diag(self.Qnn)
self.beta_star = self.likelihood.precision/(1. + self.likelihood.precision*self.Diag0[:,None]) #Includes Diag0 in the precision
self.V_star = self.beta_star * self.likelihood.Y
# The rather complex computations of self.A
if self.has_uncertain_inputs:
raise NotImplementedError
else:
if self.likelihood.is_heteroscedastic:
assert self.likelihood.D == 1
tmp = self.psi1 * (np.sqrt(self.beta_star.flatten().reshape(1, self.N)))
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
self.A = tdot(tmp)
# factor B
self.B = np.eye(self.M) + self.A
self.LB = jitchol(self.B)
self.LBi = chol_inv(self.LB)
self.psi1V = np.dot(self.psi1, self.V_star)
Lmi_psi1V, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(Lmi_psi1V), lower=1, trans=0)
Kmmipsi1 = np.dot(self.Lmi.T,Lmipsi1)
b_psi1_Ki = self.beta_star * Kmmipsi1.T
Ki_pbp_Ki = np.dot(Kmmipsi1,b_psi1_Ki)
Kmmi = np.dot(self.Lmi.T,self.Lmi)
LBiLmi = np.dot(self.LBi,self.Lmi)
LBL_inv = np.dot(LBiLmi.T,LBiLmi)
VVT = np.outer(self.V_star,self.V_star)
VV_p_Ki = np.dot(VVT,Kmmipsi1.T)
Ki_pVVp_Ki = np.dot(Kmmipsi1,VV_p_Ki)
psi1beta = self.psi1*self.beta_star.T
H = self.Kmm + mdot(self.psi1,psi1beta.T)
LH = jitchol(H)
LHi = chol_inv(LH)
Hi = np.dot(LHi.T,LHi)
betapsi1TLmiLBi = np.dot(psi1beta.T,LBiLmi.T)
alpha = np.array([np.dot(a.T,a) for a in betapsi1TLmiLBi])[:,None]
gamma_1 = mdot(VVT,self.psi1.T,Hi)
pHip = mdot(self.psi1.T,Hi,self.psi1)
gamma_2 = mdot(self.beta_star*pHip,self.V_star)
gamma_3 = self.V_star * gamma_2
self._dL_dpsi0 = -0.5 * self.beta_star#dA_dpsi0: logdet(self.beta_star)
self._dL_dpsi0 += .5 * self.V_star**2 #dA_psi0: yT*beta_star*y
self._dL_dpsi0 += .5 *alpha #dC_dpsi0
self._dL_dpsi0 += 0.5*mdot(self.beta_star*pHip,self.V_star)**2 - self.V_star * mdot(self.V_star.T,pHip*self.beta_star).T #dD_dpsi0
self._dL_dpsi1 = b_psi1_Ki.copy() #dA_dpsi1: logdet(self.beta_star)
self._dL_dpsi1 += -np.dot(psi1beta.T,LBL_inv) #dC_dpsi1
self._dL_dpsi1 += gamma_1 - mdot(psi1beta.T,Hi,self.psi1,gamma_1) #dD_dpsi1
self._dL_dKmm = -0.5 * np.dot(Kmmipsi1,b_psi1_Ki) #dA_dKmm: logdet(self.beta_star)
self._dL_dKmm += .5*(LBL_inv - Kmmi) + mdot(LBL_inv,psi1beta,Kmmipsi1.T) #dC_dKmm
self._dL_dKmm += -.5 * mdot(Hi,self.psi1,gamma_1) #dD_dKmm
self._dpsi1_dtheta = 0
self._dpsi1_dX = 0
self._dKmm_dtheta = 0
self._dKmm_dX = 0
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):
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
_dpsi1 = (-V_n**2 - alpha_n + 2.*gamma_k - gamma_n**2) * Kmmipsi1.T[i:(i+1),:]
#Diag_dKmm = Diag_dA_dKmm: yT*beta_star*y +Diag_dC_dKmm +Diag_dD_dKmm
_dKmm = .5*(V_n**2 + alpha_n + gamma_n**2 - 2.*gamma_k) * K_pp_K #Diag_dD_dKmm
self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1,self.X[i:i+1,:],self.Z)
self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm,self.Z)
self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm ,self.Z)
self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T,self.Z,self.X[i:i+1,:])
# the partial derivative vector for the likelihood
if self.likelihood.Nparams == 0:
# save computation here.
self.partial_for_likelihood = None
elif self.likelihood.is_heteroscedastic:
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
# likelihood is not heterscedatic
dbstar_dnoise = self.likelihood.precision * (self.beta_star**2 * self.Diag0[:,None] - self.beta_star)
Lmi_psi1 = mdot(self.Lmi,self.psi1)
LBiLmipsi1 = np.dot(self.LBi,Lmi_psi1)
aux_0 = np.dot(self._LBi_Lmi_psi1V.T,LBiLmipsi1)
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)
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_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)
dD_dnoise = dD_dnoise_1 + dD_dnoise_2
self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise
def log_likelihood(self):
""" Compute the (lower bound on the) log marginal likelihood """
A = -0.5 * self.N * self.D * 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.D * (np.sum(np.log(np.diag(self.LB))))
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
return A + C + D
def _log_likelihood_gradients(self):
pass
return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
def dL_dtheta(self):
if self.has_uncertain_inputs:
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
else:
dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0,self.X)
dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1,self.X,self.Z)
dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm,X=self.Z)
dL_dtheta += self._dKmm_dtheta
dL_dtheta += self._dpsi1_dtheta
return dL_dtheta
def dL_dZ(self):
if self.has_uncertain_inputs:
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
else:
dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T,self.Z,self.X)
dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm,X=self.Z)
dL_dZ += self._dpsi1_dX
dL_dZ += self._dKmm_dX
return dL_dZ
def _raw_predict(self, Xnew, which_parts, full_cov=False):
if self.likelihood.is_heteroscedastic:
Iplus_Dprod_i = 1./(1.+ self.Diag0 * self.likelihood.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.M) + 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.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)
"""
Make a prediction for the generalized FITC model
Arguments
---------
X : Input prediction data - Nx1 numpy array (floats)
"""
# 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
# = 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.M) - 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)
self.mu_H = mu_H
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)
if full_cov:
Kxx = self.kern.K(Xnew,which_parts=which_parts)
var = Kxx + np.dot(KR0T,np.dot(Sigma_H - np.eye(self.M),KR0T.T))
else:
Kxx = self.kern.Kdiag(Xnew,which_parts=which_parts)
var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
return mu_star[:,None],var
else:
raise NotImplementedError, "homoscedastic fitc not implemented"
"""
Kx = self.kern.K(self.Z, Xnew)
mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
if full_cov:
Kxx = self.kern.K(Xnew)
var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
else:
Kxx = self.kern.Kdiag(Xnew)
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
return mu,var[:,None]
"""

17
GPy/models/__init__.py
View file

@ -1,14 +1,11 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from GP_regression import GP_regression
from GP_classification import GP_classification
from sparse_GP_regression import sparse_GP_regression
from sparse_GP_classification import sparse_GP_classification
from FITC_classification import FITC_classification
from GPLVM import GPLVM
from warped_GP import warpedGP
from sparse_GPLVM import sparse_GPLVM
from Bayesian_GPLVM import Bayesian_GPLVM
from gp_regression import GPRegression
from sparse_gp_regression import SparseGPRegression
from sparse_gp_classification import SparseGPClassification
from fitc_classification import FITCClassification
from gplvm import GPLVM
from warped_gp import WarpedGP
from bayesian_gplvm import BayesianGPLVM
from mrd import MRD

51
GPy/models/Bayesian_GPLVM.py → GPy/models/bayesian_gplvm.py
View file

@ -2,21 +2,16 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import pylab as pb
import sys, pdb
from GPLVM import GPLVM
from ..core import sparse_GP
from GPy.util.linalg import pdinv
from ..core import SparseGP
from ..likelihoods import Gaussian
from .. import kern
from numpy.linalg.linalg import LinAlgError
import itertools
from matplotlib.colors import colorConverter
from matplotlib.figure import SubplotParams
from GPy.inference.optimization import SCG
from GPy.util import plot_latent
from GPy.models.gplvm import GPLVM
class Bayesian_GPLVM(sparse_GP, GPLVM):
class BayesianGPLVM(SparseGP, GPLVM):
"""
Bayesian Gaussian Process Latent Variable Model
@ -64,7 +59,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
self._savedpsiKmm = []
self._savedABCD = []
sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, X_variance=X_variance, **kwargs)
SparseGP.__init__(self, X, likelihood, kernel, Z=Z, X_variance=X_variance, **kwargs)
self._set_params(self._get_params())
@property
@ -80,19 +75,19 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
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)], [])
return (X_names + S_names + sparse_GP._get_param_names(self))
return (X_names + S_names + SparseGP._get_param_names(self))
def _get_params(self):
"""
Horizontally stacks the parameters in order to present them to the optimizer.
The resulting 1-D array has this structure:
The resulting 1-input_dim array has this structure:
===============================================================
| mu | S | Z | theta | beta |
===============================================================
"""
x = np.hstack((self.X.flatten(), self.X_variance.flatten(), sparse_GP._get_params(self)))
x = np.hstack((self.X.flatten(), self.X_variance.flatten(), SparseGP._get_params(self)))
return x
def _clipped(self, x):
@ -104,7 +99,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
N, input_dim = self.N, 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()
sparse_GP._set_params(self, x[(2 * N * input_dim):])
SparseGP._set_params(self, x[(2 * N * input_dim):])
# self.oldps = x
# except (LinAlgError, FloatingPointError, ZeroDivisionError):
# print "\rWARNING: Caught LinAlgError, continueing without setting "
@ -134,7 +129,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
return 0.5 * (var_mean + var_S) - 0.5 * self.input_dim * self.N
def log_likelihood(self):
ll = sparse_GP.log_likelihood(self)
ll = SparseGP.log_likelihood(self)
kl = self.KL_divergence()
# if ll < -2E4:
@ -151,14 +146,14 @@ class Bayesian_GPLVM(sparse_GP, 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.D * 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.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A) * sf2)
B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
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)
# 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.D * (np.log(2.*np.pi) + np.log(self.likelihood._variance)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
# B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A) * sf2)
B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
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
# 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))
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
self._savedABCD.append([self.f_call, A, B, C, D])
@ -181,7 +176,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
# d_dS = (dL_dS).flatten()
# ========================
self.dbound_dmuS = np.hstack((d_dmu, d_dS))
self.dbound_dZtheta = sparse_GP._log_likelihood_gradients(self)
self.dbound_dZtheta = SparseGP._log_likelihood_gradients(self)
return self._clipped(np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta)))
def plot_latent(self, *args, **kwargs):
@ -200,7 +195,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
means = np.zeros((N_test, input_dim))
covars = np.zeros((N_test, input_dim))
dpsi0 = -0.5 * self.D * self.likelihood.precision
dpsi0 = -0.5 * self.input_dim * self.likelihood.precision
dpsi2 = self.dL_dpsi2[0][None, :, :] # TODO: this may change if we ignore het. likelihoods
V = self.likelihood.precision * Y
dpsi1 = np.dot(self.Cpsi1V, V.T)
@ -263,7 +258,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
def __getstate__(self):
return (self.likelihood, self.input_dim, self.X, self.X_variance,
self.init, self.M, self.Z, self.kern,
self.init, self.num_inducing, self.Z, self.kern,
self.oldpsave, self._debug)
def __setstate__(self, state):
@ -274,8 +269,8 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
X = x[start:end].reshape(self.N, self.input_dim)
start, end = end, end + self.X_variance.size
X_v = x[start:end].reshape(self.N, self.input_dim)
start, end = end, end + (self.M * self.input_dim)
Z = x[start:end].reshape(self.M, 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
theta = x[start:]
return X, X_v, Z, theta
@ -353,12 +348,12 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
figs.append(pylab.figure("BGPLVM DEBUG Kmm", figsize=(12, 6)))
fig = figs[-1]
ax8 = fig.add_subplot(121)
ax8.text(.5, .5, r"${\mathbf{A,B,C,D}}$", color='k', alpha=.5, transform=ax8.transAxes,
ax8.text(.5, .5, r"${\mathbf{A,B,C,input_dim}}$", color='k', alpha=.5, transform=ax8.transAxes,
ha='center', va='center')
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 1], label='A')
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 2], label='B')
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 3], label='C')
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 4], label='D')
ax8.plot(ABCD_dict[:, 0], ABCD_dict[:, 4], label='input_dim')
ax8.legend()
figs[-1].canvas.draw()
figs[-1].tight_layout(rect=(.15, 0, 1, .86))

