KLCholeskyInferenceMethod.cpp

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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.
 *
 * Code adapted from
 * http://hannes.nickisch.org/code/approxXX.tar.gz
 * and Gaussian Process Machine Learning Toolbox
 * http://www.gaussianprocess.org/gpml/code/matlab/doc/
 * and the reference paper is
 * Challis, Edward, and David Barber.
 * "Concave Gaussian variational approximations for inference in large-scale Bayesian linear models."
 * International conference on Artificial Intelligence and Statistics. 2011.
 *
 * This code specifically adapted from function in approxKL.m and infKL.m
 */

#include <shogun/machine/gp/KLCholeskyInferenceMethod.h>

#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/Math.h>
#include <shogun/mathematics/Statistics.h>
#include <shogun/machine/gp/VariationalGaussianLikelihood.h>

using namespace Eigen;

namespace shogun
{

CKLCholeskyInferenceMethod::CKLCholeskyInferenceMethod() : CKLLowerTriangularInference()
{
    init();
}

CKLCholeskyInferenceMethod::CKLCholeskyInferenceMethod(CKernel* kern,
        CFeatures* feat, CMeanFunction* m, CLabels* lab, CLikelihoodModel* mod)
        : CKLLowerTriangularInference(kern, feat, m, lab, mod)
{
    init();
}

void CKLCholeskyInferenceMethod::init()
{
    SG_ADD(&m_C, "C",
        "The Cholesky represention of the variational co-variance matrix",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_InvK_C, "invK_C",
        " The K^{-1}C matrix",
        MS_NOT_AVAILABLE);
}

CKLCholeskyInferenceMethod* CKLCholeskyInferenceMethod::obtain_from_generic(
        CInference* inference)
{
    if (inference==NULL)
        return NULL;

    if (inference->get_inference_type()!=INF_KL_CHOLESKY)
        SG_SERROR("Provided inference is not of type CKLCholeskyInferenceMethod!\n")

    SG_REF(inference);
    return (CKLCholeskyInferenceMethod*)inference;
}

SGVector<float64_t> CKLCholeskyInferenceMethod::get_alpha()
{
    if (parameter_hash_changed())
        update();

    index_t len=m_mu.vlen;
    SGVector<float64_t> result(len);

    Map<VectorXd> eigen_result(result.vector, len);
    Map<VectorXd> eigen_alpha(m_alpha.vector, len);

    eigen_result=eigen_alpha;

    return result;
}

CKLCholeskyInferenceMethod::~CKLCholeskyInferenceMethod()
{
}

bool CKLCholeskyInferenceMethod::precompute()
{
    index_t len=m_mean_vec.vlen;
    Map<VectorXd> eigen_mean(m_mean_vec.vector, m_mean_vec.vlen);
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
    Map<VectorXd> eigen_alpha(m_alpha.vector, len);

    Map<VectorXd> eigen_mu(m_mu.vector, m_mu.vlen);
    //mu=K*alpha+m
    eigen_mu=eigen_K*CMath::exp(m_log_scale*2.0)*eigen_alpha+eigen_mean;

    update_C();
    Map<MatrixXd> eigen_C(m_C.matrix, m_C.num_rows, m_C.num_cols);
    Map<VectorXd> eigen_s2(m_s2.vector, m_s2.vlen);
    //s2=sum(C.*C,2);
    eigen_s2=(eigen_C.array()*eigen_C.array()).rowwise().sum().matrix();

    CVariationalGaussianLikelihood * lik=get_variational_likelihood();
    bool status = lik->set_variational_distribution(m_mu, m_s2, m_labels);
    if (status)
    {
        Map<MatrixXd> eigen_InvK_C(m_InvK_C.matrix, m_InvK_C.num_rows, m_InvK_C.num_cols);
        eigen_InvK_C=solve_inverse(eigen_C);
    }
    return status;
}

void CKLCholeskyInferenceMethod::get_gradient_of_nlml_wrt_parameters(SGVector<float64_t> gradient)
{
    REQUIRE(gradient.vlen==m_alpha.vlen,
        "The length of gradients (%d) should the same as the length of parameters (%d)\n",
        gradient.vlen, m_alpha.vlen);

    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
    Map<MatrixXd> eigen_C(m_C.matrix, m_C.num_rows, m_C.num_cols);

    index_t len=m_mu.vlen;
    Map<VectorXd> eigen_alpha(m_alpha.vector, len);
    Map<VectorXd> eigen_C_seq(m_alpha.vector+len, m_alpha.vlen-len);

