KLCovarianceInferenceMethod.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
 * Nickisch, Hannes, and Carl Edward Rasmussen.
 * "Approximations for Binary Gaussian Process Classification."
 * Journal of Machine Learning Research 9.10 (2008).
 *
 * This code specifically adapted from function in approxKL.m and infKL.m
 */

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

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

using namespace Eigen;

namespace shogun
{

CKLCovarianceInferenceMethod::CKLCovarianceInferenceMethod() : CKLInference()
{
    init();
}

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

void CKLCovarianceInferenceMethod::init()
{
    SG_ADD(&m_V, "V",
        "V is L'*V=diag(sW)*K",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_A, "A",
        "A is A=I-K*diag(sW)*inv(L)'*inv(L)*diag(sW)",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_W, "W",
        "noise matrix W",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_sW, "sW",
        "Square root of noise matrix W",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_dv, "dv",
        "the gradient of the variational expection wrt sigma2",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_df, "df",
        "the gradient of the variational expection wrt mu",
        MS_NOT_AVAILABLE);
}


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

    index_t len=m_alpha.vlen/2;
    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;
}

CKLCovarianceInferenceMethod::~CKLCovarianceInferenceMethod()
{
}

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

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

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

bool CKLCovarianceInferenceMethod::precompute()
{
    SGVector<float64_t> mean=m_mean->get_mean_vector(m_features);
    Map<VectorXd> eigen_mean(mean.vector, mean.vlen);

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

    index_t len=m_alpha.vlen/2;
    //construct mu
    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;

    //construct s2
    Map<VectorXd> eigen_log_neg_lambda(m_alpha.vector+len, len);

    Map<VectorXd> eigen_W(m_W.vector, m_W.vlen);
    eigen_W=(2.0*eigen_log_neg_lambda.array().exp()).matrix();

    Map<VectorXd> eigen_sW(m_sW.vector, m_sW.vlen);
    eigen_sW=eigen_W.array().sqrt().matrix();

    m_L=CMatrixOperations::get_choleksy(m_W, m_sW, m_ktrtr, CMath::exp(m_log_scale));
    Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);

    //solve L'*V=diag(sW)*K
    Map<MatrixXd> eigen_V(m_V.matrix, m_V.num_rows, m_V.num_cols);
    eigen_V=eigen_L.triangularView<Upper>().adjoint().solve(eigen_sW.asDiagonal()*eigen_K*CMath::exp(m_log_scale*2.0));
    Map<VectorXd> eigen_s2(m_s2.vector, m_s2.vlen);
    //Sigma=inv(inv(K)-2*diag(lambda))=K-K*diag(sW)*inv(L)'*inv(L)*diag(sW)*K
    //v=abs(diag(Sigma))
    eigen_s2=(eigen_K.diagonal().array()*CMath::exp(m_log_scale*2.0)-(eigen_V.array().pow(2).colwise().sum().transpose())).abs().matrix();

    CVariationalGaussianLikelihood * lik=get_variational_likelihood();
    bool status = lik->set_variational_distribution(m_mu, m_s2, m_labels);
    return status;
}

void CKLCovarianceInferenceMethod::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_L(m_L.matrix, m_L.num_rows, m_L.num_cols);
    Map<VectorXd> eigen_sW(m_sW.vector, m_sW.vlen);
    Map<MatrixXd> eigen_V(m_V.matrix, m_V.num_rows, m_V.num_cols);
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
    Map<VectorXd> eigen_s2(m_s2.vector, m_s2.vlen);

    index_t len=m_alpha.vlen/2;
    Map<VectorXd> eigen_alpha(m_alpha.vector, len);
    Map<VectorXd> eigen_log_neg_lambda(m_alpha.vector+len, len);

    CVariationalGaussianLikelihood * lik=get_variational_likelihood();
    lik->set_variational_distribution(m_mu, m_s2, m_labels);

