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James Hensman 2014-03-18 12:32:03 +00:00
commit 02872b66bd
10 changed files with 185 additions and 46 deletions
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7
GPy/core/sparse_gp.py
View file

@ -31,7 +31,7 @@ class SparseGP(GP):
"""
def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp'):
def __init__(self, X, Y, Z, kernel, likelihood, inference_method=None, name='sparse gp', Y_metadata=None):
#pick a sensible inference method
if inference_method is None:
@ -45,7 +45,7 @@ class SparseGP(GP):
self.Z = Param('inducing inputs', Z)
self.num_inducing = Z.shape[0]
GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name)
GP.__init__(self, X, Y, kernel, likelihood, inference_method=inference_method, name=name, Y_metadata=Y_metadata)
self.add_parameter(self.Z, index=0)
@ -53,7 +53,7 @@ class SparseGP(GP):
return isinstance(self.X, VariationalPosterior)
def parameters_changed(self):
self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y)
self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.Z, self.likelihood, self.Y, self.Y_metadata)
self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
if isinstance(self.X, VariationalPosterior):
#gradients wrt kernel
@ -75,7 +75,6 @@ class SparseGP(GP):
target += self.kern.gradient
self.kern.update_gradients_full(self.grad_dict['dL_dKmm'], self.Z, None)
self.kern.gradient += target
#gradients wrt Z
self.Z.gradient[:,self.kern.active_dims] = self.kern.gradients_X(self.grad_dict['dL_dKmm'], self.Z)
self.Z.gradient[:,self.kern.active_dims] += self.kern.gradients_X(self.grad_dict['dL_dKnm'].T, self.Z, self.X)

50
GPy/examples/coreg_example.py
View file

@ -2,6 +2,55 @@ import numpy as np
import pylab as pb
import GPy
pb.ion()
pb.close('all')
X1 = np.arange(3)[:,None]
X2 = np.arange(4)[:,None]
I1 = np.zeros_like(X1)
I2 = np.ones_like(X2)
_X = np.vstack([ X1, X2 ])
_I = np.vstack([ I1, I2 ])
X = np.hstack([ _X, _I ])
Y1 = np.sin(X1/8.)
Y2 = np.cos(X2/8.)
Bias = GPy.kern.Bias(1,active_dims=[0])
Coreg = GPy.kern.Coregionalize(1,2,active_dims=[1])
K = Bias.prod(Coreg,name='X')
#K.coregion.W = 0
#print K.coregion.W
#print Bias.K(_X,_X)
#print K.K(X,X)
#pb.matshow(K.K(X,X))
Mlist = [GPy.kern.Matern32(1,lengthscale=20.,name="Mat")]
kern = GPy.util.multioutput.LCM(input_dim=1,num_outputs=2,kernels_list=Mlist,name='H')
kern.B.W = 0
kern.B.kappa = 1.
#kern.B.W.fix()
#kern.B.kappa.fix()
#m = GPy.models.GPCoregionalizedRegression(X_list=[X1,X2], Y_list=[Y1,Y2], kernel=kern)
m = GPy.models.SparseGPCoregionalizedRegression(X_list=[X1], Y_list=[Y1], kernel=kern)
#m.optimize()
m.checkgrad(verbose=1)
fig = pb.figure()
ax0 = fig.add_subplot(211)
ax1 = fig.add_subplot(212)
slices = GPy.util.multioutput.get_slices([Y1,Y2])
m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],ax=ax0)
#m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],ax=ax1)
"""
X1 = 100 * np.random.rand(100)[:,None]
X2 = 100 * np.random.rand(100)[:,None]
@ -28,3 +77,4 @@ slices = GPy.util.multioutput.get_slices([Y1,Y2])
m.plot(fixed_inputs=[(1,0)],which_data_rows=slices[0],ax=ax0)
m.plot(fixed_inputs=[(1,1)],which_data_rows=slices[1],ax=ax1)
"""

