/
KLCovarianceInfernceMethod_unittest.cc
1361 lines (1130 loc) · 54.7 KB
/
KLCovarianceInfernceMethod_unittest.cc
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/*
* Copyright (c) The Shogun Machine Learning Toolbox
* Written (w) 2014 Wu Lin
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are those
* of the authors and should not be interpreted as representing official policies,
* either expressed or implied, of the Shogun Development Team.
*
*
*/
#include <shogun/lib/config.h>
#ifdef HAVE_EIGEN3
#include <shogun/labels/RegressionLabels.h>
#include <shogun/labels/BinaryLabels.h>
#include <shogun/features/DenseFeatures.h>
#include <shogun/kernel/GaussianKernel.h>
#include <shogun/machine/gp/ZeroMean.h>
#include <shogun/machine/gp/GaussianLikelihood.h>
#include <shogun/machine/gp/KLCovarianceInferenceMethod.h>
#include <shogun/machine/gp/LogitVGLikelihood.h>
#include <shogun/machine/gp/ProbitVGLikelihood.h>
#include <shogun/machine/gp/StudentsTVGLikelihood.h>
#include <gtest/gtest.h>
#include <shogun/mathematics/Math.h>
using namespace shogun;
TEST(KLCovarianceInferenceMethod,get_cholesky_t_likelihood)
{
// create some easy regression data:
// y approximately equals to 1/5*sin(10*x) + sqrt(x)
index_t n=5;
SGMatrix<float64_t> feat_train(1, n);
SGVector<float64_t> lab_train(n);
feat_train[0]=0.27815;
feat_train[1]=1.12759;
feat_train[2]=1.26760;
feat_train[3]=1.52883;
feat_train[4]=2.96195;
lab_train[0]=0.59787;
lab_train[1]=0.86969;
lab_train[2]=1.14778;
lab_train[3]=1.31794;
lab_train[4]=1.52609;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CRegressionLabels* labels_train=new CRegressionLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// Student's-T likelihood with sigma = 1, df = 3
CStudentsTVGLikelihood* likelihood=new CStudentsTVGLikelihood(1, 3);
// specify GP regression with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// L =
//
//1.407423685644243 0.515497460024622 0.443065894253950 0.319410344939164 0.016180892181750
// 0 1.355918485894513 0.619918738844402 0.588106670839222 0.115276398753254
// 0 0 1.214360350469977 0.394486954116069 0.104931348884614
// 0 0 0 1.175209056259849 0.157509505562212
// 0 0 0 0 1.288734252271706
//
SGMatrix<float64_t> L=inf->get_cholesky();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(1.407423685644243, rel_tolerance);
EXPECT_NEAR(L(0,0), 1.407423685644243, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.515497460024622, rel_tolerance);
EXPECT_NEAR(L(0,1), 0.515497460024622, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.443065894253950, rel_tolerance);
EXPECT_NEAR(L(0,2), 0.443065894253950, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.319410344939164, rel_tolerance);
EXPECT_NEAR(L(0,3), 0.319410344939164, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.016180892181750, rel_tolerance);
EXPECT_NEAR(L(0,4), 0.016180892181750, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(1,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.355918485894513, rel_tolerance);
EXPECT_NEAR(L(1,1), 1.355918485894513, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.619918738844402, rel_tolerance);
EXPECT_NEAR(L(1,2), 0.619918738844402, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.588106670839222, rel_tolerance);
EXPECT_NEAR(L(1,3), 0.588106670839222, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.115276398753254, rel_tolerance);
EXPECT_NEAR(L(1,4), 0.115276398753254, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(2,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(2,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.214360350469977, rel_tolerance);
EXPECT_NEAR(L(2,2), 1.214360350469977, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.394486954116069, rel_tolerance);
EXPECT_NEAR(L(2,3), 0.394486954116069, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.104931348884614, rel_tolerance);
EXPECT_NEAR(L(2,4), 0.104931348884614, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,2), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.175209056259849, rel_tolerance);
EXPECT_NEAR(L(3,3), 1.175209056259849, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.157509505562212, rel_tolerance);
EXPECT_NEAR(L(3,4), 0.157509505562212, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,2), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,3), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.288734252271706, rel_tolerance);
EXPECT_NEAR(L(4,4), 1.288734252271706, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_cholesky_logit_likelihood)
{
// create some easy classification data:
// y=sign(sqrt(x1.^2+x2.^2)-1)
index_t n=5;
SGMatrix<float64_t> feat_train(2, n);
SGVector<float64_t> lab_train(n);
feat_train(0, 0)=0.8822936;
feat_train(0, 1)=-0.7160792;
feat_train(0, 2)=0.9178174;
feat_train(0, 3)=-0.0135544;
feat_train(0, 4)=-0.5275911;
feat_train(1, 0)=-0.9597321;
feat_train(1, 1)=0.0231289;