252
GPy/models/fitc.py Normal file
View file

@ -0,0 +1,252 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# 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, tdot, symmetrify, pdinv
from ..util.plot import gpplot
from .. import kern
from scipy import stats, linalg
from GPy.core.sparse_gp import SparseGP
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
class FITC(SparseGP):
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
super(FITC, self).__init__(X, likelihood, kernel, normalize_X=normalize_X)
def update_likelihood_approximation(self):
"""
Approximates a non-gaussian likelihood using Expectation Propagation
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
this function does nothing
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in SparseGP.
The true precison is now 'true_precision' not 'precision'.
"""
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._set_params(self._get_params()) # update the GP
def _computations(self):
# factor Kmm
self.Lm = jitchol(self.Kmm)
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).copy()
self.Diag0 = self.psi0 - np.diag(self.Qnn)
self.beta_star = self.likelihood.precision / (1. + self.likelihood.precision * self.Diag0[:, None]) # Includes Diag0 in the precision
self.V_star = self.beta_star * self.likelihood.Y
# The rather complex computations of self.A
if self.has_uncertain_inputs:
raise NotImplementedError
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, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
self.A = tdot(tmp)
# factor B
self.B = np.eye(self.num_inducing) + self.A
self.LB = jitchol(self.B)
self.LBi = chol_inv(self.LB)
self.psi1V = np.dot(self.psi1, self.V_star)
Lmi_psi1V, info = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(self.psi1V), lower=1, trans=0)
self._LBi_Lmi_psi1V, _ = linalg.lapack.flapack.dtrtrs(self.LB, np.asfortranarray(Lmi_psi1V), lower=1, trans=0)
Kmmipsi1 = np.dot(self.Lmi.T, Lmipsi1)
b_psi1_Ki = self.beta_star * Kmmipsi1.T
Ki_pbp_Ki = np.dot(Kmmipsi1, b_psi1_Ki)
Kmmi = np.dot(self.Lmi.T, self.Lmi)
LBiLmi = np.dot(self.LBi, self.Lmi)
LBL_inv = np.dot(LBiLmi.T, LBiLmi)
VVT = np.outer(self.V_star, self.V_star)
VV_p_Ki = np.dot(VVT, Kmmipsi1.T)
Ki_pVVp_Ki = np.dot(Kmmipsi1, VV_p_Ki)
psi1beta = self.psi1 * self.beta_star.T
H = self.Kmm + mdot(self.psi1, psi1beta.T)
LH = jitchol(H)
LHi = chol_inv(LH)
Hi = np.dot(LHi.T, LHi)
betapsi1TLmiLBi = np.dot(psi1beta.T, LBiLmi.T)
alpha = np.array([np.dot(a.T, a) for a in betapsi1TLmiLBi])[:, None]
gamma_1 = mdot(VVT, self.psi1.T, Hi)
pHip = mdot(self.psi1.T, Hi, self.psi1)
gamma_2 = mdot(self.beta_star * pHip, self.V_star)
gamma_3 = self.V_star * gamma_2
self._dL_dpsi0 = -0.5 * self.beta_star # dA_dpsi0: logdet(self.beta_star)
self._dL_dpsi0 += .5 * self.V_star ** 2 # dA_psi0: yT*beta_star*y
self._dL_dpsi0 += .5 * alpha # dC_dpsi0
self._dL_dpsi0 += 0.5 * mdot(self.beta_star * pHip, self.V_star) ** 2 - self.V_star * mdot(self.V_star.T, pHip * self.beta_star).T # dD_dpsi0
self._dL_dpsi1 = b_psi1_Ki.copy() # dA_dpsi1: logdet(self.beta_star)
self._dL_dpsi1 += -np.dot(psi1beta.T, LBL_inv) # dC_dpsi1
self._dL_dpsi1 += gamma_1 - mdot(psi1beta.T, Hi, self.psi1, gamma_1) # dD_dpsi1
self._dL_dKmm = -0.5 * np.dot(Kmmipsi1, b_psi1_Ki) # dA_dKmm: logdet(self.beta_star)
self._dL_dKmm += .5 * (LBL_inv - Kmmi) + mdot(LBL_inv, psi1beta, Kmmipsi1.T) # dC_dKmm
self._dL_dKmm += -.5 * mdot(Hi, self.psi1, gamma_1) # dD_dKmm
self._dpsi1_dtheta = 0
self._dpsi1_dX = 0
self._dKmm_dtheta = 0
self._dKmm_dX = 0
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):
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
_dpsi1 = (-V_n ** 2 - alpha_n + 2.*gamma_k - gamma_n ** 2) * Kmmipsi1.T[i:(i + 1), :]
# Diag_dKmm = Diag_dA_dKmm: yT*beta_star*y +Diag_dC_dKmm +Diag_dD_dKmm
_dKmm = .5 * (V_n ** 2 + alpha_n + gamma_n ** 2 - 2.*gamma_k) * K_pp_K # Diag_dD_dKmm
self._dpsi1_dtheta += self.kern.dK_dtheta(_dpsi1, self.X[i:i + 1, :], self.Z)
self._dKmm_dtheta += self.kern.dK_dtheta(_dKmm, self.Z)
self._dKmm_dX += 2.*self.kern.dK_dX(_dKmm , self.Z)
self._dpsi1_dX += self.kern.dK_dX(_dpsi1.T, self.Z, self.X[i:i + 1, :])
# the partial derivative vector for the likelihood
if self.likelihood.Nparams == 0:
# save computation here.
self.partial_for_likelihood = None
elif self.likelihood.is_heteroscedastic:
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
# likelihood is not heterscedatic
dbstar_dnoise = self.likelihood.precision * (self.beta_star ** 2 * self.Diag0[:, None] - self.beta_star)
Lmi_psi1 = mdot(self.Lmi, self.psi1)
LBiLmipsi1 = np.dot(self.LBi, Lmi_psi1)
aux_0 = np.dot(self._LBi_Lmi_psi1V.T, LBiLmipsi1)
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.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.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)
dD_dnoise = dD_dnoise_1 + dD_dnoise_2
self.partial_for_likelihood = dA_dnoise + dC_dnoise + dD_dnoise
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)
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
def _log_likelihood_gradients(self):
pass
return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
def dL_dtheta(self):
if self.has_uncertain_inputs:
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
else:
dL_dtheta = self.kern.dKdiag_dtheta(self._dL_dpsi0, self.X)
dL_dtheta += self.kern.dK_dtheta(self._dL_dpsi1, self.X, self.Z)
dL_dtheta += self.kern.dK_dtheta(self._dL_dKmm, X=self.Z)
dL_dtheta += self._dKmm_dtheta
dL_dtheta += self._dpsi1_dtheta
return dL_dtheta
def dL_dZ(self):
if self.has_uncertain_inputs:
raise NotImplementedError, "FITC approximation not implemented for uncertain inputs"
else:
dL_dZ = self.kern.dK_dX(self._dL_dpsi1.T, self.Z, self.X)
dL_dZ += 2. * self.kern.dK_dX(self._dL_dKmm, X=self.Z)
dL_dZ += self._dpsi1_dX
dL_dZ += self._dKmm_dX
return dL_dZ
def _raw_predict(self, Xnew, which_parts, full_cov=False):
if self.likelihood.is_heteroscedastic:
Iplus_Dprod_i = 1. / (1. + self.Diag0 * self.likelihood.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.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)
"""
Make a prediction for the generalized FITC model
Arguments
---------
X : Input prediction data - Nx1 numpy array (floats)
"""
# q(u|f) = N(u| R0i*mu_u*f, R0i*C*R0i.T)
# Ci = I + (RPT0)Di(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)
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)
self.mu_H = mu_H
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)
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))
else:
Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
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"
"""
Kx = self.kern.K(self.Z, Xnew)
mu = mdot(Kx.T, self.C/self.scale_factor, self.psi1V)
if full_cov:
Kxx = self.kern.K(Xnew)
var = Kxx - mdot(Kx.T, (self.Kmmi - self.C/self.scale_factor**2), Kx) #NOTE this won't work for plotting
else:
Kxx = self.kern.Kdiag(Xnew)
var = Kxx - np.sum(Kx*np.dot(self.Kmmi - self.C/self.scale_factor**2, Kx),0)
return mu,var[:,None]
"""