30
GPy/inference/latent_function_inference/dtc.py
View file

@ -91,8 +91,12 @@ class vDTC(object):
def __init__(self):
self.const_jitter = 1e-6
def inference(self, kern, X, Z, likelihood, Y):
#assert X_variance is None, "cannot use X_variance with DTC. Try varDTC."
def inference(self, kern, X, X_variance, Z, likelihood, Y):
assert X_variance is None, "cannot use X_variance with DTC. Try varDTC."
#TODO: MAX! fix this!
from ...util.misc import param_to_array
Y = param_to_array(Y)
num_inducing, _ = Z.shape
num_data, output_dim = Y.shape
@ -105,14 +109,15 @@ class vDTC(object):
Kmm = kern.K(Z)
Knn = kern.Kdiag(X)
Knm = kern.K(X, Z)
KnmY = np.dot(Knm.T,Y)
U = Knm
Uy = np.dot(U.T,Y)
#factor Kmm
Kmmi, L, Li, _ = pdinv(Kmm)
# Compute A
LiKmnbeta = np.dot(Li, Knm.T)*np.sqrt(beta)
A_ = tdot(LiKmnbeta)
LiUTbeta = np.dot(Li, U.T)*np.sqrt(beta)
A_ = tdot(LiUTbeta)
trace_term = -0.5*(np.sum(Knn)*beta - np.trace(A_))
A = A_ + np.eye(num_inducing)
@ -120,7 +125,7 @@ class vDTC(object):
LA = jitchol(A)
# back substutue to get b, P, v
tmp, _ = dtrtrs(L, KnmY, lower=1)
tmp, _ = dtrtrs(L, Uy, lower=1)
b, _ = dtrtrs(LA, tmp*beta, lower=1)
tmp, _ = dtrtrs(LA, b, lower=1, trans=1)
v, _ = dtrtrs(L, tmp, lower=1, trans=1)
@ -140,18 +145,19 @@ class vDTC(object):
LAL = Li.T.dot(A).dot(Li)
dL_dK = Kmmi - 0.5*(vvT_P + LAL)
# Compute dL_dKnm
# Compute dL_dU
vY = np.dot(v.reshape(-1,1),Y.T)
dL_dKmn = vY - np.dot(vvT_P - Kmmi, Knm.T)
dL_dKmn *= beta
#dL_dU = vY - np.dot(vvT_P, U.T)
dL_dU = vY - np.dot(vvT_P - Kmmi, U.T)
dL_dU *= beta
#compute dL_dR
Knmv = np.dot(Knm, v)
dL_dR = 0.5*(np.sum(Knm*np.dot(Knm,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Knmv*Y, 1) + np.sum(np.square(Knmv), 1) )*beta**2
Uv = np.dot(U, v)
dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - 1./beta + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) + np.sum(np.square(Uv), 1) )*beta**2
dL_dR -=beta*trace_term/num_data
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*beta, 'dL_dKnm':dL_dKmn.T, 'dL_dthetaL':dL_dthetaL}
grad_dict = {'dL_dKmm': dL_dK, 'dL_dKdiag':np.zeros_like(Knn) + -0.5*beta, 'dL_dKnm':dL_dU.T, 'dL_dthetaL':dL_dthetaL}
#construct a posterior object
post = Posterior(woodbury_inv=Kmmi-P, woodbury_vector=v, K=Kmm, mean=None, cov=None, K_chol=L)

2
GPy/inference/latent_function_inference/exact_gaussian_inference.py
View file

@ -52,6 +52,6 @@ class ExactGaussianInference(object):
dL_dK = 0.5 * (tdot(alpha) - Y.shape[1] * Wi)
dL_dthetaL = likelihood.exact_inference_gradients(np.diag(dL_dK))
dL_dthetaL = likelihood.exact_inference_gradients(np.diag(dL_dK),Y_metadata)
return Posterior(woodbury_chol=LW, woodbury_vector=alpha, K=K), log_marginal, {'dL_dK':dL_dK, 'dL_dthetaL':dL_dthetaL}

