swh:1:snp:636001a7d28e32091113da06cec462052713b3b6
Tip revision: ce5ad7ea75687fb0bf178b25f62855fc861eb10f authored by Artem Artemev on 11 November 2017, 18:24:39 UTC
Merge pull request #546 from GPflow/release/0.5
Merge pull request #546 from GPflow/release/0.5
Tip revision: ce5ad7e
test_variational.py
# Copyright 2016 the GPflow authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.from __future__ import print_function
import gpflow
import tensorflow as tf
import numpy as np
import unittest
from .reference import referenceRbfKernel
from testing.gpflow_testcase import GPflowTestCase
def referenceUnivariateLogMarginalLikelihood(y, K, noiseVariance):
return (-0.5 * y * y / (K + noiseVariance)
-0.5 * np.log(K + noiseVariance)
-0.5 * np.log(np.pi * 2.))
def referenceUnivariatePosterior(y, K, noiseVariance):
mean = K * y / (K + noiseVariance)
variance = K - K / (K + noiseVariance)
return mean, variance
def referenceUnivariatePriorKL(meanA, meanB, varA, varB):
# KL[ qA | qB ] = E_{qA} \log [qA / qB] where qA and qB are univariate normal distributions.
return (0.5 * (np.log(varB) - np.log(varA) - 1. + varA/varB +
(meanB-meanA) * (meanB - meanA) / varB))
def referenceMultivariatePriorKL(meanA, covA, meanB, covB):
# KL[ qA | qB ] = E_{qA} \log [qA / qB] where qA and aB are
# K dimensional multivariate normal distributions.
# Analytically tractable and equal to...
# 0.5 * (Tr(covB^{-1} covA) + (meanB - meanA)^T covB^{-1} (meanB - meanA)
# - K + log(det(covB)) - log (det(covA)))
K = covA.shape[0]
traceTerm = 0.5 * np.trace(np.linalg.solve(covB, covA))
delta = meanB - meanA
mahalanobisTerm = 0.5 * np.dot(delta.T, np.linalg.solve(covB, delta))
constantTerm = -0.5 * K
priorLogDeterminantTerm = 0.5*np.linalg.slogdet(covB)[1]
variationalLogDeterminantTerm = -0.5 * np.linalg.slogdet(covA)[1]
return traceTerm + mahalanobisTerm + constantTerm + priorLogDeterminantTerm + variationalLogDeterminantTerm
def kernel(kernelVariance=1, lengthScale=1.):
kern = gpflow.kernels.RBF(1)
kern.variance = kernelVariance
kern.lengthscales = lengthScale
return kern
class VariationalUnivariateTest(GPflowTestCase):
def setUp(self):
self.y_real = 2.
self.K = 1.
self.noiseVariance = 0.5
self.univariate = 1
self.oneLatentFunction = 1
self.meanZero = 0.
self.X = np.atleast_2d(np.array([0.]))
self.Y = np.atleast_2d(np.array([self.y_real]))
self.Z = self.X.copy()
self.lik = gpflow.likelihoods.Gaussian()
self.lik.variance = self.noiseVariance
self.posteriorMean, self.posteriorVariance = referenceUnivariatePosterior(
y=self.y_real, K=self.K,
noiseVariance=self.noiseVariance)
self.posteriorStd = np.sqrt(self.posteriorVariance)
def get_model(self, is_diagonal, is_whitened):
m = gpflow.svgp.SVGP(X=self.X, Y=self.Y,
kern=kernel(kernelVariance=self.K),
likelihood=self.lik, Z=self.Z, q_diag=is_diagonal, whiten=is_whitened)
if is_diagonal:
m.q_sqrt = (np.ones((self.univariate, self.oneLatentFunction))
* self.posteriorStd)
else:
m.q_sqrt = (np.ones((self.univariate, self.univariate, self.oneLatentFunction))
* self.posteriorStd)
m.q_mu = np.ones((self.univariate, self.oneLatentFunction)) * self.posteriorMean
return m
def test_prior_KL(self):
with self.test_session():
meanA = self.posteriorMean
varA = self.posteriorVariance
meanB = self.meanZero # Assumes a zero
varB = self.K
referenceKL = referenceUnivariatePriorKL(meanA, meanB, varA, varB)
for is_diagonal in [True, False]:
for is_whitened in [True, False]:
m = self.get_model(is_diagonal, is_whitened)
test_prior_KL = gpflow.param.AutoFlow()(m.build_prior_KL.__func__)(m)