feat_train(1, 2)=0.8284935;
feat_train(1, 3)=0.0023812;
feat_train(1, 4)=-0.7218931;
lab_train[0]=1.0;
lab_train[1]=-1.0;
lab_train[2]=1.0;
lab_train[3]=-1.0;
lab_train[4]=-1.0;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CBinaryLabels* labels_train=new CBinaryLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// logit likelihood
CLogitVGLikelihood* likelihood=new CLogitVGLikelihood();
// specify GP classification with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior cholesky with result:
// L =
//1.101033636127231 0.031935435514485 0.038838470404416 0.080505388829644 0.067456404131013
// 0 1.093577781758797 0.034349943478487 0.142357943078213 0.133350176799401
// 0 0 1.099289233197989 0.080619635381560 0.013257570410259
// 0 0 0 1.084046011513489 0.103671309031576
// 0 0 0 0 1.080493372046284
SGMatrix<float64_t> L=inf->get_cholesky();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(1.101033636127231, rel_tolerance);
EXPECT_NEAR(L(0,0), 1.101033636127231, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.031935435514485, rel_tolerance);
EXPECT_NEAR(L(0,1), 0.031935435514485, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.038838470404416, rel_tolerance);
EXPECT_NEAR(L(0,2), 0.038838470404416, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.080505388829644, rel_tolerance);
EXPECT_NEAR(L(0,3), 0.080505388829644, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.067456404131013, rel_tolerance);
EXPECT_NEAR(L(0,4), 0.067456404131013, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(1,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.093577781758797, rel_tolerance);
EXPECT_NEAR(L(1,1), 1.093577781758797, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.034349943478487, rel_tolerance);
EXPECT_NEAR(L(1,2), 0.034349943478487, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.142357943078213, rel_tolerance);
EXPECT_NEAR(L(1,3), 0.142357943078213, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.133350176799401, rel_tolerance);
EXPECT_NEAR(L(1,4), 0.133350176799401, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(2,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(2,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.099289233197989, rel_tolerance);
EXPECT_NEAR(L(2,2), 1.099289233197989, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.080619635381560, rel_tolerance);
EXPECT_NEAR(L(2,3), 0.080619635381560, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.013257570410259, rel_tolerance);
EXPECT_NEAR(L(2,4), 0.013257570410259, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,2), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.084046011513489, rel_tolerance);
EXPECT_NEAR(L(3,3), 1.084046011513489, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.103671309031576, rel_tolerance);
EXPECT_NEAR(L(3,4), 0.103671309031576, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,2), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,3), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.080493372046284, rel_tolerance);
EXPECT_NEAR(L(4,4), 1.080493372046284, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_cholesky_probit_likelihood)
{
// create some easy random classification data
index_t n=5;
SGMatrix<float64_t> feat_train(2, n);
SGVector<float64_t> lab_train(n);
feat_train(0, 0)=-1.07932;
feat_train(0, 1)=1.15768;
feat_train(0, 2)=3.26631;
feat_train(0, 3)=1.79009;
feat_train(0, 4)=-3.66051;
feat_train(1, 0)=-1.83544;
feat_train(1, 1)=2.91702;
feat_train(1, 2)=-3.85663;
feat_train(1, 3)=0.11949;
feat_train(1, 4)=1.75159;
lab_train[0]=-1.0;
lab_train[1]=1.0;
lab_train[2]=1.0;
lab_train[3]=1.0;
lab_train[4]=-1.0;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CBinaryLabels* labels_train=new CBinaryLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// probit likelihood
CProbitVGLikelihood* likelihood=new CProbitVGLikelihood();
// specify GP classification with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior cholesky with result:
// L =
//1.216420672271186 0.000000401780554 0.000004054670173 0.000949334832622 0.000022647889665
// 0 1.215717061852584 0.000000000003300 0.006432557084865 0.000001816526618
// 0 0 1.216327485101524 0.000048851822686 -0.000000000075498
// 0 0 0 1.215786494210340 0.000000009487969
// 0 0 0 0 1.216329768018010
SGMatrix<float64_t> L=inf->get_cholesky();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(1.216420672271186, rel_tolerance);
EXPECT_NEAR(L(0,0), 1.216420672271186, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000000401780554, rel_tolerance);
EXPECT_NEAR(L(0,1), 0.000000401780554, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000004054670173, rel_tolerance);
EXPECT_NEAR(L(0,2), 0.000004054670173, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000949334832622, rel_tolerance);
EXPECT_NEAR(L(0,3), 0.000949334832622, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000022647889665, rel_tolerance);