    CVariationalGaussianLikelihood * lik=get_variational_likelihood();
    //[a,df,dV] = a_related2(mu,s2,y,lik);
    TParameter* s2_param=lik->m_parameters->get_parameter("sigma2");
    SGVector<float64_t> dv=lik->get_variational_first_derivative(s2_param);
    Map<VectorXd> eigen_dv(dv.vector, dv.vlen);

    TParameter* mu_param=lik->m_parameters->get_parameter("mu");
    SGVector<float64_t> df=lik->get_variational_first_derivative(mu_param);
    Map<VectorXd> eigen_df(df.vector, df.vlen);

    Map<VectorXd> eigen_dnlz_alpha(gradient.vector, len);
    //dnlZ_alpha  = -K*(df-alpha);
    eigen_dnlz_alpha=eigen_K*CMath::exp(m_log_scale*2.0)*(-eigen_df+eigen_alpha);

    Map<VectorXd> eigen_dnlz_C_seq(gradient.vector+len, gradient.vlen-len);

    SGVector<float64_t> tmp(eigen_dnlz_C_seq.rows());
    Map<VectorXd> eigen_tmp(tmp.vector, tmp.vlen);

    //dnlZ_C=low_matrix_to_vector(invK_C)-convert_diag(1.0./diag(C))-2*(alla(n+1:end,1).*convert_dC(dv));
    float64_t offset=0;
    for (index_t i=0; i<len; i++)
    {
        eigen_tmp.block(offset, 0, len-i, 1)=VectorXd::Map(eigen_dv.data()+i, len-i);
        offset+=(len-i);
    }

    //-2*(alla(n+1:end,1).*convert_dC(dV))
    eigen_dnlz_C_seq=(-2.0*(eigen_C_seq.array()*eigen_tmp.array())).matrix();
    //low_matrix_to_vector(invK_C)
    get_lower_triangular_vector(m_InvK_C, tmp);
    eigen_dnlz_C_seq+=eigen_tmp;

    Map<VectorXd> eigen_tmp2(tmp.vector, eigen_C.rows());
    //-convert_diag(1.0./diag(C))
    eigen_tmp2=(1.0/eigen_C.diagonal().array()).matrix();

    offset=0;
    for (index_t i=0; i<len; i++)
    {
        eigen_dnlz_C_seq.block(offset,0,1,1)-=VectorXd::Map(eigen_tmp2.data()+i,1);
        offset+=(len-i);
    }
}

float64_t CKLCholeskyInferenceMethod::get_negative_log_marginal_likelihood_helper()
{
    Map<VectorXd> eigen_alpha(m_alpha.vector, m_mu.vlen);
    Map<VectorXd> eigen_mu(m_mu.vector, m_mu.vlen);
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
    //get mean vector and create eigen representation of it
    Map<VectorXd> eigen_mean(m_mean_vec.vector, m_mean_vec.vlen);

    Map<MatrixXd> eigen_InvK_C(m_InvK_C.matrix, m_InvK_C.num_rows, m_InvK_C.num_cols);
    Map<MatrixXd> eigen_C(m_C.matrix, m_C.num_rows, m_C.num_cols);

    CVariationalGaussianLikelihood * lik=get_variational_likelihood();
    float64_t a=SGVector<float64_t>::sum(lik->get_variational_expection());

    //float64_t log_det=2.0*log_det(eigen_C)-m_log_det_Kernel;
    float64_t log_det=2.0*eigen_C.diagonal().array().abs().log().sum()-m_log_det_Kernel;
    float64_t trace=(eigen_InvK_C.array()*eigen_C.array()).sum();

    //nlZ = -a -logdet(V*inv(K))/2 -n/2 +(alpha'*K*alpha)/2 +trace(V*inv(K))/2;
    float64_t result=-a+0.5*(-eigen_K.rows()+eigen_alpha.dot(eigen_mu-eigen_mean)+trace-log_det);
    return result;
}

void CKLCholeskyInferenceMethod::update_alpha()
{
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);

    float64_t nlml_new=0;
    float64_t nlml_def=0;

    index_t len=m_labels->get_num_labels();
    index_t total_len=len*(len+3);

    if (m_alpha.vlen*2 == total_len)
    {
        nlml_new=get_negative_log_marginal_likelihood_helper();