31
GPy/inference/latent_function_inference/var_dtc.py
View file

@ -2,7 +2,7 @@
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from posterior import Posterior
from ...util.linalg import jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify
from ...util.linalg import mdot, jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify
from ...util import diag
from ...core.parameterization.variational import VariationalPosterior
import numpy as np
@ -74,7 +74,7 @@ class VarDTC(object):
trYYT = self.get_trYYT(Y)
# do the inference:
het_noise = beta.size < 1
het_noise = beta.size > 1
num_inducing = Z.shape[0]
num_data = Y.shape[0]
# kernel computations, using BGPLVM notation
@ -134,16 +134,16 @@ class VarDTC(object):
# log marginal likelihood
log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise,
psi0, A, LB, trYYT, data_fit)
psi0, A, LB, trYYT, data_fit, Y)
#put the gradients in the right places
dL_dR = _compute_dL_dR(likelihood,
het_noise, uncertain_inputs, LB,
_LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
psi0, psi1, beta,
data_fit, num_data, output_dim, trYYT)
data_fit, num_data, output_dim, trYYT, Y)
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR)
dL_dthetaL = likelihood.exact_inference_gradients(dL_dR,Y_metadata)
if uncertain_inputs:
grad_dict = {'dL_dKmm': dL_dKmm,
@ -387,7 +387,7 @@ def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, C
return dL_dpsi0, dL_dpsi1, dL_dpsi2
def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT):
def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT, Y):
# the partial derivative vector for the likelihood
if likelihood.size == 0:
# save computation here.
@ -396,19 +396,20 @@ def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf,
if uncertain_inputs:
raise NotImplementedError, "heteroscedatic derivates with uncertain inputs not implemented"
else:
from ...util.linalg import chol_inv
LBi = chol_inv(LB)
#from ...util.linalg import chol_inv
#LBi = chol_inv(LB)
LBi, _ = dtrtrs(LB,np.eye(LB.shape[0]))
Lmi_psi1, nil = dtrtrs(Lm, psi1.T, lower=1, trans=0)
_LBi_Lmi_psi1, _ = dtrtrs(LB, Lmi_psi1, lower=1, trans=0)
dL_dR = -0.5 * beta + 0.5 * likelihood.V**2
dL_dR = -0.5 * beta + 0.5 * (beta*Y)**2
dL_dR += 0.5 * output_dim * (psi0 - np.sum(Lmi_psi1**2,0))[:,None] * beta**2
dL_dR += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*beta**2
dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * likelihood.Y * beta**2
dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * Y * beta**2
dL_dR += 0.5*np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * beta**2
else:
# likelihood is not heteroscedatic
dL_dR = -0.5 * num_data * output_dim * beta + 0.5 * trYYT * beta ** 2
@ -416,11 +417,11 @@ def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf,
dL_dR += beta * (0.5 * np.sum(A * DBi_plus_BiPBi) - data_fit)
return dL_dR
def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit):
#compute log marginal likelihood
def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit,Y):
#compute log marginal likelihood
if het_noise:
lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(likelihood.V * likelihood.Y)
lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A))
lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(beta * Y**2)
lik_2 = -0.5 * output_dim * (np.sum(beta.flatten() * psi0) - np.trace(A))
else:
lik_1 = -0.5 * num_data * output_dim * (np.log(2. * np.pi) - np.log(beta)) - 0.5 * beta * trYYT
lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A))

6
GPy/likelihoods/gaussian.py
View file

@ -50,7 +50,11 @@ class Gaussian(Likelihood):
if isinstance(gp_link, link_functions.Identity):
self.log_concave = True
def gaussian_variance(self, Y, Y_metadata=None):
def betaY(self,Y,Y_metadata=None):
#TODO: ~Ricardo this does not live here
return Y/self.gaussian_variance(Y_metadata)
def gaussian_variance(self, Y_metadata=None):
return self.variance
def update_gradients(self, grad):

30
GPy/likelihoods/mixed_noise.py
View file

@ -18,6 +18,17 @@ class MixedNoise(Likelihood):
self.likelihoods_list = likelihoods_list
self.log_concave = False
def gaussian_variance(self, Y_metadata):
assert all([isinstance(l, Gaussian) for l in self.likelihoods_list])
ind = Y_metadata['output_index'].flatten()
variance = np.zeros(ind.size)
for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))):
variance[ind==j] = lik.variance
return variance[:,None]
def betaY(self,Y,Y_metadata):
return Y/self.gaussian_variance(Y_metadata=Y_metadata)
def update_gradients(self, gradients):
self.gradient = gradients
@ -32,13 +43,9 @@ class MixedNoise(Likelihood):
_variance = np.array([self.likelihoods_list[j].variance for j in ind ])
if full_cov:
var += np.eye(var.shape[0])*_variance
#d = 2*np.sqrt(np.diag(var))
#low, up = mu - d, mu + d
else:
var += _variance
#d = 2*np.sqrt(var)
#low, up = mu - d, mu + d
return mu, var#, low, up
return mu, var
else:
raise NotImplementedError
@ -51,12 +58,13 @@ class MixedNoise(Likelihood):
def covariance_matrix(self, Y, Y_metadata):
assert all([isinstance(l, Gaussian) for l in self.likelihoods_list])
ind = Y_metadata['output_index'].flatten()
variance = np.zeros(Y.shape[0])
for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))):
variance[ind==j] = lik.variance
return np.diag(variance)
#assert all([isinstance(l, Gaussian) for l in self.likelihoods_list])
#ind = Y_metadata['output_index'].flatten()
#variance = np.zeros(Y.shape[0])
#for lik, j in zip(self.likelihoods_list, range(len(self.likelihoods_list))):
# variance[ind==j] = lik.variance
#return np.diag(variance)
return np.diag(self.gaussian_variance(Y_metadata).flatten())
def samples(self, gp, Y_metadata):