EXPECT_NEAR(L(0,4), 0.000022647889665, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(1,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.215717061852584, rel_tolerance);
EXPECT_NEAR(L(1,1), 1.215717061852584, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000000000003300, rel_tolerance);
EXPECT_NEAR(L(1,2), 0.000000000003300, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.006432557084865, rel_tolerance);
EXPECT_NEAR(L(1,3), 0.006432557084865, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000001816526618, rel_tolerance);
EXPECT_NEAR(L(1,4), 0.000001816526618, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(2,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(2,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.216327485101524, rel_tolerance);
EXPECT_NEAR(L(2,2), 1.216327485101524, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000048851822686, rel_tolerance);
EXPECT_NEAR(L(2,3), 0.000048851822686, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000000000075498, rel_tolerance);
EXPECT_NEAR(L(2,4), -0.000000000075498, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(3,2), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.215786494210340, rel_tolerance);
EXPECT_NEAR(L(3,3), 1.215786494210340, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000000009487969, rel_tolerance);
EXPECT_NEAR(L(3,4), 0.000000009487969, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,0), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,1), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,2), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0, rel_tolerance);
EXPECT_NEAR(L(4,3), 0, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(1.216329768018010, rel_tolerance);
EXPECT_NEAR(L(4,4), 1.216329768018010, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_posterior_mean_t_likelihood)
{
// create some easy regression data:
// y approximately equals to 1/5*sin(10*x) + sqrt(x)
index_t n=5;
SGMatrix<float64_t> feat_train(1, n);
SGVector<float64_t> lab_train(n);
feat_train[0]=0.27815;
feat_train[1]=1.12759;
feat_train[2]=1.26760;
feat_train[3]=1.52883;
feat_train[4]=2.96195;
lab_train[0]=0.59787;
lab_train[1]=0.86969;
lab_train[2]=1.14778;
lab_train[3]=1.31794;
lab_train[4]=1.52609;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CRegressionLabels* labels_train=new CRegressionLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// Student's-T likelihood with sigma = 1, df = 3
CStudentsTVGLikelihood* likelihood=new CStudentsTVGLikelihood(1, 3);
// specify GP regression with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior posterior_mean with result:
// posterior_mean =
//0.489965084229748
//0.847314396373669
//0.889161956923399
//0.946680542914168
//0.814125447090175
//
SGVector<float64_t> posterior_mean=inf->get_posterior_mean();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(0.489965084229748, rel_tolerance);
EXPECT_NEAR(posterior_mean[0], 0.489965084229748, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.847314396373669, rel_tolerance);
EXPECT_NEAR(posterior_mean[1], 0.847314396373669, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.889161956923399, rel_tolerance);
EXPECT_NEAR(posterior_mean[2], 0.889161956923399, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.946680542914168, rel_tolerance);
EXPECT_NEAR(posterior_mean[3], 0.946680542914168, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.814125447090175, rel_tolerance);
EXPECT_NEAR(posterior_mean[4], 0.814125447090175, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_posterior_covariance_t_likelihood)
{
// create some easy regression data:
// y approximately equals to 1/5*sin(10*x) + sqrt(x)
index_t n=5;
SGMatrix<float64_t> feat_train(1, n);
SGVector<float64_t> lab_train(n);
feat_train[0]=0.27815;
feat_train[1]=1.12759;
feat_train[2]=1.26760;
feat_train[3]=1.52883;
feat_train[4]=2.96195;
lab_train[0]=0.59787;
lab_train[1]=0.86969;
lab_train[2]=1.14778;
lab_train[3]=1.31794;
lab_train[4]=1.52609;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CRegressionLabels* labels_train=new CRegressionLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero covariance function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* covariance=new CZeroMean();
// Student's-T likelihood with sigma = 1, df = 3
CStudentsTVGLikelihood* likelihood=new CStudentsTVGLikelihood(1, 3);
// specify GP regression with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, covariance, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior posterior_covariance with result:
// posterior_covariance =
//0.414373949946085 0.143666705039313 0.094429636121475 0.017776032079365 -0.025310137089717
//0.143666705039313 0.231294061589554 0.224883475133982 0.197483047433658 0.004953399924042
//0.094429636121475 0.224883475133982 0.231567407777062 0.227352640803712 0.029816060215331