57
GPy/models/generalized_FITC.py → GPy/models/generalized_fitc.py
View file

@ -7,7 +7,11 @@ 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
def backsub_both_sides(L,X):
""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
@ -15,7 +19,7 @@ def backsub_both_sides(L,X):
return linalg.lapack.flapack.dtrtrs(L,np.asfortranarray(tmp.T),lower=1,trans=1)[0].T
class generalized_FITC(sparse_GP):
class GeneralizedFITC(SparseGP):
"""
Naish-Guzman, A. and Holden, S. (2008) implemantation of EP with FITC.
@ -28,9 +32,9 @@ class generalized_FITC(sparse_GP):
:param X_variance: The variance in the measurements of X (Gaussian variance)
:type X_variance: np.ndarray (N x input_dim) | None
:param Z: inducing inputs (optional, see note)
:type Z: np.ndarray (M x input_dim) | None
:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
:type M: int
: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)
:type num_inducing: int
:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
:type normalize_(X|Y): bool
"""
@ -38,13 +42,18 @@ class generalized_FITC(sparse_GP):
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
self.Z = Z
self.M = self.Z.shape[0]
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.M*self.input_dim].reshape(self.M, self.input_dim)
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._compute_kernel_matrices()
@ -58,7 +67,7 @@ class generalized_FITC(sparse_GP):
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
this function does nothing
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in sparse_GP.
Diag(Knn - Qnn) is added to the noise term to use the tools already implemented in SparseGP.
The true precison is now 'true_precision' not 'precision'.
"""
if self.has_uncertain_inputs:
@ -75,14 +84,14 @@ class generalized_FITC(sparse_GP):
but adds a diagonal term to the covariance matrix: diag(Knn - Qnn).
This function:
- computes the FITC diagonal term
- removes the extra terms computed in the sparse_GP approximation
- 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'
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.M),lower=1)
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)
@ -94,7 +103,7 @@ class generalized_FITC(sparse_GP):
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.M) + np.dot(self.RPT0,((1. - Iplus_Dprod_i)/self.Diag0)[:,None]*self.RPT0.T))
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)
@ -122,7 +131,7 @@ class generalized_FITC(sparse_GP):
sf2 = sf**2
# Remove extra term from dL_dKmm
self.dL_dKmm += 0.5 * self.D * 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
@ -133,8 +142,8 @@ class generalized_FITC(sparse_GP):
else:
raise NotImplementedError, "homoscedastic derivatives not implemented"
#likelihood is not heterscedatic
#self.partial_for_likelihood = - 0.5 * self.N*self.D*self.likelihood.precision + 0.5 * np.sum(np.square(self.likelihood.Y))*self.likelihood.precision**2
#self.partial_for_likelihood += 0.5 * self.D * trace_dot(self.Bi,self.A)*self.likelihood.precision
#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.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
@ -146,7 +155,7 @@ class generalized_FITC(sparse_GP):
if self.has_uncertain_inputs:
raise NotImplementedError, "heteroscedatic derivates not implemented"
else:
#NOTE in sparse_GP this would include the gradient wrt psi0
#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
@ -155,11 +164,11 @@ class generalized_FITC(sparse_GP):
""" Compute the (lower bound on the) log marginal likelihood """
sf2 = self.scale_factor**2
if self.likelihood.is_heteroscedastic:
A = -0.5*self.N*self.D*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.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)
else:
A = -0.5*self.N*self.D*(np.log(2.*np.pi) + np.log(self.likelihood._variance)) -0.5*self.likelihood.precision*self.likelihood.trYYT
C = -self.D * (np.sum(np.log(np.diag(self.LB))) + 0.5*self.M*np.log(sf2))
#C = -0.5*self.D * (self.B_logdet + self.M*np.log(sf2))
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
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)
@ -177,13 +186,13 @@ class generalized_FITC(sparse_GP):
# 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)
V,info = linalg.flapack.dtrtrs(U,self.RPT0.T,lower=1)
C = np.eye(self.M) - np.dot(V.T,V)
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
@ -199,12 +208,12 @@ class generalized_FITC(sparse_GP):
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.M),KR0T.T))
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.M),KR0T.T)) # TODO: RA, is this line needed?
var = (Kxx + np.sum(KR0T.T*np.dot(Sigma_H - np.eye(self.M),KR0T.T),0))[:,None]
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"

4
GPy/models/GP_classification.py → GPy/models/gp_classification.py
View file

@ -15,7 +15,7 @@ class GP_classification(GP):
: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
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
:type normalize_X: False|True
@ -31,7 +31,7 @@ class GP_classification(GP):
kernel = kern.rbf(X.shape[1])
if likelihood is None:
distribution = likelihoods.likelihood_functions.binomial()
distribution = likelihoods.likelihood_functions.Binomial()
likelihood = likelihoods.EP(Y, distribution)
elif Y is not None:
if not all(Y.flatten() == likelihood.data.flatten()):

2
GPy/models/GP_regression.py → GPy/models/gp_regression.py
View file

@ -7,7 +7,7 @@ from ..core import GP
from .. import likelihoods
from .. import kern
class GP_regression(GP):
class GPRegression(GP):
"""
Gaussian Process model for regression

0
GPy/models/GPLVM.py → GPy/models/gplvm.py
View file

33
GPy/models/mrd.py
View file

@ -4,14 +4,13 @@ Created on 10 Apr 2013
@author: Max Zwiessele
'''
from GPy.core import model
from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
from GPy.core import sparse_GP
from GPy.core import SparseGP
from GPy.util.linalg import PCA
from scipy import linalg
import numpy
import itertools
import pylab
from GPy.kern.kern import kern
from GPy.models.bayesian_gplvm import BayesianGPLVM
class MRD(model):
"""
@ -38,7 +37,7 @@ class MRD(model):
*concat: PCA on concatenated outputs
*single: PCA on each output
*random: random
:param M:
:param num_inducing:
number of inducing inputs to use
:param Z:
initial inducing inputs
@ -62,22 +61,22 @@ class MRD(model):
assert not ('kernel' in kw), "pass kernels through `kernels` argument"
self.input_dim = input_dim
self.M = M
self.num_inducing = M
self._debug = _debug
self._init = True
X = self._init_X(initx, likelihood_or_Y_list)
Z = self._init_Z(initz, X)
self.bgplvms = [Bayesian_GPLVM(l, input_dim=input_dim, kernel=k, X=X, Z=Z, M=self.M, **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, M=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] + [sparse_GP._get_params(g).size - g.Z.size for g in self.bgplvms])
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.MQ = self.M * self.input_dim
self.MQ = self.num_inducing * self.input_dim
model.__init__(self) # @UndefinedVariable
self._set_params(self._get_params())
@ -151,7 +150,7 @@ class MRD(model):
itertools.izip(ns,
itertools.repeat(name)))
return list(itertools.chain(n1var, *(map_names(\
sparse_GP._get_param_names(g)[self.MQ:], n) \
SparseGP._get_param_names(g)[self.MQ:], n) \
for g, n in zip(self.bgplvms, self.names))))
def _get_params(self):
@ -165,14 +164,14 @@ class MRD(model):
X = self.gref.X.ravel()
X_var = self.gref.X_variance.ravel()
Z = self.gref.Z.ravel()
thetas = [sparse_GP._get_params(g)[g.Z.size:] for g in self.bgplvms]
thetas = [SparseGP._get_params(g)[g.Z.size:] for g in self.bgplvms]
params = numpy.hstack([X, X_var, Z, numpy.hstack(thetas)])
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.Z = Z.reshape(self.M, self.input_dim)
# g.Z = Z.reshape(self.num_inducing, self.input_dim)
#
# def _set_kern_params(self, g, p):
# g.kern._set_params(p[:g.kern.Nparam])
@ -206,7 +205,7 @@ class MRD(model):
def log_likelihood(self):
ll = -self.gref.KL_divergence()
for g in self.bgplvms:
ll += sparse_GP.log_likelihood(g)
ll += SparseGP.log_likelihood(g)
return ll
def _log_likelihood_gradients(self):
@ -215,7 +214,7 @@ class MRD(model):
dLdmu -= dKLmu
dLdS -= dKLdS
dLdmuS = numpy.hstack((dLdmu.flatten(), dLdS.flatten())).flatten()
dldzt1 = reduce(lambda a, b: a + b, (sparse_GP._log_likelihood_gradients(g)[:self.MQ] for g in self.bgplvms))
dldzt1 = reduce(lambda a, b: a + b, (SparseGP._log_likelihood_gradients(g)[:self.MQ] for g in self.bgplvms))
return numpy.hstack((dLdmuS,
dldzt1,
@ -250,9 +249,9 @@ class MRD(model):
if X is None:
X = self.X
if init in "permute":
Z = numpy.random.permutation(X.copy())[:self.M]
Z = numpy.random.permutation(X.copy())[:self.num_inducing]
elif init in "random":
Z = numpy.random.randn(self.M, self.input_dim) * X.var()
Z = numpy.random.randn(self.num_inducing, self.input_dim) * X.var()
self.Z = Z
return Z
@ -274,8 +273,8 @@ class MRD(model):
else:
return pylab.gcf()
def plot_X_1d(self):
return self.gref.plot_X_1d()
def plot_X_1d(self, *a, **kw):
return self.gref.plot_X_1d(*a, **kw)
def plot_X(self, fignum=None, ax=None):
fig = self._handle_plotting(fignum, ax, lambda i, g, ax: ax.imshow(g.X))

61
GPy/models/sparse_GPLVM.py
View file

@ -1,61 +0,0 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import pylab as pb
import sys, pdb
# from .. import kern
# from ..core import model
# from ..util.linalg import pdinv, PCA
from GPLVM import GPLVM
from sparse_GP_regression import sparse_GP_regression
class sparse_GPLVM(sparse_GP_regression, GPLVM):
"""
Sparse Gaussian Process Latent Variable Model
:param Y: observed data
:type Y: np.ndarray
:param input_dim: latent dimensionality
:type input_dim: int
:param init: initialisation method for the latent space
:type init: 'PCA'|'random'
"""
def __init__(self, Y, input_dim, kernel=None, init='PCA', M=10):
X = self.initialise_latent(init, input_dim, Y)
sparse_GP_regression.__init__(self, X, Y, kernel=kernel,M=M)
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)],[])
+ sparse_GP_regression._get_param_names(self))
def _get_params(self):
return np.hstack((self.X.flatten(), sparse_GP_regression._get_params(self)))
def _set_params(self,x):
self.X = x[:self.X.size].reshape(self.N,self.input_dim).copy()
sparse_GP_regression._set_params(self, x[self.X.size:])
def log_likelihood(self):
return sparse_GP_regression.log_likelihood(self)
def dL_dX(self):
dL_dX = self.kern.dKdiag_dX(self.dL_dpsi0,self.X)
dL_dX += self.kern.dK_dX(self.dL_dpsi1.T,self.X,self.Z)
return dL_dX
def _log_likelihood_gradients(self):
return np.hstack((self.dL_dX().flatten(), sparse_GP_regression._log_likelihood_gradients(self)))
def plot(self):
GPLVM.plot(self)
#passing Z without a small amout of jitter will induce the white kernel where we don;t want it!
mu, var, upper, lower = sparse_GP_regression.predict(self, self.Z+np.random.randn(*self.Z.shape)*0.0001)
pb.plot(mu[:, 0] , mu[:, 1], 'ko')
def plot_latent(self, *args, **kwargs):
input_1, input_2 = GPLVM.plot_latent(*args, **kwargs)
pb.plot(m.Z[:, input_1], m.Z[:, input_2], '^w')

