KLDualInferenceMethod.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
 * Mohammad Emtiyaz Khan, Aleksandr Y. Aravkin, Michael P. Friedlander, Matthias Seeger
 * Fast Dual Variational Inference for Non-Conjugate Latent Gaussian Models. ICML2013*
 *
 * This code specifically adapted from function in approxKL.m and infKL.m
 */

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

#ifdef HAVE_EIGEN3
#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/Math.h>
#include <shogun/machine/gp/MatrixOperations.h>
#include <shogun/machine/gp/DualVariationalGaussianLikelihood.h>
#include <shogun/labels/BinaryLabels.h>

using namespace Eigen;

namespace shogun
{

CKLDualInferenceMethod::CKLDualInferenceMethod() : CKLInferenceMethod()
{
    init();
}

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

CKLDualInferenceMethod* CKLDualInferenceMethod::obtain_from_generic(
        CInferenceMethod* inference)
{
    if (inference==NULL)
        return NULL;

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

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

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

    SGVector<float64_t> result(m_alpha);
    return result;
}

CKLDualInferenceMethod::~CKLDualInferenceMethod()
{
}

void CKLDualInferenceMethod::check_dual_inference(CLikelihoodModel* mod) const
{
    CDualVariationalGaussianLikelihood * lik=dynamic_cast<CDualVariationalGaussianLikelihood *>(mod);
    REQUIRE(lik,
        "The provided likelihood model is not a variational dual Likelihood model.\n");
}

void CKLDualInferenceMethod::set_model(CLikelihoodModel* mod)
{
    check_dual_inference(mod);
    CKLInferenceMethod::set_model(mod);
}

CDualVariationalGaussianLikelihood* CKLDualInferenceMethod::get_dual_variational_likelihood() const
{
    check_dual_inference(m_model);
    CDualVariationalGaussianLikelihood * lik=dynamic_cast<CDualVariationalGaussianLikelihood *>(m_model);
    return lik;
}

void CKLDualInferenceMethod::init()
{
    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);
    SG_ADD(&m_is_dual_valid, "is_dual_valid",
        "whether the lambda (m_W) is valid or not",
        MS_NOT_AVAILABLE);
    m_is_dual_valid=false;
}

bool CKLDualInferenceMethod::lbfgs_precompute()
{
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);
    CDualVariationalGaussianLikelihood *lik= get_dual_variational_likelihood();
    Map<VectorXd> eigen_W(m_W.vector, m_W.vlen);

    lik->set_dual_parameters(m_W, m_labels);
    m_is_dual_valid=lik->dual_parameters_valid();

    if (!m_is_dual_valid)
        return false;

    //construct alpha
    m_alpha=lik->get_mu_dual_parameter();
    Map<VectorXd> eigen_alpha(m_alpha.vector, m_alpha.vlen);
    eigen_alpha=-eigen_alpha;

    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)+diag(W))=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();

    //construct mu
    SGVector<float64_t> mean=m_mean->get_mean_vector(m_features);
    Map<VectorXd> eigen_mean(mean.vector, mean.vlen);
    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;
    return true;
}

float64_t CKLDualInferenceMethod::get_dual_objective_wrt_parameters()
{
    if (!m_is_dual_valid)
        return CMath::INFTY;

    SGVector<float64_t> mean=m_mean->get_mean_vector(m_features);
    Map<VectorXd> eigen_mean(mean.vector, mean.vlen);
    Map<VectorXd> eigen_mu(m_mu.vector, m_mu.vlen);
    Map<VectorXd> eigen_alpha(m_alpha.vector, m_alpha.vlen);
    Map<MatrixXd> eigen_L(m_L.matrix, m_L.num_rows, m_L.num_cols);

    CDualVariationalGaussianLikelihood *lik= get_dual_variational_likelihood();

    float64_t a=SGVector<float64_t>::sum(lik->get_dual_objective_value());
    float64_t result=0.5*eigen_alpha.dot(eigen_mu-eigen_mean)+a;
    result+=eigen_mean.dot(eigen_alpha);
    result-=eigen_L.diagonal().array().log().sum();

    return result;
}

void CKLDualInferenceMethod::get_gradient_of_dual_objective_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);

    if (!m_is_dual_valid)
        return;

    Map<VectorXd> eigen_gradient(gradient.vector, gradient.vlen);

    CDualVariationalGaussianLikelihood *lik= get_dual_variational_likelihood();

    TParameter* lambda_param=lik->m_parameters->get_parameter("lambda");
    SGVector<float64_t>d_lambda=lik->get_dual_first_derivative(lambda_param);
    Map<VectorXd> eigen_d_lambda(d_lambda.vector, d_lambda.vlen);