//0.017776032079365 0.197483047433658 0.227352640803712 0.269271328474079 0.096502018273666
//-0.025310137089717 0.004953399924042 0.029816060215331 0.096502018273666 0.560250726200816
//
SGMatrix<float64_t> posterior_covariance=inf->get_posterior_covariance();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(0.414373949946085, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,0), 0.414373949946085, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.143666705039313, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,1), 0.143666705039313, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.094429636121475, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,2), 0.094429636121475, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.017776032079365, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,3), 0.017776032079365, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.025310137089717, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,4), -0.025310137089717, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.143666705039313, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,0), 0.143666705039313, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.231294061589554, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,1), 0.231294061589554, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.224883475133982, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,2), 0.224883475133982, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.197483047433658, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,3), 0.197483047433658, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.004953399924042, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,4), 0.004953399924042, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.094429636121475, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,0), 0.094429636121475, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.224883475133982, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,1), 0.224883475133982, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.231567407777062, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,2), 0.231567407777062, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.227352640803712, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,3), 0.227352640803712, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.029816060215331, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,4), 0.029816060215331, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.017776032079365, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,0), 0.017776032079365, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.197483047433658, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,1), 0.197483047433658, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.227352640803712, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,2), 0.227352640803712, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.269271328474079, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,3), 0.269271328474079, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.096502018273666, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,4), 0.096502018273666, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.025310137089717, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,0), -0.025310137089717, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.004953399924042, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,1), 0.004953399924042, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.029816060215331, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,2), 0.029816060215331, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.096502018273666, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,3), 0.096502018273666, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.560250726200816, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,4), 0.560250726200816, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_posterior_mean_logit_likelihood)
{
// create some easy classification data:
// y=sign(sqrt(x1.^2+x2.^2)-1)
index_t n=5;
SGMatrix<float64_t> feat_train(2, n);
SGVector<float64_t> lab_train(n);
feat_train(0, 0)=0.8822936;
feat_train(0, 1)=-0.7160792;
feat_train(0, 2)=0.9178174;
feat_train(0, 3)=-0.0135544;
feat_train(0, 4)=-0.5275911;
feat_train(1, 0)=-0.9597321;
feat_train(1, 1)=0.0231289;
feat_train(1, 2)=0.8284935;
feat_train(1, 3)=0.0023812;
feat_train(1, 4)=-0.7218931;
lab_train[0]=1.0;
lab_train[1]=-1.0;
lab_train[2]=1.0;
lab_train[3]=-1.0;
lab_train[4]=-1.0;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CBinaryLabels* labels_train=new CBinaryLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// logit likelihood
CLogitVGLikelihood* likelihood=new CLogitVGLikelihood();
// specify GP classification with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior posterior_mean with result:
// posterior_mean =
//0.195075001254701
//-0.752239725258407
//0.254676683453462
//-0.503016798305133
//-0.666267998053423
SGVector<float64_t> posterior_mean=inf->get_posterior_mean();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(0.195075001254701, rel_tolerance);
EXPECT_NEAR(posterior_mean[0], 0.195075001254701, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.752239725258407, rel_tolerance);
EXPECT_NEAR(posterior_mean[1], -0.752239725258407, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.254676683453462, rel_tolerance);
EXPECT_NEAR(posterior_mean[2], 0.254676683453462, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.503016798305133, rel_tolerance);
EXPECT_NEAR(posterior_mean[3], -0.503016798305133, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.666267998053423, rel_tolerance);
EXPECT_NEAR(posterior_mean[4], -0.666267998053423, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_posterior_covariance_logit_likelihood)
{
// create some easy classification data:
// y=sign(sqrt(x1.^2+x2.^2)-1)
index_t n=5;
SGMatrix<float64_t> feat_train(2, n);
SGVector<float64_t> lab_train(n);
feat_train(0, 0)=0.8822936;
feat_train(0, 1)=-0.7160792;
feat_train(0, 2)=0.9178174;
feat_train(0, 3)=-0.0135544;
feat_train(0, 4)=-0.5275911;
feat_train(1, 0)=-0.9597321;
feat_train(1, 1)=0.0231289;
feat_train(1, 2)=0.8284935;
feat_train(1, 3)=0.0023812;
feat_train(1, 4)=-0.7218931;
lab_train[0]=1.0;
lab_train[1]=-1.0;
lab_train[2]=1.0;
lab_train[3]=-1.0;
lab_train[4]=-1.0;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CBinaryLabels* labels_train=new CBinaryLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// logit likelihood
CLogitVGLikelihood* likelihood=new CLogitVGLikelihood();
// specify GP classification with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior posterior_covariance with result:
// posterior_covariance =
//0.788613922080216 0.055365603952762 0.113585701478720 0.250515288102739 0.211318414874201
//0.055365603952762 0.705059022635855 0.086020351983001 0.492913876934693 0.471026718609916
//0.113585701478720 0.086020351983001 0.795196757855660 0.295546558157168 0.020998235505635
//0.250515288102739 0.492913876934693 0.295546558157168 0.677608447921106 0.400514239283206
//0.211318414874201 0.471026718609916 0.020998235505635 0.400514239283206 0.714639675393856
//
SGMatrix<float64_t> posterior_covariance=inf->get_posterior_covariance();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(0.788613922080216, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,0), 0.788613922080216, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.055365603952762, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,1), 0.055365603952762, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.113585701478720, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,2), 0.113585701478720, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.250515288102739, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,3), 0.250515288102739, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.211318414874201, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,4), 0.211318414874201, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.055365603952762, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,0), 0.055365603952762, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.705059022635855, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,1), 0.705059022635855, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.086020351983001, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,2), 0.086020351983001, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.492913876934693, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,3), 0.492913876934693, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.471026718609916, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,4), 0.471026718609916, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.113585701478720, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,0), 0.113585701478720, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.086020351983001, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,1), 0.086020351983001, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.795196757855660, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,2), 0.795196757855660, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.295546558157168, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,3), 0.295546558157168, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.020998235505635, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,4), 0.020998235505635, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.250515288102739, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,0), 0.250515288102739, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.492913876934693, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,1), 