4
GPy/models/sparse_GP_classification.py → GPy/models/sparse_gp_classification.py
View file

@ -16,7 +16,7 @@ class sparse_GP_classification(sparse_GP):
: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
@ -31,7 +31,7 @@ class sparse_GP_classification(sparse_GP):
kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1],1e-3)
if likelihood is None:
distribution = likelihoods.likelihood_functions.binomial()
distribution = likelihoods.likelihood_functions.Binomial()
likelihood = likelihoods.EP(Y, distribution)
elif Y is not None:
if not all(Y.flatten() == likelihood.data.flatten()):

22
GPy/models/sparse_GP_regression.py → GPy/models/sparse_gp_regression.py
View file

@ -3,17 +3,15 @@
import numpy as np
from ..core import sparse_GP
from ..core import SparseGP
from .. import likelihoods
from .. import kern
from ..likelihoods import likelihood
from GP_regression import GP_regression
class sparse_GP_regression(sparse_GP):
class SparseGPRegression(SparseGP):
"""
Gaussian Process model for regression
This is a thin wrapper around the sparse_GP class, with a set of sensible defalts
This is a thin wrapper around the SparseGP class, with a set of sensible defalts
:param X: input observations
:param Y: observed values
@ -29,19 +27,19 @@ class sparse_GP_regression(sparse_GP):
"""
def __init__(self, X, Y, kernel=None, normalize_X=False, normalize_Y=False, Z=None, M=10, X_variance=None):
#kern defaults to rbf (plus white for stability)
# 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)
kernel = kern.rbf(X.shape[1]) + kern.white(X.shape[1], 1e-3)
#Z defaults to a subset of the data
# Z defaults to a subset of the data
if Z is None:
i = np.random.permutation(X.shape[0])[:M]
Z = X[i].copy()
else:
assert Z.shape[1]==X.shape[1]
assert Z.shape[1] == X.shape[1]
#likelihood defaults to Gaussian
likelihood = likelihoods.Gaussian(Y,normalize=normalize_Y)
# likelihood defaults to Gaussian
likelihood = likelihoods.Gaussian(Y, normalize=normalize_Y)
sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X, X_variance=X_variance)
SparseGP.__init__(self, X, likelihood, kernel, Z=Z, normalize_X=normalize_X, X_variance=X_variance)
self._set_params(self._get_params())

61
GPy/models/sparse_gplvm.py Normal file
View file

@ -0,0 +1,61 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
import pylab as pb
import sys, pdb
from GPy.models.sparse_gp_regression import SparseGPRegression
from GPy.models.gplvm import GPLVM
# from .. import kern
# from ..core import model
# from ..util.linalg import pdinv, PCA
class SparseGPLVM(SparseGPRegression, GPLVM):
"""
Sparse Gaussian Process Latent Variable Model
:param Y: observed data
:type Y: np.ndarray
:param input_dim: latent dimensionality
:type input_dim: int
:param init: initialisation method for the latent space
:type init: 'PCA'|'random'
"""
def __init__(self, Y, input_dim, kernel=None, init='PCA', M=10):
X = self.initialise_latent(init, input_dim, Y)
SparseGPRegression.__init__(self, X, Y, kernel=kernel, M=M)
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)], [])
+ 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()
SparseGPRegression._set_params(self, x[self.X.size:])
def log_likelihood(self):
return SparseGPRegression.log_likelihood(self)
def dL_dX(self):
dL_dX = self.kern.dKdiag_dX(self.dL_dpsi0, self.X)
dL_dX += self.kern.dK_dX(self.dL_dpsi1.T, self.X, self.Z)
return dL_dX
def _log_likelihood_gradients(self):
return np.hstack((self.dL_dX().flatten(), SparseGPRegression._log_likelihood_gradients(self)))
def plot(self):
GPLVM.plot(self)
# passing Z without a small amout of jitter will induce the white kernel where we don;t want it!
mu, var, upper, lower = SparseGPRegression.predict(self, self.Z + np.random.randn(*self.Z.shape) * 0.0001)
pb.plot(mu[:, 0] , mu[:, 1], 'ko')
def plot_latent(self, *args, **kwargs):
input_1, input_2 = GPLVM.plot_latent(*args, **kwargs)
pb.plot(m.Z[:, input_1], m.Z[:, input_2], '^w')

26
GPy/models/warped_GP.py → GPy/models/warped_gp.py
View file

@ -3,25 +3,21 @@
import numpy as np
from .. import kern
from ..core import model
from ..util.linalg import pdinv
from ..util.plot import gpplot
from ..util.warping_functions import *
from GP_regression import GP_regression
from ..core import GP
from .. import likelihoods
from .. import kern
from GPy.util.warping_functions import TanhWarpingFunction_d
from GPy import kern
class warpedGP(GP):
def __init__(self, X, Y, kernel=None, warping_function = None, warping_terms = 3, normalize_X=False, normalize_Y=False):
class WarpedGP(GP):
def __init__(self, X, Y, kernel=None, warping_function=None, warping_terms=3, normalize_X=False, normalize_Y=False):
if kernel is None:
kernel = kern.rbf(X.shape[1])
if warping_function == None:
self.warping_function = TanhWarpingFunction_d(warping_terms)
self.warping_params = (np.random.randn(self.warping_function.n_terms*3+1,) * 1)
self.warping_params = (np.random.randn(self.warping_function.n_terms * 3 + 1,) * 1)
Y = self._scale_data(Y)
self.has_uncertain_inputs = False
@ -35,10 +31,10 @@ class warpedGP(GP):
def _scale_data(self, Y):
self._Ymax = Y.max()
self._Ymin = Y.min()
return (Y-self._Ymin)/(self._Ymax-self._Ymin) - 0.5
return (Y - self._Ymin) / (self._Ymax - self._Ymin) - 0.5
def _unscale_data(self, Y):
return (Y + 0.5)*(self._Ymax - self._Ymin) + self._Ymin
return (Y + 0.5) * (self._Ymax - self._Ymin) + self._Ymin
def _set_params(self, x):
self.warping_params = x[:self.warping_function.num_parameters]
@ -68,15 +64,15 @@ class warpedGP(GP):
alpha = np.dot(self.Ki, self.likelihood.Y.flatten())
warping_grads = self.warping_function_gradients(alpha)
warping_grads = np.append(warping_grads[:,:-1].flatten(), warping_grads[0,-1])
warping_grads = np.append(warping_grads[:, :-1].flatten(), warping_grads[0, -1])
return np.hstack((warping_grads.flatten(), ll_grads.flatten()))
def warping_function_gradients(self, Kiy):
grad_y = self.warping_function.fgrad_y(self.Y_untransformed, self.warping_params)
grad_y_psi, grad_psi = self.warping_function.fgrad_y_psi(self.Y_untransformed, self.warping_params,
return_covar_chain = True)
djac_dpsi = ((1.0/grad_y[:,:, None, None])*grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:,None,None,None] * grad_psi).sum(axis=0).sum(axis=0)
return_covar_chain=True)
djac_dpsi = ((1.0 / grad_y[:, :, None, None]) * grad_y_psi).sum(axis=0).sum(axis=0)
dquad_dpsi = (Kiy[:, None, None, None] * grad_psi).sum(axis=0).sum(axis=0)
return -dquad_dpsi + djac_dpsi

21
GPy/testing/bgplvm_tests.py
View file

@ -4,6 +4,7 @@
import unittest
import numpy as np
import GPy
from GPy.models.bayesian_gplvm import BayesianGPLVM
class BGPLVMTests(unittest.TestCase):
def test_bias_kern(self):
@ -11,10 +12,10 @@ class BGPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel = k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@ -24,10 +25,10 @@ class BGPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel = k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@ -37,10 +38,10 @@ class BGPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel = k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@ -50,10 +51,10 @@ class BGPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel = k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@ -64,10 +65,10 @@ class BGPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel = k, M=M)
m = BayesianGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())

12
GPy/testing/examples_tests.py
View file

@ -9,6 +9,7 @@ import pkgutil
import os
import random
from nose.tools import nottest
import sys
class ExamplesTests(unittest.TestCase):
def _checkgrad(self, model):
@ -40,9 +41,9 @@ def model_instance(model):
@nottest
def test_models():
examples_path = os.path.dirname(GPy.examples.__file__)
#Load modules
# Load modules
for loader, module_name, is_pkg in pkgutil.iter_modules([examples_path]):
#Load examples
# Load examples
module_examples = loader.find_module(module_name).load_module(module_name)
print "MODULE", module_examples
print "Before"
@ -56,11 +57,11 @@ def test_models():
continue
print "Testing example: ", example[0]
#Generate model
# Generate model
model = example[1]()
print model
#Create tests for instance check
# Create tests for instance check
"""
test = model_instance_generator(model)
test.__name__ = 'test_instance_%s' % example[0]
@ -78,4 +79,5 @@ def test_models():
if __name__ == "__main__":
print "Running unit tests, please be (very) patient..."
unittest.main()
# unittest.main()
test_models()

6
GPy/testing/gplvm_tests.py
View file

@ -11,7 +11,7 @@ class GPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.GPLVM(Y, input_dim, kernel = k)
m.ensure_default_constraints()
@ -23,7 +23,7 @@ class GPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.GPLVM(Y, input_dim, kernel = k)
m.ensure_default_constraints()
@ -35,7 +35,7 @@ class GPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.GPLVM(Y, input_dim, kernel = k)
m.ensure_default_constraints()