    Map<VectorXd> eigen_mu(m_mu.vector, m_mu.vlen);
    Map<VectorXd> eigen_s2(m_s2.vector, m_s2.vlen);

    eigen_gradient=-eigen_mu-0.5*eigen_s2+eigen_d_lambda;
}

float64_t CKLDualInferenceMethod::get_nlml_wrapper(SGVector<float64_t> alpha, SGVector<float64_t> mu, SGMatrix<float64_t> L)
{
    Map<MatrixXd> eigen_L(L.matrix, L.num_rows, L.num_cols);
    Map<VectorXd> eigen_alpha(alpha.vector, alpha.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_mu(mu.vector, mu.vlen);
    Map<VectorXd> eigen_mean(mean.vector, mean.vlen);

    CDualVariationalGaussianLikelihood *lik=get_dual_variational_likelihood();

    SGVector<float64_t>lab=((CBinaryLabels*)m_labels)->get_labels();
    Map<VectorXd> eigen_lab(lab.vector, lab.vlen);

    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 CKLDualInferenceMethod::get_negative_log_marginal_likelihood_helper()
{
    CDualVariationalGaussianLikelihood *lik=get_dual_variational_likelihood();
    bool status = lik->set_variational_distribution(m_mu, m_s2, m_labels);
    if (status)
        return get_nlml_wrapper(m_alpha, m_mu, m_L);
    return CMath::NOT_A_NUMBER;
}

float64_t CKLDualInferenceMethod::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);

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

    index_t len=m_W.vlen;
    //U=inv(L')*diag(sW)
    MatrixXd eigen_U=eigen_L.triangularView<Upper>().adjoint().solve(MatrixXd(eigen_sW.asDiagonal()));
    //A=I-K*diag(sW)*inv(L)*inv(L')*diag(sW)
    Map<MatrixXd> eigen_V(m_V.matrix, m_V.num_rows, m_V.num_cols);
    MatrixXd eigen_A=MatrixXd::Identity(len, len)-eigen_V.transpose()*eigen_U;

    //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();

    float64_t result=eigen_alpha.dot(eigen_dK*(eigen_alpha/2.0-eigen_df))-z.dot(eigen_dv);

    return result;
}

void CKLDualInferenceMethod::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);
    CDualVariationalGaussianLikelihood *lik= get_dual_variational_likelihood();

    if (m_alpha.vlen == m_labels->get_num_labels())
    {
        nlml_new=get_negative_log_marginal_likelihood_helper();
        index_t len=m_labels->get_num_labels();
        SGVector<float64_t> W_tmp(len);
        Map<VectorXd> eigen_W(W_tmp.vector, W_tmp.vlen);
        eigen_W.fill(0.5);
        SGVector<float64_t> sW_tmp(len);
        Map<VectorXd> eigen_sW(sW_tmp.vector, sW_tmp.vlen);
        eigen_sW=eigen_W.array().sqrt().matrix();
        SGMatrix<float64_t> L_tmp=CMatrixOperations::get_choleksy(W_tmp, sW_tmp, m_ktrtr, CMath::exp(m_log_scale*2.0));
        Map<MatrixXd> eigen_L(L_tmp.matrix, L_tmp.num_rows, L_tmp.num_cols);

        lik->set_dual_parameters(W_tmp, m_labels);

        //construct alpha
        SGVector<float64_t> alpha_tmp=lik->get_mu_dual_parameter();
        Map<VectorXd> eigen_alpha(alpha_tmp.vector, alpha_tmp.vlen);
        eigen_alpha=-eigen_alpha;
        //construct mu
        SGVector<float64_t> mean=m_mean->get_mean_vector(m_features);
        Map<VectorXd> eigen_mean(mean.vector, mean.vlen);
        SGVector<float64_t> mu_tmp(len);
        Map<VectorXd> eigen_mu(mu_tmp.vector, mu_tmp.vlen);
        //mu=K*alpha+m
        eigen_mu=eigen_K*CMath::exp(m_log_scale*2.0)*eigen_alpha+eigen_mean;
        //construct s2
        MatrixXd eigen_V=eigen_L.triangularView<Upper>().adjoint().solve(eigen_sW.asDiagonal()*eigen_K*CMath::exp(m_log_scale*2.0));
        SGVector<float64_t> s2_tmp(len);
        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();

        lik->set_variational_distribution(mu_tmp, s2_tmp, m_labels);

        nlml_def=get_nlml_wrapper(alpha_tmp, mu_tmp, L_tmp);