self.assertTrue(np.abs(referenceKL - test_prior_KL) < 1e-4)
def test_build_likelihood(self):
with self.test_session():
# reference marginal likelihood
log_marginal_likelihood = referenceUnivariateLogMarginalLikelihood(
y=self.y_real, K=self.K, noiseVariance=self.noiseVariance)
for is_diagonal in [True, False]:
for is_whitened in [True, False]:
model = self.get_model(is_diagonal, is_whitened)
model_likelihood = model.compute_log_likelihood()
self.assertTrue(
np.abs(model_likelihood - log_marginal_likelihood) < 1e-4)
def testUnivariateConditionals(self):
with self.test_session() as sess:
for is_diagonal in [True, False]:
for is_whitened in [True, False]:
m = self.get_model(is_diagonal, is_whitened)
free_vars = tf.placeholder(tf.float64)
m.make_tf_array(free_vars)
with m.tf_mode():
if is_whitened:
args = (self.X,
self.Z,
m.kern,
m.q_mu,
m.q_sqrt,
self.oneLatentFunction)
fmean_func, fvar_func = gpflow.conditionals.gaussian_gp_predict_whitened(*args)
else:
args = (self.X,
self.Z,
m.kern,
m.q_mu,
m.q_sqrt,
self.oneLatentFunction)
fmean_func, fvar_func = gpflow.conditionals.gaussian_gp_predict(*args)
mean_value = fmean_func.eval(
session=sess, feed_dict={free_vars: m.get_free_state()})[0, 0]
var_value = fvar_func.eval(
session=sess, feed_dict={free_vars: m.get_free_state()})[0, 0]
self.assertTrue(np.abs(mean_value - self.posteriorMean) < 1e-4)
self.assertTrue(np.abs(var_value - self.posteriorVariance) < 1e-4)
class VariationalMultivariateTest(GPflowTestCase):
def setUp(self):
self.nDimensions = 3
self.rng = np.random.RandomState(1)
self.Y = self.rng.randn(self.nDimensions, 1)
self.X = self.rng.randn(self.nDimensions, 1)
self.Z = self.X.copy()
self.noiseVariance = 0.5
self.signalVariance = 1.5
self.lengthScale = 1.7
self.oneLatentFunction = 1
self.lik = gpflow.likelihoods.Gaussian()
self.lik.variance = self.noiseVariance
self.q_mean = self.rng.randn(self.nDimensions, self.oneLatentFunction)
self.q_sqrt_diag = self.rng.rand(self.nDimensions, self.oneLatentFunction)
self.q_sqrt_full = np.tril(self.rng.rand(self.nDimensions, self.nDimensions))
def getModel(self, is_diagonal, is_whitened):
model = gpflow.svgp.SVGP(
X=self.X, Y=self.Y,
kern=kernel(kernelVariance=self.signalVariance, lengthScale=self.lengthScale),
likelihood=self.lik,
Z=self.Z,
q_diag=is_diagonal,
whiten=is_whitened)
if is_diagonal:
model.q_sqrt = self.q_sqrt_diag
else:
model.q_sqrt = self.q_sqrt_full[:, :, None]
model.q_mu = self.q_mean
return model
def test_refrence_implementation_consistency(self):
with self.test_session():
rng = np.random.RandomState(10)
qMean = rng.randn()
qCov = rng.rand()
pMean = rng.rand()
pCov = rng.rand()
univariate_KL = referenceUnivariatePriorKL(qMean, pMean, qCov, pCov)
multivariate_KL = referenceMultivariatePriorKL(
np.array([[qMean]]), np.array([[qCov]]),
np.array([[pMean]]), np.array([[pCov]]))
self.assertTrue(np.abs(univariate_KL - multivariate_KL) < 1e-4)
def test_prior_KL_fullQ(self):
with self.test_session():
covQ = np.dot(self.q_sqrt_full, self.q_sqrt_full.T)
mean_prior = np.zeros((self.nDimensions, 1))
for is_whitened in [True, False]:
m = self.getModel(False, is_whitened)
if is_whitened:
cov_prior = np.eye(self.nDimensions)
else:
cov_prior = referenceRbfKernel(
self.X, self.lengthScale, self.signalVariance)
referenceKL = referenceMultivariatePriorKL(
self.q_mean, covQ, mean_prior, cov_prior)
# now get test KL.
test_prior_KL = gpflow.param.AutoFlow()(m.build_prior_KL.__func__)(m)
self.assertTrue(np.abs(referenceKL - test_prior_KL) < 1e-4)
if __name__ == "__main__":
unittest.main()