8
GPy/testing/kernel_tests.py
View file

@ -12,7 +12,7 @@ class KernelTests(unittest.TestCase):
K.constrain_fixed('2')
X = np.random.rand(5,5)
Y = np.ones((5,1))
m = GPy.models.GP_regression(X,Y,K)
m = GPy.models.GPRegression(X,Y,K)
self.assertTrue(m.checkgrad())
def test_fixedkernel(self):
@ -23,7 +23,7 @@ class KernelTests(unittest.TestCase):
K = np.dot(X, X.T)
kernel = GPy.kern.fixed(4, K)
Y = np.ones((30,1))
m = GPy.models.GP_regression(X,Y,kernel=kernel)
m = GPy.models.GPRegression(X,Y,kernel=kernel)
self.assertTrue(m.checkgrad())
def test_coregionalisation(self):
@ -36,9 +36,9 @@ class KernelTests(unittest.TestCase):
Y = np.vstack((Y1,Y2))
k1 = GPy.kern.rbf(1) + GPy.kern.bias(1)
k2 = GPy.kern.coregionalise(2,1)
k2 = GPy.kern.Coregionalise(2,1)
k = k1.prod(k2,tensor=True)
m = GPy.models.GP_regression(X,Y,kernel=k)
m = GPy.models.GPRegression(X,Y,kernel=k)
self.assertTrue(m.checkgrad())

2
GPy/testing/mrd_tests.py
View file

@ -20,7 +20,7 @@ class MRDTests(unittest.TestCase):
k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim)
K = k.K(X)
Ylist = [np.random.multivariate_normal(np.zeros(N), K, D).T for _ in range(num_m)]
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)

6
GPy/testing/prior_tests.py
View file

@ -13,7 +13,7 @@ class PriorTests(unittest.TestCase):
y = b*X + C + 1*np.sin(X)
y += 0.05*np.random.randn(len(X))
X, y = X[:, None], y[:, None]
m = GPy.models.GP_regression(X, y)
m = GPy.models.GPRegression(X, y)
m.ensure_default_constraints()
lognormal = GPy.priors.LogGaussian(1, 2)
m.set_prior('rbf', lognormal)
@ -27,7 +27,7 @@ class PriorTests(unittest.TestCase):
y = b*X + C + 1*np.sin(X)
y += 0.05*np.random.randn(len(X))
X, y = X[:, None], y[:, None]
m = GPy.models.GP_regression(X, y)
m = GPy.models.GPRegression(X, y)
m.ensure_default_constraints()
Gamma = GPy.priors.Gamma(1, 1)
m.set_prior('rbf', Gamma)
@ -41,7 +41,7 @@ class PriorTests(unittest.TestCase):
y = b*X + C + 1*np.sin(X)
y += 0.05*np.random.randn(len(X))
X, y = X[:, None], y[:, None]
m = GPy.models.GP_regression(X, y)
m = GPy.models.GPRegression(X, y)
m.ensure_default_constraints()
gaussian = GPy.priors.Gaussian(1, 1)
success = False

52
GPy/testing/psi_stat_expactation_tests.py
View file

@ -21,36 +21,36 @@ def ard(p):
@testing.deepTest(__test__)
class Test(unittest.TestCase):
D = 9
M = 4
input_dim = 9
num_inducing = 4
N = 3
Nsamples = 6e6
def setUp(self):
self.kerns = (
# (GPy.kern.rbf(self.D, ARD=True) +
# GPy.kern.linear(self.D, ARD=True) +
# GPy.kern.bias(self.D) +
# GPy.kern.white(self.D)),
(GPy.kern.rbf(self.D, np.random.rand(), np.random.rand(self.D), ARD=True) +
GPy.kern.rbf(self.D, np.random.rand(), np.random.rand(self.D), ARD=True) +
GPy.kern.linear(self.D, np.random.rand(self.D), ARD=True) +
GPy.kern.bias(self.D) +
GPy.kern.white(self.D)),
# GPy.kern.rbf(self.D), GPy.kern.rbf(self.D, ARD=True),
# GPy.kern.linear(self.D, ARD=False), GPy.kern.linear(self.D, ARD=True),
# GPy.kern.linear(self.D) + GPy.kern.bias(self.D),
# GPy.kern.rbf(self.D) + GPy.kern.bias(self.D),
# GPy.kern.linear(self.D) + GPy.kern.bias(self.D) + GPy.kern.white(self.D),
# GPy.kern.rbf(self.D) + GPy.kern.bias(self.D) + GPy.kern.white(self.D),
# GPy.kern.bias(self.D), GPy.kern.white(self.D),
# (GPy.kern.rbf(self.input_dim, ARD=True) +
# GPy.kern.linear(self.input_dim, ARD=True) +
# GPy.kern.bias(self.input_dim) +
# GPy.kern.white(self.input_dim)),
(GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) +
GPy.kern.rbf(self.input_dim, np.random.rand(), np.random.rand(self.input_dim), ARD=True) +
GPy.kern.linear(self.input_dim, np.random.rand(self.input_dim), ARD=True) +
GPy.kern.bias(self.input_dim) +
GPy.kern.white(self.input_dim)),
# GPy.kern.rbf(self.input_dim), GPy.kern.rbf(self.input_dim, ARD=True),
# GPy.kern.linear(self.input_dim, ARD=False), GPy.kern.linear(self.input_dim, ARD=True),
# GPy.kern.linear(self.input_dim) + GPy.kern.bias(self.input_dim),
# GPy.kern.rbf(self.input_dim) + GPy.kern.bias(self.input_dim),
# GPy.kern.linear(self.input_dim) + GPy.kern.bias(self.input_dim) + GPy.kern.white(self.input_dim),
# GPy.kern.rbf(self.input_dim) + GPy.kern.bias(self.input_dim) + GPy.kern.white(self.input_dim),
# GPy.kern.bias(self.input_dim), GPy.kern.white(self.input_dim),
)
self.q_x_mean = np.random.randn(self.D)
self.q_x_variance = np.exp(np.random.randn(self.D))
self.q_x_samples = np.random.randn(self.Nsamples, self.D) * np.sqrt(self.q_x_variance) + self.q_x_mean
self.Z = np.random.randn(self.M, self.D)
self.q_x_mean.shape = (1, self.D)
self.q_x_variance.shape = (1, self.D)
self.q_x_mean = np.random.randn(self.input_dim)
self.q_x_variance = np.exp(np.random.randn(self.input_dim))
self.q_x_samples = np.random.randn(self.Nsamples, self.input_dim) * np.sqrt(self.q_x_variance) + self.q_x_mean
self.Z = np.random.randn(self.num_inducing, self.input_dim)
self.q_x_mean.shape = (1, self.input_dim)
self.q_x_variance.shape = (1, self.input_dim)
def test_psi0(self):
for kern in self.kerns:
@ -63,7 +63,7 @@ class Test(unittest.TestCase):
for kern in self.kerns:
Nsamples = 100
psi1 = kern.psi1(self.Z, self.q_x_mean, self.q_x_variance)
K_ = np.zeros((Nsamples, self.M))
K_ = np.zeros((Nsamples, self.num_inducing))
diffs = []
for i, q_x_sample_stripe in enumerate(np.array_split(self.q_x_samples, self.Nsamples / Nsamples)):
K = kern.K(q_x_sample_stripe, self.Z)
@ -89,7 +89,7 @@ class Test(unittest.TestCase):
for kern in self.kerns:
Nsamples = 100
psi2 = kern.psi2(self.Z, self.q_x_mean, self.q_x_variance)
K_ = np.zeros((self.M, self.M))
K_ = np.zeros((self.num_inducing, self.num_inducing))
diffs = []
for i, q_x_sample_stripe in enumerate(np.array_split(self.q_x_samples, self.Nsamples / Nsamples)):
K = kern.K(q_x_sample_stripe, self.Z)