        SGVector<float64_t> s2_tmp(m_s2.vlen);
        Map<VectorXd> eigen_s2(s2_tmp.vector, s2_tmp.vlen);
        eigen_s2.fill(1.0);
        CVariationalGaussianLikelihood * lik=get_variational_likelihood();
        lik->set_variational_distribution(m_mean_vec, s2_tmp, m_labels);
        float64_t a=SGVector<float64_t>::sum(lik->get_variational_expection());
        MatrixXd inv_K=solve_inverse(MatrixXd::Identity(m_ktrtr.num_rows, m_ktrtr.num_cols));
        float64_t trace=inv_K.diagonal().array().sum();
        nlml_def=-a+0.5*(-eigen_K.rows()+trace+m_log_det_Kernel);

        if (nlml_new<=nlml_def)
            lik->set_variational_distribution(m_mu, m_s2, m_labels);
    }

    if (m_alpha.vlen*2 != total_len || nlml_def<nlml_new)
    {
        if(m_alpha.vlen*2 != total_len)
            m_alpha = SGVector<float64_t>(total_len/2);
        m_alpha.zero();
        index_t offset=0;
        index_t count=0;
        //init
        for (index_t i=0; i<m_alpha.vlen; i++)
        {
            if (i-len==offset)
            {
                m_alpha[i]=1.0;
                offset+=(len-count);
                count++;
            }
        }
        m_InvK_C=SGMatrix<float64_t>(len, len);
        m_C=SGMatrix<float64_t>(len, len);
        m_C.zero();
        m_mu=SGVector<float64_t>(len);
        m_s2=SGVector<float64_t>(len);
    }

    nlml_new=optimization();
}

void CKLCholeskyInferenceMethod::update_C()
{
    ASSERT(m_C.num_rows == m_C.num_cols);
    index_t len=m_C.num_rows;
    ASSERT(m_alpha.vlen*2 == len*(len+3));

    Map<MatrixXd> eigen_C(m_C.matrix, m_C.num_rows, m_C.num_cols);
    Map<VectorXd> eigen_C_seq(m_alpha.vector+len, m_alpha.vlen-len);

    index_t offset=0;
    for (index_t i=0; i<len; i++)
    {
        eigen_C.block(i, i, len-i ,1)=VectorXd::Map(eigen_C_seq.data()+offset, len-i);
        offset+=(len-i);
    }
}

void CKLCholeskyInferenceMethod::get_lower_triangular_vector(SGMatrix<float64_t> square_matrix,
    SGVector<float64_t> target)
{
    ASSERT(square_matrix.num_rows == square_matrix.num_cols);
    index_t len=m_InvK_C.num_rows;
    ASSERT(target.vlen*2 == len*(len+1));

    Map<MatrixXd> eigen_square_matrix(square_matrix.matrix, len, len);
    Map<VectorXd> eigen_result(target.vector, target.vlen);

    index_t offset=0;
    for (index_t i=0; i<len; i++)
    {
        eigen_result.block(offset, 0, len-i, 1)=eigen_square_matrix.block(i, i, len-i, 1);
        offset+=(len-i);
    }
}

void CKLCholeskyInferenceMethod::update_Sigma()
{
    m_Sigma=SGMatrix<float64_t>(m_mu.vlen, m_mu.vlen);
    Map<MatrixXd> eigen_Sigma(m_Sigma.matrix, m_Sigma.num_rows, m_Sigma.num_cols);
    Map<MatrixXd> eigen_C(m_C.matrix, m_C.num_rows, m_C.num_cols);
    eigen_Sigma=eigen_C*(eigen_C.transpose());
}

void CKLCholeskyInferenceMethod::update_InvK_Sigma()
{
    m_InvK_Sigma=SGMatrix<float64_t>(m_ktrtr.num_rows, m_ktrtr.num_cols);
    Map<MatrixXd> eigen_InvK_Sigma(m_InvK_Sigma.matrix, m_InvK_Sigma.num_rows, m_InvK_Sigma.num_cols);
    Map<MatrixXd> eigen_InvK_C(m_InvK_C.matrix, m_InvK_C.num_rows, m_InvK_C.num_cols);
    Map<MatrixXd> eigen_C(m_C.matrix, m_C.num_rows, m_C.num_cols);
    eigen_InvK_Sigma=eigen_InvK_C*(eigen_C.transpose());
}

} /* namespace shogun */