1
GPy/models/__init__.py
View file

@ -15,4 +15,5 @@ from mrd import MRD
from gradient_checker import GradientChecker
from ss_gplvm import SSGPLVM
from gp_coregionalized_regression import GPCoregionalizedRegression
from sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression
#.py file not included!!! #from sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression

66
GPy/models/sparse_gp_coregionalized_regression.py Normal file
View file

@ -0,0 +1,66 @@
# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt)
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from ..core import SparseGP
from ..inference.latent_function_inference import VarDTC
from .. import likelihoods
from .. import kern
from .. import util
class SparseGPCoregionalizedRegression(SparseGP):
"""
Sparse Gaussian Process model for heteroscedastic multioutput regression
This is a thin wrapper around the SparseGP class, with a set of sensible defaults
:param X_list: list of input observations corresponding to each output
:type X_list: list of numpy arrays
:param Y_list: list of observed values related to the different noise models
:type Y_list: list of numpy arrays
:param Z_list: list of inducing inputs (optional)
:type Z_list: empty list | list of numpy arrays
:param kernel: a GPy kernel, defaults to RBF ** Coregionalized
:type kernel: None | GPy.kernel defaults
:likelihoods_list: a list of likelihoods, defaults to list of Gaussian likelihoods
:type likelihoods_list: None | a list GPy.likelihoods
:param num_inducing: number of inducing inputs, defaults to 10 per output (ignored if Z_list is not empty)
:type num_inducing: integer | list of integers
:param name: model name
:type name: string
:param W_rank: number tuples of the corregionalization parameters 'W' (see coregionalize kernel documentation)
:type W_rank: integer
:param kernel_name: name of the kernel
:type kernel_name: string
"""
def __init__(self, X_list, Y_list, Z_list=[], kernel=None, likelihoods_list=None, num_inducing=10, X_variance=None, name='SGPCR',W_rank=1,kernel_name='X'):
#Input and Output
X,Y,self.output_index = util.multioutput.build_XY(X_list,Y_list)
Ny = len(Y_list)
#Kernel
if kernel is None:
kernel = util.multioutput.ICM(input_dim=X.shape[1]-1, num_outputs=Ny, kernel=GPy.kern.rbf(X.shape[1]-1), W_rank=1,name=kernel_name)
#Likelihood
likelihood = util.multioutput.build_likelihood(Y_list,self.output_index,likelihoods_list)
#Inducing inputs list
if len(Z_list):
assert len(Z_list) == self.output_dim, 'Number of outputs do not match length of inducing inputs list.'
else:
if isinstance(num_inducing,np.int):
num_inducing = [num_inducing] * Ny
num_inducing = np.asarray(num_inducing)
assert num_inducing.size == Ny, 'Number of outputs do not match length of inducing inputs list.'
for ni,Xi in zip(num_inducing,X_list):
i = np.random.permutation(Xi.shape[0])[:ni]
Z_list.append(Xi[i].copy())
Z, _, Iz = util.multioutput.build_XY(Z_list)
super(SparseGPCoregionalizedRegression, self).__init__(X, Y, Z, kernel, likelihood, inference_method=VarDTC(), Y_metadata={'output_index':self.output_index})
self['.*inducing'][:,-1].fix()

6
GPy/plotting/matplot_dep/models_plots.py
View file

@ -7,6 +7,7 @@ import Tango
from base_plots import gpplot, x_frame1D, x_frame2D
from ...util.misc import param_to_array
from ...models.gp_coregionalized_regression import GPCoregionalizedRegression
from ...models.sparse_gp_coregionalized_regression import SparseGPCoregionalizedRegression
def plot_fit(model, plot_limits=None, which_data_rows='all',
@ -86,7 +87,10 @@ def plot_fit(model, plot_limits=None, which_data_rows='all',
lower = m - 2*np.sqrt(v)
upper = m + 2*np.sqrt(v)
else:
meta = {'output_index': Xgrid[:,-1:].astype(np.int)} if isinstance(model,GPCoregionalizedRegression) else None
if isinstance(model,GPCoregionalizedRegression) or isinstance(model,SparseGPCoregionalizedRegression):
meta = {'output_index': Xgrid[:,-1:].astype(np.int)}
else:
meta = None
m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta)
lower, upper = model.predict_quantiles(Xgrid, Y_metadata=meta)