46
GPy/testing/psi_stat_gradient_tests.py
View file

@ -17,14 +17,14 @@ class PsiStatModel(model):
self.X_variance = X_variance
self.Z = Z
self.N, self.input_dim = X.shape
self.M, input_dim = Z.shape
self.num_inducing, input_dim = Z.shape
assert self.input_dim == input_dim, "shape missmatch: Z:{!s} X:{!s}".format(Z.shape, X.shape)
self.kern = kernel
super(PsiStatModel, self).__init__()
self.psi_ = self.kern.__getattribute__(self.which)(self.Z, self.X, self.X_variance)
def _get_param_names(self):
Xnames = ["{}_{}_{}".format(what, i, j) for what, i, j in itertools.product(['X', 'X_variance'], range(self.N), range(self.input_dim))]
Znames = ["Z_{}_{}".format(i, j) for i, j in itertools.product(range(self.M), range(self.input_dim))]
Znames = ["Z_{}_{}".format(i, j) for i, j in itertools.product(range(self.num_inducing), range(self.input_dim))]
return Xnames + Znames + self.kern._get_param_names()
def _get_params(self):
return numpy.hstack([self.X.flatten(), self.X_variance.flatten(), self.Z.flatten(), self.kern._get_params()])
@ -34,7 +34,7 @@ class PsiStatModel(model):
start, end = end, end + self.X_variance.size
self.X_variance = x[start: end].reshape(self.N, self.input_dim)
start, end = end, end + self.Z.size
self.Z = x[start: end].reshape(self.M, self.input_dim)
self.Z = x[start: end].reshape(self.num_inducing, self.input_dim)
self.kern._set_params(x[end:])
def log_likelihood(self):
return self.kern.__getattribute__(self.which)(self.Z, self.X, self.X_variance).sum()
@ -43,19 +43,19 @@ class PsiStatModel(model):
try:
psiZ = self.kern.__getattribute__("d" + self.which + "_dZ")(numpy.ones_like(self.psi_), self.Z, self.X, self.X_variance)
except AttributeError:
psiZ = numpy.zeros(self.M * self.input_dim)
psiZ = numpy.zeros(self.num_inducing * self.input_dim)
thetagrad = self.kern.__getattribute__("d" + self.which + "_dtheta")(numpy.ones_like(self.psi_), self.Z, self.X, self.X_variance).flatten()
return numpy.hstack((psimu.flatten(), psiS.flatten(), psiZ.flatten(), thetagrad))
class DPsiStatTest(unittest.TestCase):
input_dim = 5
N = 50
M = 10
D = 20
num_inducing = 10
input_dim = 20
X = numpy.random.randn(N, input_dim)
X_var = .5 * numpy.ones_like(X) + .4 * numpy.clip(numpy.random.randn(*X.shape), 0, 1)
Z = numpy.random.permutation(X)[:M]
Y = X.dot(numpy.random.randn(input_dim, D))
Z = numpy.random.permutation(X)[:num_inducing]
Y = X.dot(numpy.random.randn(input_dim, input_dim))
# kernels = [GPy.kern.linear(input_dim, ARD=True, variances=numpy.random.rand(input_dim)), GPy.kern.rbf(input_dim, ARD=True), GPy.kern.bias(input_dim)]
kernels = [GPy.kern.linear(input_dim), GPy.kern.rbf(input_dim), GPy.kern.bias(input_dim),
@ -65,7 +65,7 @@ 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.M, kernel=k)
M=self.num_inducing, kernel=k)
try:
assert m.checkgrad(), "{} x psi0".format("+".join(map(lambda x: x.name, k.parts)))
except:
@ -80,27 +80,27 @@ class DPsiStatTest(unittest.TestCase):
def testPsi2_lin(self):
k = self.kernels[0]
m = PsiStatModel('psi2', X=self.X, X_variance=self.X_var, Z=self.Z,
M=self.M, kernel=k)
M=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.M, kernel=k)
M=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.M, kernel=k)
M=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.M, kernel=k)
M=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.M, kernel=k)
M=self.num_inducing, kernel=k)
assert m.checkgrad(), "{} x psi2".format("+".join(map(lambda x: x.name, k.parts)))
@ -108,14 +108,14 @@ if __name__ == "__main__":
import sys
interactive = 'i' in sys.argv
if interactive:
# N, M, input_dim, D = 30, 5, 4, 30
# N, num_inducing, input_dim, input_dim = 30, 5, 4, 30
# X = numpy.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 = numpy.random.multivariate_normal(numpy.zeros(N), K, D).T
# Y = numpy.random.multivariate_normal(numpy.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 = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel=k, M=M)
# m = GPy.models.Bayesian_GPLVM(Y, input_dim, kernel=k, num_inducing=num_inducing)
# m.ensure_default_constraints()
# m.randomize()
# # self.assertTrue(m.checkgrad())
@ -136,22 +136,22 @@ if __name__ == "__main__":
# for k in kernels:
# m = PsiStatModel('psi1', X=X, X_variance=X_var, Z=Z,
# M=M, kernel=k)
# num_inducing=num_inducing, kernel=k)
# assert m.checkgrad(), "{} x psi1".format("+".join(map(lambda x: x.name, k.parts)))
#
# m0 = PsiStatModel('psi0', X=X, X_variance=X_var, Z=Z,
# M=M, kernel=GPy.kern.linear(input_dim))
# num_inducing=num_inducing, kernel=GPy.kern.linear(input_dim))
# m1 = PsiStatModel('psi1', X=X, X_variance=X_var, Z=Z,
# M=M, kernel=kernel)
# num_inducing=num_inducing, kernel=kernel)
# m1 = PsiStatModel('psi1', X=X, X_variance=X_var, Z=Z,
# M=M, kernel=kernel)
# num_inducing=num_inducing, kernel=kernel)
# m2 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z,
# M=M, kernel=GPy.kern.rbf(input_dim))
# 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)))
m3.ensure_default_constraints()
# + GPy.kern.bias(input_dim))
# m4 = PsiStatModel('psi2', X=X, X_variance=X_var, Z=Z,
# M=M, kernel=GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim))
# num_inducing=num_inducing, kernel=GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim))
else:
unittest.main()

13
GPy/testing/sparse_gplvm_tests.py
View file

@ -4,6 +4,7 @@
import unittest
import numpy as np
import GPy
from GPy.models.sparse_gplvm import SparseGPLVM
class sparse_GPLVMTests(unittest.TestCase):
def test_bias_kern(self):
@ -11,9 +12,9 @@ class sparse_GPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.sparse_GPLVM(Y, input_dim, kernel = k, M=M)
m = SparseGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@ -24,9 +25,9 @@ class sparse_GPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.sparse_GPLVM(Y, input_dim, kernel = k, M=M)
m = SparseGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())
@ -36,9 +37,9 @@ class sparse_GPLVMTests(unittest.TestCase):
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,D).T
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 = GPy.models.sparse_GPLVM(Y, input_dim, kernel = k, M=M)
m = SparseGPLVM(Y, input_dim, kernel=k, M=M)
m.ensure_default_constraints()
m.randomize()
self.assertTrue(m.checkgrad())

