KLInferenceMethod.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.
 *
 * This code specifically adapted from function in approxKL.m and infKL.m
 */

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

#ifdef HAVE_EIGEN3
#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/Math.h>

using namespace Eigen;

namespace shogun
{

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

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

void CKLInferenceMethod::check_variational_likelihood(CLikelihoodModel* mod) const
{
    REQUIRE(mod, "the likelihood model must not be NULL\n")
    CVariationalGaussianLikelihood* lik= dynamic_cast<CVariationalGaussianLikelihood*>(mod);
    REQUIRE(lik,
        "The provided likelihood model (%s) must support variational Gaussian inference. ",
        "Please use a Variational Gaussian Likelihood model\n",
        mod->get_name());
}

void CKLInferenceMethod::set_model(CLikelihoodModel* mod)
{
    check_variational_likelihood(mod);
    CInferenceMethod::set_model(mod);
}

void CKLInferenceMethod::init()
{
    m_noise_factor=1e-10;
    m_max_attempt=0;
    m_exp_factor=2;
    m_min_coeff_kernel=1e-5;
    SG_ADD(&m_noise_factor, "noise_factor",
        "The noise factor used for correcting Kernel matrix",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_exp_factor, "exp_factor",
        "The exponential factor used for increasing noise_factor",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_max_attempt, "max_attempt",
        "The max number of attempt to correct Kernel matrix",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_min_coeff_kernel, "min_coeff_kernel",
        "The minimum coeefficient of kernel matrix in LDLT factorization used to check whether the kernel matrix is positive definite or not",
        MS_NOT_AVAILABLE);

    set_lbfgs_parameters();
    SG_ADD(&m_m, "m",
        "The number of corrections to approximate the inverse Hessian matrix",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_max_linesearch, "max_linesearch",
        "The maximum number of trials to do line search for each L-BFGS update",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_linesearch, "linesearch",
        "The line search algorithm",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_max_iterations, "max_iterations",
        "The maximum number of iterations for L-BFGS update",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_delta, "delta",
        "Delta for convergence test based on the change of function value",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_past, "past",
        "Distance for delta-based convergence test",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_epsilon, "epsilon",
        "Epsilon for convergence test based on the change of gradient",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_min_step, "min_step",
        "The minimum step of the line search",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_max_step, "max_step",
        "The maximum step of the line search",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_ftol, "ftol",
        "A parameter used in Armijo condition",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_wolfe, "wolfe",
        "A parameter used in curvature condition",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_gtol, "gtol",
        "A parameter used in Morethuente linesearch to control the accuracy",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_xtol, "xtol",
        "The machine precision for floating-point values",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_orthantwise_c, "orthantwise_c",
        "Coeefficient for the L1 norm of variables",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_orthantwise_start, "orthantwise_start",
        "Start index for computing L1 norm of the variables",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_orthantwise_end, "orthantwise_end",
        "End index for computing L1 norm of the variables",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_s2, "s2",
        "Variational parameter sigma2",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_mu, "mu",
        "Variational parameter mu and posterior mean",
        MS_NOT_AVAILABLE);
    SG_ADD(&m_Sigma, "Sigma",
        "Posterior covariance matrix Sigma",
        MS_NOT_AVAILABLE);
}

CKLInferenceMethod::~CKLInferenceMethod()
{
}

void CKLInferenceMethod::compute_gradient()
{
    CInferenceMethod::compute_gradient();

    if (!m_gradient_update)
    {
        update_approx_cov();
        update_deriv();
        m_gradient_update=true;
        update_parameter_hash();
    }
}

void CKLInferenceMethod::update()
{
    SG_DEBUG("entering\n");

    CInferenceMethod::update();
    update_init();
    update_alpha();
    update_chol();
    m_gradient_update=false;
    update_parameter_hash();

    SG_DEBUG("leaving\n");
}

void CKLInferenceMethod::set_noise_factor(float64_t noise_factor)
{
    REQUIRE(noise_factor>=0, "The noise_factor %.20f should be non-negative\n", noise_factor);
    m_noise_factor=noise_factor;
}

void CKLInferenceMethod::set_min_coeff_kernel(float64_t min_coeff_kernel)
{
    REQUIRE(min_coeff_kernel>=0, "The min_coeff_kernel %.20f should be non-negative\n", min_coeff_kernel);
    m_min_coeff_kernel=min_coeff_kernel;
}

void CKLInferenceMethod::set_max_attempt(index_t max_attempt)
{
    REQUIRE(max_attempt>=0, "The max_attempt %d should be non-negative. 0 means inifity attempts\n", max_attempt);
    m_max_attempt=max_attempt;
}

void CKLInferenceMethod::set_exp_factor(float64_t exp_factor)
{
    REQUIRE(exp_factor>1.0, "The exp_factor %f should be greater than 1.0.\n", exp_factor);
    m_exp_factor=exp_factor;
}

void CKLInferenceMethod::update_init()
{
    update_init_helper();
}

Eigen::LDLT<Eigen::MatrixXd> CKLInferenceMethod::update_init_helper()
{
    Map<MatrixXd> eigen_K(m_ktrtr.matrix, m_ktrtr.num_rows, m_ktrtr.num_cols);

    eigen_K=eigen_K+m_noise_factor*MatrixXd::Identity(m_ktrtr.num_rows, m_ktrtr.num_cols);