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

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

        index_t len=m_alpha.vlen;

        m_W=SGVector<float64_t>(len);
        for (index_t i=0; i<m_W.vlen; i++)
            m_W[i]=0.5;

        lik->set_dual_parameters(m_W, m_labels);
        m_sW=SGVector<float64_t>(len);
        m_mu=SGVector<float64_t>(len);
        m_s2=SGVector<float64_t>(len);
        m_Sigma=SGMatrix<float64_t>(len, len);
        m_V=SGMatrix<float64_t>(len, len);
    }

    nlml_new=lbfgs_optimization();
    lik->set_variational_distribution(m_mu, m_s2, m_labels);
    TParameter* s2_param=lik->m_parameters->get_parameter("sigma2");
    m_dv=lik->get_variational_first_derivative(s2_param);
    TParameter* mu_param=lik->m_parameters->get_parameter("mu");
    m_df=lik->get_variational_first_derivative(mu_param);
}

float64_t CKLDualInferenceMethod::adjust_step(void *obj,
    const float64_t *parameters, const float64_t *direction,
    const int dim, const float64_t step)
{
    /* Note that parameters = parameters_pre_iter - step * gradient_pre_iter */
    CKLDualInferenceMethod * obj_prt
        = static_cast<CKLDualInferenceMethod *>(obj);

    ASSERT(obj_prt != NULL);

    float64_t *non_const_direction=const_cast<float64_t *>(direction);
    SGVector<float64_t> sg_direction(non_const_direction, dim, false);

    CDualVariationalGaussianLikelihood* lik= obj_prt->get_dual_variational_likelihood();

    float64_t adjust_stp=lik->adjust_step_wrt_dual_parameter(sg_direction, step);
    return adjust_stp;
}

float64_t CKLDualInferenceMethod::evaluate(void *obj, const float64_t *parameters,
    float64_t *gradient, const int dim, const float64_t step)
{
    /* Note that parameters = parameters_pre_iter - step * gradient_pre_iter */
    CKLDualInferenceMethod * obj_prt
        = static_cast<CKLDualInferenceMethod *>(obj);

    ASSERT(obj_prt != NULL);

    bool status=obj_prt->lbfgs_precompute();
    if (status)
    {
        float64_t nlml=obj_prt->get_dual_objective_wrt_parameters();

        SGVector<float64_t> sg_gradient(gradient, dim, false);
        Map<VectorXd> eigen_g(sg_gradient.vector, sg_gradient.vlen);
        obj_prt->get_gradient_of_dual_objective_wrt_parameters(sg_gradient);

        return nlml;
    }
    return CMath::NOT_A_NUMBER;
}

float64_t CKLDualInferenceMethod::lbfgs_optimization()
{
    lbfgs_parameter_t lbfgs_param;
    lbfgs_param.m = m_m;
    lbfgs_param.max_linesearch = m_max_linesearch;
    lbfgs_param.linesearch = m_linesearch;
    lbfgs_param.max_iterations = m_max_iterations;
    lbfgs_param.delta = m_delta;
    lbfgs_param.past = m_past;
    lbfgs_param.epsilon = m_epsilon;
    lbfgs_param.min_step = m_min_step;
    lbfgs_param.max_step = m_max_step;
    lbfgs_param.ftol = m_ftol;
    lbfgs_param.wolfe = m_wolfe;
    lbfgs_param.gtol = m_gtol;
    lbfgs_param.xtol = m_xtol;
    lbfgs_param.orthantwise_c = m_orthantwise_c;
    lbfgs_param.orthantwise_start = m_orthantwise_start;
    lbfgs_param.orthantwise_end = m_orthantwise_end;

    float64_t nlml_opt=0;
    void * obj_prt = static_cast<void *>(this);

    Map<VectorXd> eigen_W(m_W.vector, m_W.vlen);
    lbfgs(m_W.vlen, m_W.vector, &nlml_opt,
        CKLDualInferenceMethod::evaluate,
        NULL, obj_prt, &lbfgs_param, CKLDualInferenceMethod::adjust_step);
    return nlml_opt;
}

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

    return SGVector<float64_t>(m_sW);
}

void CKLDualInferenceMethod::update_deriv()
{
    /* get_derivative_related_cov(MatrixXd eigen_dK) does the similar job
     * Therefore, this function body is empty
     */
}

void CKLDualInferenceMethod::update_chol()
{
    /* L is automatically updated when update_alpha is called
     * Therefore, this function body is empty
     */
}

void CKLDualInferenceMethod::update_approx_cov()
{
    m_Sigma=CMatrixOperations::get_inverse(m_L, m_ktrtr, m_sW, m_V, CMath::exp(m_log_scale));
}

} /* namespace shogun */

#endif /* HAVE_EIGEN3 */