0.492913876934693, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.295546558157168, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,2), 0.295546558157168, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.677608447921106, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,3), 0.677608447921106, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.400514239283206, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,4), 0.400514239283206, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.211318414874201, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,0), 0.211318414874201, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.471026718609916, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,1), 0.471026718609916, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.020998235505635, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,2), 0.020998235505635, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.400514239283206, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,3), 0.400514239283206, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.714639675393856, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,4), 0.714639675393856, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_posterior_mean_probit_likelihood)
{
// create some easy random classification data
index_t n=5;
SGMatrix<float64_t> feat_train(2, n);
SGVector<float64_t> lab_train(n);
feat_train(0, 0)=-1.07932;
feat_train(0, 1)=1.15768;
feat_train(0, 2)=3.26631;
feat_train(0, 3)=1.79009;
feat_train(0, 4)=-3.66051;
feat_train(1, 0)=-1.83544;
feat_train(1, 1)=2.91702;
feat_train(1, 2)=-3.85663;
feat_train(1, 3)=0.11949;
feat_train(1, 4)=1.75159;
lab_train[0]=-1.0;
lab_train[1]=1.0;
lab_train[2]=1.0;
lab_train[3]=1.0;
lab_train[4]=-1.0;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CBinaryLabels* labels_train=new CBinaryLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// probit likelihood
CProbitVGLikelihood* likelihood=new CProbitVGLikelihood();
// specify GP classification with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior posterior_mean with result:
// posterior_mean =
//-0.562633450485667
//0.569793845834907
//0.563581584765779
//0.568910892345396
//-0.563558402061117
//
SGVector<float64_t> posterior_mean=inf->get_posterior_mean();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(-0.562633450485667, rel_tolerance);
EXPECT_NEAR(posterior_mean[0], -0.562633450485667, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.569793845834907, rel_tolerance);
EXPECT_NEAR(posterior_mean[1], 0.569793845834907, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.563581584765779, rel_tolerance);
EXPECT_NEAR(posterior_mean[2], 0.563581584765779, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.568910892345396, rel_tolerance);
EXPECT_NEAR(posterior_mean[3], 0.568910892345396, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.563558402061117, rel_tolerance);
EXPECT_NEAR(posterior_mean[4], -0.563558402061117, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_posterior_covariance_probit_likelihood)
{
// create some easy random classification data
index_t n=5;
SGMatrix<float64_t> feat_train(2, n);
SGVector<float64_t> lab_train(n);
feat_train(0, 0)=-1.07932;
feat_train(0, 1)=1.15768;
feat_train(0, 2)=3.26631;
feat_train(0, 3)=1.79009;
feat_train(0, 4)=-3.66051;
feat_train(1, 0)=-1.83544;
feat_train(1, 1)=2.91702;
feat_train(1, 2)=-3.85663;
feat_train(1, 3)=0.11949;
feat_train(1, 4)=1.75159;
lab_train[0]=-1.0;
lab_train[1]=1.0;
lab_train[2]=1.0;
lab_train[3]=1.0;
lab_train[4]=-1.0;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CBinaryLabels* labels_train=new CBinaryLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// probit likelihood
CProbitVGLikelihood* likelihood=new CProbitVGLikelihood();
// specify GP classification with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// comparison of posterior posterior_covariance with result:
// posterior_covariance =
//0.675821281453662 -0.000005367710037 0.000004653883433 0.001102425357803 0.000026241600793
//-0.000005367710037 0.676565020447684 -0.000000300323282 0.007487585977222 0.000002109695855
//0.000004653883433 -0.000000300323282 0.675925696916253 0.000056747602632 -0.000000000087947
//0.001102425357803 0.007487585977222 0.000056747602632 0.676467549296978 0.000000011016475
//0.000026241600793 0.000002109695855 -0.000000000087947 0.000000011016475 0.675923161214598
SGMatrix<float64_t> posterior_covariance=inf->get_posterior_covariance();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(0.675821281453662, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,0), 0.675821281453662, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000005367710037, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,1), -0.000005367710037, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000004653883433, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,2), 0.000004653883433, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.001102425357803, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,3), 0.001102425357803, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000026241600793, rel_tolerance);