143
GPy/testing/unit_tests.py
View file

@ -5,33 +5,33 @@
import unittest
import numpy as np
import GPy
from GPy.likelihoods.likelihood_functions import Binomial
class GradientTests(unittest.TestCase):
def setUp(self):
######################################
## 1 dimensional example
# # 1 dimensional example
# sample inputs and outputs
self.X1D = np.random.uniform(-3.,3.,(20,1))
self.Y1D = np.sin(self.X1D)+np.random.randn(20,1)*0.05
self.X1D = np.random.uniform(-3., 3., (20, 1))
self.Y1D = np.sin(self.X1D) + np.random.randn(20, 1) * 0.05
######################################
## 2 dimensional example
# # 2 dimensional example
# sample inputs and outputs
self.X2D = np.random.uniform(-3.,3.,(40,2))
self.Y2D = np.sin(self.X2D[:,0:1]) * np.sin(self.X2D[:,1:2])+np.random.randn(40,1)*0.05
self.X2D = np.random.uniform(-3., 3., (40, 2))
self.Y2D = np.sin(self.X2D[:, 0:1]) * np.sin(self.X2D[:, 1:2]) + np.random.randn(40, 1) * 0.05
def check_model_with_white(self, kern, model_type='GP_regression', dimension=1):
#Get the correct gradients
def check_model_with_white(self, kern, model_type='GPRegression', dimension=1):
# Get the correct gradients
if dimension == 1:
X = self.X1D
Y = self.Y1D
else:
X = self.X2D
Y = self.Y2D
#Get model type (GP_regression, GP_sparse_regression, etc)
# Get model type (GPRegression, SparseGPRegression, etc)
model_fit = getattr(GPy.models, model_type)
noise = GPy.kern.white(dimension)
@ -42,114 +42,114 @@ class GradientTests(unittest.TestCase):
# contrain all parameters to be positive
self.assertTrue(m.checkgrad())
def test_gp_regression_rbf_1d(self):
def test_GPRegression_rbf_1d(self):
''' Testing the GP regression with rbf kernel with white kernel on 1d data '''
rbf = GPy.kern.rbf(1)
self.check_model_with_white(rbf, model_type='GP_regression', dimension=1)
self.check_model_with_white(rbf, model_type='GPRegression', dimension=1)
def test_GP_regression_rbf_2D(self):
def test_GPRegression_rbf_2D(self):
''' Testing the GP regression with rbf and white kernel on 2d data '''
rbf = GPy.kern.rbf(2)
self.check_model_with_white(rbf, model_type='GP_regression', dimension=2)
self.check_model_with_white(rbf, model_type='GPRegression', dimension=2)
def test_GP_regression_rbf_ARD_2D(self):
def test_GPRegression_rbf_ARD_2D(self):
''' Testing the GP regression with rbf and white kernel on 2d data '''
k = GPy.kern.rbf(2,ARD=True)
self.check_model_with_white(k, model_type='GP_regression', dimension=2)
k = GPy.kern.rbf(2, ARD=True)
self.check_model_with_white(k, model_type='GPRegression', dimension=2)
def test_GP_regression_matern52_1D(self):
def test_GPRegression_matern52_1D(self):
''' Testing the GP regression with matern52 kernel on 1d data '''
matern52 = GPy.kern.Matern52(1)
self.check_model_with_white(matern52, model_type='GP_regression', dimension=1)
self.check_model_with_white(matern52, model_type='GPRegression', dimension=1)
def test_GP_regression_matern52_2D(self):
def test_GPRegression_matern52_2D(self):
''' Testing the GP regression with matern52 kernel on 2d data '''
matern52 = GPy.kern.Matern52(2)
self.check_model_with_white(matern52, model_type='GP_regression', dimension=2)
self.check_model_with_white(matern52, model_type='GPRegression', dimension=2)
def test_GP_regression_matern52_ARD_2D(self):
def test_GPRegression_matern52_ARD_2D(self):
''' Testing the GP regression with matern52 kernel on 2d data '''
matern52 = GPy.kern.Matern52(2,ARD=True)
self.check_model_with_white(matern52, model_type='GP_regression', dimension=2)
matern52 = GPy.kern.Matern52(2, ARD=True)
self.check_model_with_white(matern52, model_type='GPRegression', dimension=2)
def test_GP_regression_matern32_1D(self):
def test_GPRegression_matern32_1D(self):
''' Testing the GP regression with matern32 kernel on 1d data '''
matern32 = GPy.kern.Matern32(1)
self.check_model_with_white(matern32, model_type='GP_regression', dimension=1)
self.check_model_with_white(matern32, model_type='GPRegression', dimension=1)
def test_GP_regression_matern32_2D(self):
def test_GPRegression_matern32_2D(self):
''' Testing the GP regression with matern32 kernel on 2d data '''
matern32 = GPy.kern.Matern32(2)
self.check_model_with_white(matern32, model_type='GP_regression', dimension=2)
self.check_model_with_white(matern32, model_type='GPRegression', dimension=2)
def test_GP_regression_matern32_ARD_2D(self):
def test_GPRegression_matern32_ARD_2D(self):
''' Testing the GP regression with matern32 kernel on 2d data '''
matern32 = GPy.kern.Matern32(2,ARD=True)
self.check_model_with_white(matern32, model_type='GP_regression', dimension=2)
matern32 = GPy.kern.Matern32(2, ARD=True)
self.check_model_with_white(matern32, model_type='GPRegression', dimension=2)
def test_GP_regression_exponential_1D(self):
def test_GPRegression_exponential_1D(self):
''' Testing the GP regression with exponential kernel on 1d data '''
exponential = GPy.kern.exponential(1)
self.check_model_with_white(exponential, model_type='GP_regression', dimension=1)
self.check_model_with_white(exponential, model_type='GPRegression', dimension=1)
def test_GP_regression_exponential_2D(self):
def test_GPRegression_exponential_2D(self):
''' Testing the GP regression with exponential kernel on 2d data '''
exponential = GPy.kern.exponential(2)
self.check_model_with_white(exponential, model_type='GP_regression', dimension=2)
self.check_model_with_white(exponential, model_type='GPRegression', dimension=2)
def test_GP_regression_exponential_ARD_2D(self):
def test_GPRegression_exponential_ARD_2D(self):
''' Testing the GP regression with exponential kernel on 2d data '''
exponential = GPy.kern.exponential(2,ARD=True)
self.check_model_with_white(exponential, model_type='GP_regression', dimension=2)
exponential = GPy.kern.exponential(2, ARD=True)
self.check_model_with_white(exponential, model_type='GPRegression', dimension=2)
def test_GP_regression_bias_kern_1D(self):
def test_GPRegression_bias_kern_1D(self):
''' Testing the GP regression with bias kernel on 1d data '''
bias = GPy.kern.bias(1)
self.check_model_with_white(bias, model_type='GP_regression', dimension=1)
self.check_model_with_white(bias, model_type='GPRegression', dimension=1)
def test_GP_regression_bias_kern_2D(self):
def test_GPRegression_bias_kern_2D(self):
''' Testing the GP regression with bias kernel on 2d data '''
bias = GPy.kern.bias(2)
self.check_model_with_white(bias, model_type='GP_regression', dimension=2)
self.check_model_with_white(bias, model_type='GPRegression', dimension=2)
def test_GP_regression_linear_kern_1D_ARD(self):
def test_GPRegression_linear_kern_1D_ARD(self):
''' Testing the GP regression with linear kernel on 1d data '''
linear = GPy.kern.linear(1,ARD=True)
self.check_model_with_white(linear, model_type='GP_regression', dimension=1)
linear = GPy.kern.linear(1, ARD=True)
self.check_model_with_white(linear, model_type='GPRegression', dimension=1)
def test_GP_regression_linear_kern_2D_ARD(self):
def test_GPRegression_linear_kern_2D_ARD(self):
''' Testing the GP regression with linear kernel on 2d data '''
linear = GPy.kern.linear(2,ARD=True)
self.check_model_with_white(linear, model_type='GP_regression', dimension=2)
linear = GPy.kern.linear(2, ARD=True)
self.check_model_with_white(linear, model_type='GPRegression', dimension=2)
def test_GP_regression_linear_kern_1D(self):
def test_GPRegression_linear_kern_1D(self):
''' Testing the GP regression with linear kernel on 1d data '''
linear = GPy.kern.linear(1)
self.check_model_with_white(linear, model_type='GP_regression', dimension=1)
self.check_model_with_white(linear, model_type='GPRegression', dimension=1)
def test_GP_regression_linear_kern_2D(self):
def test_GPRegression_linear_kern_2D(self):
''' Testing the GP regression with linear kernel on 2d data '''
linear = GPy.kern.linear(2)
self.check_model_with_white(linear, model_type='GP_regression', dimension=2)
self.check_model_with_white(linear, model_type='GPRegression', dimension=2)
def test_sparse_GP_regression_rbf_white_kern_1d(self):
def test_SparseGPRegression_rbf_white_kern_1d(self):
''' Testing the sparse GP regression with rbf kernel with white kernel on 1d data '''
rbf = GPy.kern.rbf(1)
self.check_model_with_white(rbf, model_type='sparse_GP_regression', dimension=1)
self.check_model_with_white(rbf, model_type='SparseGPRegression', dimension=1)
def test_sparse_GP_regression_rbf_white_kern_2D(self):
def test_SparseGPRegression_rbf_white_kern_2D(self):
''' Testing the sparse GP regression with rbf and white kernel on 2d data '''
rbf = GPy.kern.rbf(2)
self.check_model_with_white(rbf, model_type='sparse_GP_regression', dimension=2)
self.check_model_with_white(rbf, model_type='SparseGPRegression', dimension=2)
def test_GPLVM_rbf_bias_white_kern_2D(self):
""" Testing GPLVM with rbf + bias and white kernel """
N, input_dim, D = 50, 1, 2
X = np.random.rand(N, input_dim)
k = GPy.kern.rbf(input_dim, 0.5, 0.9*np.ones((1,))) + GPy.kern.bias(input_dim, 0.1) + GPy.kern.white(input_dim, 0.05)
k = GPy.kern.rbf(input_dim, 0.5, 0.9 * np.ones((1,))) + GPy.kern.bias(input_dim, 0.1) + GPy.kern.white(input_dim, 0.05)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
m = GPy.models.GPLVM(Y, input_dim, kernel = k)
Y = np.random.multivariate_normal(np.zeros(N), K, input_dim).T
m = GPy.models.GPLVM(Y, input_dim, kernel=k)
m.ensure_default_constraints()
self.assertTrue(m.checkgrad())
@ -159,42 +159,43 @@ class GradientTests(unittest.TestCase):
X = np.random.rand(N, input_dim)
k = GPy.kern.linear(input_dim) + GPy.kern.bias(input_dim, 0.1) + GPy.kern.white(input_dim, 0.05)
K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N),K,D).T
m = GPy.models.GPLVM(Y, input_dim, init = 'PCA', kernel = k)
Y = np.random.multivariate_normal(np.zeros(N), K, input_dim).T
m = GPy.models.GPLVM(Y, input_dim, init='PCA', kernel=k)
m.ensure_default_constraints()
self.assertTrue(m.checkgrad())
def test_GP_EP_probit(self):
N = 20
X = np.hstack([np.random.normal(5,2,N/2),np.random.normal(10,2,N/2)])[:,None]
Y = np.hstack([np.ones(N/2),np.zeros(N/2)])[:,None]
X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None]
Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None]
kernel = GPy.kern.rbf(1)
distribution = GPy.likelihoods.likelihood_functions.binomial()
distribution = GPy.likelihoods.likelihood_functions.Binomial()
likelihood = GPy.likelihoods.EP(Y, distribution)
m = GPy.core.GP(X, likelihood, kernel)
m.ensure_default_constraints()
m.update_likelihood_approximation()
self.assertTrue(m.checkgrad())
#self.assertTrue(m.EPEM)
# self.assertTrue(m.EPEM)
def test_sparse_EP_DTC_probit(self):
N = 20
X = np.hstack([np.random.normal(5,2,N/2),np.random.normal(10,2,N/2)])[:,None]
Y = np.hstack([np.ones(N/2),np.zeros(N/2)])[:,None]
Z = np.linspace(0,15,4)[:,None]
X = np.hstack([np.random.normal(5, 2, N / 2), np.random.normal(10, 2, N / 2)])[:, None]
Y = np.hstack([np.ones(N / 2), np.zeros(N / 2)])[:, None]
Z = np.linspace(0, 15, 4)[:, None]
kernel = GPy.kern.rbf(1)
distribution = GPy.likelihoods.likelihood_functions.binomial()
distribution = GPy.likelihoods.likelihood_functions.Binomial()
likelihood = GPy.likelihoods.EP(Y, distribution)
m = GPy.core.sparse_GP(X, likelihood, kernel,Z)
m = GPy.core.SparseGP(X, likelihood, kernel, Z)
m.ensure_default_constraints()
m.update_likelihood_approximation()
self.assertTrue(m.checkgrad())
def test_generalized_FITC(self):
N = 20
X = np.hstack([np.random.rand(N/2)+1,np.random.rand(N/2)-1])[:,None]
X = np.hstack([np.random.rand(N / 2) + 1, np.random.rand(N / 2) - 1])[:, None]
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()
likelihood = GPy.likelihoods.EP(Y, distribution)
#likelihood = GPy.inference.likelihoods.binomial(Y)

2
GPy/util/datasets.py
View file

@ -13,7 +13,7 @@ default_seed = 10000
# Some general utilities.
def sample_class(f):
p = 1. / (1. + np.exp(-f))
c = np.random.binomial(1, p)
c = np.random.Binomial(1, p)
c = np.where(c, 1, -1)
return c