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

    TParameter* mu_param=lik->m_parameters->get_parameter("mu");
    m_df=lik->get_variational_first_derivative(mu_param);
    Map<VectorXd> eigen_df(m_df.vector, m_df.vlen);
    //U=inv(L')*diag(sW)
    MatrixXd eigen_U=eigen_L.triangularView<Upper>().adjoint().solve(MatrixXd(eigen_sW.asDiagonal()));
    Map<MatrixXd> eigen_A(m_A.matrix, m_A.num_rows, m_A.num_cols);
    // A=I-K*diag(sW)*inv(L)*inv(L')*diag(sW)
    eigen_A=MatrixXd::Identity(len, len)-eigen_V.transpose()*eigen_U;

    m_Sigma=CMatrixOperations::get_inverse(m_L, m_ktrtr, m_sW, m_V, CMath::exp(m_log_scale));
    Map<MatrixXd> eigen_Sigma(m_Sigma.matrix, m_Sigma.num_rows, m_Sigma.num_cols);

    Map<VectorXd> eigen_dnlz_alpha(gradient.vector, len);
    Map<VectorXd> eigen_dnlz_log_neg_lambda(gradient.vector+len, len);

    //dlZ_alpha  = K*(df-alpha);
    eigen_dnlz_alpha=eigen_K*CMath::exp(m_log_scale*2.0)*(-eigen_df+eigen_alpha);

    //dlZ_lambda = 2*(Sigma.*Sigma)*dV +v -sum(Sigma.*A,2);   % => fast diag(V*VinvK')
    //dlZ_log_neg_lambda = dlZ_lambda .* lambda;
    //dnlZ = -[dlZ_alpha; dlZ_log_neg_lambda];
    eigen_dnlz_log_neg_lambda=(eigen_Sigma.array().pow(2)*2.0).matrix()*eigen_dv+eigen_s2;
    eigen_dnlz_log_neg_lambda=eigen_dnlz_log_neg_lambda-(eigen_Sigma.array()*eigen_A.array()).rowwise().sum().matrix();
    eigen_dnlz_log_neg_lambda=(eigen_log_neg_lambda.array().exp()*eigen_dnlz_log_neg_lambda.array()).matrix();
}


float64_t CKLCovarianceInferenceMethod::get_negative_log_marginal_likelihood_helper()
{
    Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);
    Map<VectorXd> eigen_alpha(m_alpha.vector, m_alpha.vlen/2);
    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
    SGVector<float64_t> mean=m_mean->get_mean_vector(m_features);
    Map<VectorXd> eigen_mean(mean.vector, mean.vlen);

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

    float64_t trace=0;
    //L_inv=L\eye(n);
    //trace(L_inv'*L_inv)   %V*inv(K)
    MatrixXd eigen_t=eigen_L.triangularView<Upper>().adjoint().solve(MatrixXd::Identity(eigen_L.rows(),eigen_L.cols()));

    for(index_t idx=0; idx<eigen_t.rows(); idx++)
        trace +=(eigen_t.col(idx).array().pow(2)).sum();

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

float64_t CKLCovarianceInferenceMethod::get_derivative_related_cov(SGMatrix<float64_t> dK)
{
    Map<MatrixXd> eigen_dK(dK.matrix, dK.num_rows, dK.num_cols);
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
    Map<VectorXd> eigen_W(m_W.vector, m_W.vlen);
    Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);
    Map<VectorXd> eigen_sW(m_sW.vector, m_sW.vlen);
    Map<MatrixXd> eigen_Sigma(m_Sigma.matrix, m_Sigma.num_rows, m_Sigma.num_cols);
    Map<VectorXd> eigen_alpha(m_alpha.vector, m_alpha.vlen/2);
    Map<MatrixXd> eigen_A(m_A.matrix, m_A.num_rows, m_A.num_cols);

    Map<VectorXd> eigen_dv(m_dv.vector, m_dv.vlen);
    Map<VectorXd> eigen_df(m_df.vector, m_df.vlen);