EXPECT_NEAR(posterior_covariance(0,4), 0.000026241600793, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000005367710037, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,0), -0.000005367710037, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.676565020447684, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,1), 0.676565020447684, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000000300323282, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,2), -0.000000300323282, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.007487585977222, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,3), 0.007487585977222, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000002109695855, rel_tolerance);
EXPECT_NEAR(posterior_covariance(1,4), 0.000002109695855, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000004653883433, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,0), 0.000004653883433, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000000300323282, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,1), -0.000000300323282, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.675925696916253, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,2), 0.675925696916253, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000056747602632, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,3), 0.000056747602632, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000000000087947, rel_tolerance);
EXPECT_NEAR(posterior_covariance(2,4), -0.000000000087947, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.001102425357803, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,0), 0.001102425357803, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.007487585977222, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,1), 0.007487585977222, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000056747602632, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,2), 0.000056747602632, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.676467549296978, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,3), 0.676467549296978, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000000011016475, rel_tolerance);
EXPECT_NEAR(posterior_covariance(3,4), 0.000000011016475, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000026241600793, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,0), 0.000026241600793, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000002109695855, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,1), 0.000002109695855, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(-0.000000000087947, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,2), -0.000000000087947, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.000000011016475, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,3), 0.000000011016475, abs_tolerance);
abs_tolerance = CMath::get_abs_tolerance(0.675923161214598, rel_tolerance);
EXPECT_NEAR(posterior_covariance(4,4), 0.675923161214598, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_negative_marginal_likelihood_t_likelihood)
{
// create some easy regression data:
// y approximately equals to 1/5*sin(10*x) + sqrt(x)
index_t n=5;
SGMatrix<float64_t> feat_train(1, n);
SGVector<float64_t> lab_train(n);
feat_train[0]=0.27815;
feat_train[1]=1.12759;
feat_train[2]=1.26760;
feat_train[3]=1.52883;
feat_train[4]=2.96195;
lab_train[0]=0.59787;
lab_train[1]=0.86969;
lab_train[2]=1.14778;
lab_train[3]=1.31794;
lab_train[4]=1.52609;
// shogun representation of features and labels
CDenseFeatures<float64_t>* features_train=new CDenseFeatures<float64_t>(feat_train);
CRegressionLabels* labels_train=new CRegressionLabels(lab_train);
// choose Gaussian kernel with sigma = 2 and zero mean function
CGaussianKernel* kernel=new CGaussianKernel(10, 2);
CZeroMean* mean=new CZeroMean();
// Student's-T likelihood with sigma = 1, df = 3
CStudentsTVGLikelihood* likelihood=new CStudentsTVGLikelihood(1, 3);
// specify GP regression with KL inference
CKLCovarianceInferenceMethod* inf=new CKLCovarianceInferenceMethod(kernel,
features_train, mean, labels_train, likelihood);
//Reference result is generated from the Matlab code, which can be found at
//https://gist.github.com/yorkerlin/b64a015491833562d11a
//
// nlZ =
// 7.38335326307118311462
float64_t nml=inf->get_negative_log_marginal_likelihood();
float64_t rel_tolerance = 1e-2;
float64_t abs_tolerance;
abs_tolerance = CMath::get_abs_tolerance(7.38335326307118311462, rel_tolerance);
EXPECT_NEAR(nml, 7.38335326307118311462, abs_tolerance);
// clean up
SG_UNREF(inf);
}
TEST(KLCovarianceInferenceMethod,get_negative_marginal_likelihood_logit_likelihood)