177
GPy/util/linalg.py
View file

@ -1,87 +1,80 @@
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
#tdot function courtesy of Ian Murray:
# tdot function courtesy of Ian Murray:
# Iain Murray, April 2013. iain contactable via iainmurray.net
# http://homepages.inf.ed.ac.uk/imurray2/code/tdot/tdot.py
import numpy as np
from scipy import linalg, optimize, weave
import pylab as pb
import Tango
import sys
import re
import pdb
import cPickle
from scipy import linalg, weave
import types
import ctypes
from ctypes import byref, c_char, c_int, c_double # TODO
#import scipy.lib.lapack
import scipy as sp
# import scipy.lib.lapack
try:
_blaslib = ctypes.cdll.LoadLibrary(np.core._dotblas.__file__)
_blaslib = ctypes.cdll.LoadLibrary(np.core._dotblas.__file__) # @UndefinedVariable
_blas_available = True
except:
_blas_available = False
def trace_dot(a,b):
def trace_dot(a, b):
"""
efficiently compute the trace of the matrix product of a and b
"""
return np.sum(a*b)
return np.sum(a * b)
def mdot(*args):
"""Multiply all the arguments using matrix product rules.
The output is equivalent to multiplying the arguments one by one
from left to right using dot().
Precedence can be controlled by creating tuples of arguments,
for instance mdot(a,((b,c),d)) multiplies a (a*((b*c)*d)).
Note that this means the output of dot(a,b) and mdot(a,b) will differ if
a or b is a pure tuple of numbers.
"""
if len(args)==1:
return args[0]
elif len(args)==2:
return _mdot_r(args[0],args[1])
else:
return _mdot_r(args[:-1],args[-1])
"""Multiply all the arguments using matrix product rules.
The output is equivalent to multiplying the arguments one by one
from left to right using dot().
Precedence can be controlled by creating tuples of arguments,
for instance mdot(a,((b,c),d)) multiplies a (a*((b*c)*d)).
Note that this means the output of dot(a,b) and mdot(a,b) will differ if
a or b is a pure tuple of numbers.
"""
if len(args) == 1:
return args[0]
elif len(args) == 2:
return _mdot_r(args[0], args[1])
else:
return _mdot_r(args[:-1], args[-1])
def _mdot_r(a,b):
"""Recursive helper for mdot"""
if type(a)==types.TupleType:
if len(a)>1:
a = mdot(*a)
else:
a = a[0]
if type(b)==types.TupleType:
if len(b)>1:
b = mdot(*b)
else:
b = b[0]
return np.dot(a,b)
def _mdot_r(a, b):
"""Recursive helper for mdot"""
if type(a) == types.TupleType:
if len(a) > 1:
a = mdot(*a)
else:
a = a[0]
if type(b) == types.TupleType:
if len(b) > 1:
b = mdot(*b)
else:
b = b[0]
return np.dot(a, b)
def jitchol(A,maxtries=5):
def jitchol(A, maxtries=5):
A = np.asfortranarray(A)
L,info = linalg.lapack.flapack.dpotrf(A,lower=1)
if info ==0:
L, info = linalg.lapack.flapack.dpotrf(A, lower=1)
if info == 0:
return L
else:
diagA = np.diag(A)
if np.any(diagA<0.):
if np.any(diagA < 0.):
raise linalg.LinAlgError, "not pd: negative diagonal elements"
jitter= diagA.mean()*1e-6
for i in range(1,maxtries+1):
jitter = diagA.mean() * 1e-6
for i in range(1, maxtries + 1):
print 'Warning: adding jitter of {:.10e}'.format(jitter)
try:
return linalg.cholesky(A+np.eye(A.shape[0]).T*jitter, lower = True)
return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True)
except:
jitter *= 10
raise linalg.LinAlgError,"not positive definite, even with jitter."
raise linalg.LinAlgError, "not positive definite, even with jitter."
def jitchol_old(A,maxtries=5):
def jitchol_old(A, maxtries=5):
"""
:param A : An almost pd square matrix
@ -93,20 +86,20 @@ def jitchol_old(A,maxtries=5):
np.allclose(sp.linalg.cholesky(XXT, lower = True), np.triu(sp.linalg.cho_factor(XXT)[0]).T)
"""
try:
return linalg.cholesky(A, lower = True)
return linalg.cholesky(A, lower=True)
except linalg.LinAlgError:
diagA = np.diag(A)
if np.any(diagA<0.):
if np.any(diagA < 0.):
raise linalg.LinAlgError, "not pd: negative diagonal elements"
jitter= diagA.mean()*1e-6
for i in range(1,maxtries+1):
jitter = diagA.mean() * 1e-6
for i in range(1, maxtries + 1):
print '\rWarning: adding jitter of {:.10e} '.format(jitter),
try:
return linalg.cholesky(A+np.eye(A.shape[0]).T*jitter, lower = True)
return linalg.cholesky(A + np.eye(A.shape[0]).T * jitter, lower=True)
except:
jitter *= 10
raise linalg.LinAlgError,"not positive definite, even with jitter."
raise linalg.LinAlgError, "not positive definite, even with jitter."
def pdinv(A, *args):
"""
@ -125,7 +118,7 @@ def pdinv(A, *args):
logdet = 2.*np.sum(np.log(np.diag(L)))
Li = chol_inv(L)
Ai, _ = linalg.lapack.flapack.dpotri(L)
#Ai = np.tril(Ai) + np.tril(Ai,-1).T
# Ai = np.tril(Ai) + np.tril(Ai,-1).T
symmetrify(Ai)
return Ai, L, Li, logdet
@ -140,7 +133,7 @@ def chol_inv(L):
"""
return linalg.lapack.flapack.dtrtri(L, lower = True)[0]
return linalg.lapack.flapack.dtrtri(L, lower=True)[0]
def multiple_pdinv(A):
@ -155,11 +148,11 @@ def multiple_pdinv(A):
hld: 0.5* the log of the determinants of A
"""
N = A.shape[-1]
chols = [jitchol(A[:,:,i]) for i in range(N)]
chols = [jitchol(A[:, :, i]) for i in range(N)]
halflogdets = [np.sum(np.log(np.diag(L[0]))) for L in chols]
invs = [linalg.lapack.flapack.dpotri(L[0],True)[0] for L in chols]
invs = [np.triu(I)+np.triu(I,1).T for I in invs]
return np.dstack(invs),np.array(halflogdets)
invs = [linalg.lapack.flapack.dpotri(L[0], True)[0] for L in chols]
invs = [np.triu(I) + np.triu(I, 1).T for I in invs]
return np.dstack(invs), np.array(halflogdets)
def PCA(Y, input_dim):
@ -179,18 +172,18 @@ def PCA(Y, input_dim):
if not np.allclose(Y.mean(axis=0), 0.0):
print "Y is not zero mean, centering it locally (GPy.util.linalg.PCA)"
#Y -= Y.mean(axis=0)
# Y -= Y.mean(axis=0)
Z = linalg.svd(Y-Y.mean(axis=0), full_matrices = False)
[X, W] = [Z[0][:,0:input_dim], np.dot(np.diag(Z[1]), Z[2]).T[:,0:input_dim]]
Z = linalg.svd(Y - Y.mean(axis=0), full_matrices=False)
[X, W] = [Z[0][:, 0:input_dim], np.dot(np.diag(Z[1]), Z[2]).T[:, 0:input_dim]]
v = X.std(axis=0)
X /= v;
W *= v;
return X, W.T
def tdot_numpy(mat,out=None):
return np.dot(mat,mat.T,out)
def tdot_numpy(mat, out=None):
return np.dot(mat, mat.T, out)
def tdot_blas(mat, out=None):
"""returns np.dot(mat, mat.T), but faster for large 2D arrays of doubles."""
@ -198,16 +191,16 @@ def tdot_blas(mat, out=None):
return np.dot(mat, mat.T)
nn = mat.shape[0]
if out is None:
out = np.zeros((nn,nn))
out = np.zeros((nn, nn))
else:
assert(out.dtype == 'float64')
assert(out.shape == (nn,nn))
assert(out.shape == (nn, nn))
# FIXME: should allow non-contiguous out, and copy output into it:
assert(8 in out.strides)
# zeroing needed because of dumb way I copy across triangular answer
out[:] = 0.0
## Call to DSYRK from BLAS
# # Call to DSYRK from BLAS
# If already in Fortran order (rare), and has the right sorts of strides I
# could avoid the copy. I also thought swapping to cblas API would allow use
# of C order. However, I tried that and had errors with large matrices:
@ -226,17 +219,17 @@ def tdot_blas(mat, out=None):
_blaslib.dsyrk_(byref(UPLO), byref(TRANS), byref(N), byref(K),
byref(ALPHA), A, byref(LDA), byref(BETA), C, byref(LDC))
symmetrify(out,upper=True)
symmetrify(out, upper=True)
return out
def tdot(*args, **kwargs):
if _blas_available:
return tdot_blas(*args,**kwargs)
return tdot_blas(*args, **kwargs)
else:
return tdot_numpy(*args,**kwargs)
return tdot_numpy(*args, **kwargs)
def DSYR_blas(A,x,alpha=1.):
def DSYR_blas(A, x, alpha=1.):
"""
Performs a symmetric rank-1 update operation:
A <- A + alpha * np.dot(x,x.T)
@ -256,9 +249,9 @@ def DSYR_blas(A,x,alpha=1.):
INCX = c_int(1)
_blaslib.dsyr_(byref(UPLO), byref(N), byref(ALPHA),
x_, byref(INCX), A_, byref(LDA))
symmetrify(A,upper=True)
symmetrify(A, upper=True)
def DSYR_numpy(A,x,alpha=1.):
def DSYR_numpy(A, x, alpha=1.):
"""
Performs a symmetric rank-1 update operation:
A <- A + alpha * np.dot(x,x.T)
@ -269,23 +262,23 @@ def DSYR_numpy(A,x,alpha=1.):
:param x: Nx1 np.array
:param alpha: scalar
"""
A += alpha*np.dot(x[:,None],x[None,:])
A += alpha * np.dot(x[:, None], x[None, :])
def DSYR(*args, **kwargs):
if _blas_available:
return DSYR_blas(*args,**kwargs)
return DSYR_blas(*args, **kwargs)
else:
return DSYR_numpy(*args,**kwargs)
return DSYR_numpy(*args, **kwargs)
def symmetrify(A,upper=False):
def symmetrify(A, upper=False):
"""
Take the square matrix A and make it symmetrical by copting elements from the lower half to the upper
works IN PLACE.
"""
N,M = A.shape
assert N==M
N, M = A.shape
assert N == M
c_contig_code = """
int iN;
for (int i=1; i<N; i++){
@ -305,13 +298,13 @@ def symmetrify(A,upper=False):
}
"""
if A.flags['C_CONTIGUOUS'] and upper:
weave.inline(f_contig_code,['A','N'], extra_compile_args=['-O3'])
weave.inline(f_contig_code, ['A', 'N'], extra_compile_args=['-O3'])
elif A.flags['C_CONTIGUOUS'] and not upper:
weave.inline(c_contig_code,['A','N'], extra_compile_args=['-O3'])
weave.inline(c_contig_code, ['A', 'N'], extra_compile_args=['-O3'])
elif A.flags['F_CONTIGUOUS'] and upper:
weave.inline(c_contig_code,['A','N'], extra_compile_args=['-O3'])
weave.inline(c_contig_code, ['A', 'N'], extra_compile_args=['-O3'])
elif A.flags['F_CONTIGUOUS'] and not upper:
weave.inline(f_contig_code,['A','N'], extra_compile_args=['-O3'])
weave.inline(f_contig_code, ['A', 'N'], extra_compile_args=['-O3'])
else:
if upper:
tmp = np.tril(A.T)
@ -319,15 +312,15 @@ def symmetrify(A,upper=False):
tmp = np.tril(A)
A[:] = 0.0
A += tmp
A += np.tril(tmp,-1).T
A += np.tril(tmp, -1).T
def symmetrify_murray(A):
A += A.T
nn = A.shape[0]
A[[range(nn),range(nn)]] /= 2.0
A[[range(nn), range(nn)]] /= 2.0
def cholupdate(L,x):
def cholupdate(L, x):
"""
update the LOWER cholesky factor of a pd matrix IN PLACE
@ -337,7 +330,7 @@ def cholupdate(L,x):
support_code = """
#include <math.h>
"""
code="""
code = """
double r,c,s;
int j,i;
for(j=0; j<N; j++){
@ -353,11 +346,11 @@ def cholupdate(L,x):
"""
x = x.copy()
N = x.size
weave.inline(code, support_code=support_code, arg_names=['N','L','x'], type_converters=weave.converters.blitz)
weave.inline(code, support_code=support_code, arg_names=['N', 'L', 'x'], type_converters=weave.converters.blitz)
def backsub_both_sides(L, X,transpose='left'):
def backsub_both_sides(L, X, transpose='left'):
""" Return L^-T * X * L^-1, assumuing X is symmetrical and L is lower cholesky"""
if transpose=='left':
if transpose == 'left':
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
else:

2
GPy/util/visualize.py
View file

@ -221,7 +221,7 @@ class image_show(data_show):
if not self.palette == []: # Can just show the image (self.set_image() took care of setting the palette)
self.handle = self.axes.imshow(self.vals, interpolation='nearest')
else: # Use a boring gray map.
self.handle = self.axes.imshow(self.vals, cmap=plt.cm.gray, interpolation='nearest')
self.handle = self.axes.imshow(self.vals, cmap=plt.cm.gray, interpolation='nearest') # @UndefinedVariable
plt.show()
def modify(self, vals):