    //AdK = A*dK;
    MatrixXd AdK=eigen_A*eigen_dK;

    //z = diag(AdK) + sum(A.*AdK,2) - sum(A'.*AdK,1)';
    VectorXd z=AdK.diagonal()+(eigen_A.array()*AdK.array()).rowwise().sum().matrix()
        -(eigen_A.transpose().array()*AdK.array()).colwise().sum().transpose().matrix();

    //dnlZ(j) = alpha'*dK*(alpha/2-df) - z'*dv;
    return eigen_alpha.dot(eigen_dK*(eigen_alpha/2.0-eigen_df))-z.dot(eigen_dv);
}

void CKLCovarianceInferenceMethod::update_alpha()
{
    float64_t nlml_new=0;
    float64_t nlml_def=0;

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

    if (m_alpha.vlen == m_labels->get_num_labels()*2)
    {
        nlml_new=get_negative_log_marginal_likelihood_helper();

        float64_t trace=0;
        LLT<MatrixXd> llt((eigen_K*CMath::exp(m_log_scale*2.0))+
            MatrixXd::Identity(eigen_K.rows(), eigen_K.cols()));
        MatrixXd LL=llt.matrixU();
        MatrixXd tt=LL.triangularView<Upper>().adjoint().solve(MatrixXd::Identity(LL.rows(),LL.cols()));

        for(index_t idx=0; idx<tt.rows(); idx++)
            trace+=(tt.col(idx).array().pow(2)).sum();

        MatrixXd eigen_V=LL.triangularView<Upper>().adjoint().solve(eigen_K*CMath::exp(m_log_scale*2.0));
        SGVector<float64_t> s2_tmp(m_s2.vlen);
        Map<VectorXd> eigen_s2(s2_tmp.vector, s2_tmp.vlen);
        eigen_s2=(eigen_K.diagonal().array()*CMath::exp(m_log_scale*2.0)-(eigen_V.array().pow(2).colwise().sum().transpose())).abs().matrix();
        SGVector<float64_t> mean=m_mean->get_mean_vector(m_features);

        CVariationalGaussianLikelihood * lik=get_variational_likelihood();
        lik->set_variational_distribution(mean, s2_tmp, m_labels);
        float64_t a=SGVector<float64_t>::sum(lik->get_variational_expection());

        nlml_def=-a+LL.diagonal().array().log().sum();
        nlml_def+=0.5*(-eigen_K.rows()+trace);

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

    if (m_alpha.vlen != m_labels->get_num_labels()*2 || nlml_def<nlml_new)
    {
        if(m_alpha.vlen != m_labels->get_num_labels()*2)
            m_alpha = SGVector<float64_t>(m_labels->get_num_labels()*2);

        //init
        for (index_t i=0; i<m_alpha.vlen; i++)
        {
            if (i<m_alpha.vlen/2)
                m_alpha[i]=0;
            else
                m_alpha[i]=CMath::log(0.5);
        }

        index_t len=m_alpha.vlen/2;
        m_W=SGVector<float64_t>(len);
        m_sW=SGVector<float64_t>(len);
        m_mu=SGVector<float64_t>(len);
        m_s2=SGVector<float64_t>(len);
        m_V=SGMatrix<float64_t>(len, len);
        m_Sigma=SGMatrix<float64_t>(len, len);
        m_A=SGMatrix<float64_t>(len, len);
    }

    nlml_new=optimization();
}

SGVector<float64_t> CKLCovarianceInferenceMethod::get_diagonal_vector()
{
    if (parameter_hash_changed())
        update();

    return SGVector<float64_t>(m_sW);
}

void CKLCovarianceInferenceMethod::update_deriv()
{
}

void CKLCovarianceInferenceMethod::update_chol()
{
}

void CKLCovarianceInferenceMethod::update_approx_cov()
{
}

} /* namespace shogun */