    Eigen::LDLT<Eigen::MatrixXd> ldlt;
    ldlt.compute(eigen_K*CMath::exp(m_log_scale*2.0));

    float64_t attempt_count=0;
    MatrixXd Kernel_D=ldlt.vectorD();
    float64_t noise_factor=m_noise_factor;

    while (Kernel_D.minCoeff()<=m_min_coeff_kernel)
    {
        if (m_max_attempt>0 && attempt_count>m_max_attempt)
            SG_ERROR("The Kernel matrix is highly non-positive definite since the min_coeff_kernel is less than %.20f",
                " even when adding %.20f noise to the diagonal elements at max %d attempts\n",
                m_min_coeff_kernel, noise_factor, m_max_attempt);
        attempt_count++;
        float64_t pre_noise_factor=noise_factor;
        noise_factor*=m_exp_factor;
        //updat the noise  eigen_K=eigen_K+noise_factor*(m_exp_factor^attempt_count)*Identity()
        eigen_K=eigen_K+(noise_factor-pre_noise_factor)*MatrixXd::Identity(m_ktrtr.num_rows, m_ktrtr.num_cols);
        ldlt.compute(eigen_K*CMath::exp(m_log_scale*2.0));
        Kernel_D=ldlt.vectorD();
    }

    return ldlt;
}


SGVector<float64_t> CKLInferenceMethod::get_posterior_mean()
{
    compute_gradient();

    return SGVector<float64_t>(m_mu);
}

SGMatrix<float64_t> CKLInferenceMethod::get_posterior_covariance()
{
    compute_gradient();

    return SGMatrix<float64_t>(m_Sigma);
}

float64_t CKLInferenceMethod::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 */
    CKLInferenceMethod * obj_prt
        = static_cast<CKLInferenceMethod *>(obj);

    REQUIRE(obj_prt, "The instance object passed to L-BFGS optimizer should not be NULL\n");

    bool status = obj_prt->lbfgs_precompute();
    if (!status)
        return CMath::NOT_A_NUMBER;

    float64_t nlml=obj_prt->get_nlml_wrt_parameters();

    SGVector<float64_t> sg_gradient(gradient, dim, false);
    obj_prt->get_gradient_of_nlml_wrt_parameters(sg_gradient);

    return nlml;
}

CVariationalGaussianLikelihood* CKLInferenceMethod::get_variational_likelihood() const
{
    check_variational_likelihood(m_model);
    CVariationalGaussianLikelihood* lik= dynamic_cast<CVariationalGaussianLikelihood*>(m_model);
    return lik;
}

float64_t CKLInferenceMethod::get_nlml_wrt_parameters()
{
    CVariationalGaussianLikelihood * lik=get_variational_likelihood();
    lik->set_variational_distribution(m_mu, m_s2, m_labels);
    return get_negative_log_marginal_likelihood_helper();
}

void CKLInferenceMethod::set_lbfgs_parameters(
        int m,
        int max_linesearch,
        int linesearch,
        int max_iterations,
        float64_t delta,
        int past,
        float64_t epsilon,
        float64_t min_step,
        float64_t max_step,
        float64_t ftol,
        float64_t wolfe,
        float64_t gtol,
        float64_t xtol,
        float64_t orthantwise_c,
        int orthantwise_start,
        int orthantwise_end)
{
    m_m = m;
    m_max_linesearch = max_linesearch;
    m_linesearch = linesearch;
    m_max_iterations = max_iterations;
    m_delta = delta;
    m_past = past;
    m_epsilon = epsilon;
    m_min_step = min_step;
    m_max_step = max_step;
    m_ftol = ftol;
    m_wolfe = wolfe;
    m_gtol = gtol;
    m_xtol = xtol;
    m_orthantwise_c = orthantwise_c;
    m_orthantwise_start = orthantwise_start;
    m_orthantwise_end = orthantwise_end;
}

float64_t CKLInferenceMethod::get_negative_log_marginal_likelihood()
{
    if (parameter_hash_changed())
        update();

    return get_negative_log_marginal_likelihood_helper();
}

SGVector<float64_t> CKLInferenceMethod::get_derivative_wrt_likelihood_model(const TParameter* param)
{
    CVariationalLikelihood * lik=get_variational_likelihood();
    if (!lik->supports_derivative_wrt_hyperparameter())
        return SGVector<float64_t> ();

    //%lp_dhyp = likKL(v,lik,hyp.lik,y,K*post.alpha+m,[],[],j);
    SGVector<float64_t> lp_dhyp=lik->get_first_derivative_wrt_hyperparameter(param);
    Map<VectorXd> eigen_lp_dhyp(lp_dhyp.vector, lp_dhyp.vlen);
    SGVector<float64_t> result(1);
    //%dnlZ.lik(j) = -sum(lp_dhyp);
    result[0]=-eigen_lp_dhyp.sum();

    return result;
}

SGVector<float64_t> CKLInferenceMethod::get_derivative_wrt_mean(const TParameter* param)
{
    // create eigen representation of K, Z, dfhat and alpha
    Map<VectorXd> eigen_alpha(m_alpha.vector, m_alpha.vlen/2);

    REQUIRE(param, "Param not set\n");
    SGVector<float64_t> result;
    int64_t len=const_cast<TParameter *>(param)->m_datatype.get_num_elements();
    result=SGVector<float64_t>(len);

    for (index_t i=0; i<result.vlen; i++)
    {
        SGVector<float64_t> dmu;

        //%dm_t = feval(mean{:}, hyp.mean, x, j);
        if (result.vlen==1)
            dmu=m_mean->get_parameter_derivative(m_features, param);
        else
            dmu=m_mean->get_parameter_derivative(m_features, param, i);

        Map<VectorXd> eigen_dmu(dmu.vector, dmu.vlen);

        //%dnlZ.mean(j) = -alpha'*dm_t;
        result[i]=-eigen_alpha.dot(eigen_dmu);
    }

    return result;
}

float64_t CKLInferenceMethod::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);
    lbfgs(m_alpha.vlen, m_alpha.vector, &nlml_opt,
        CKLInferenceMethod::evaluate,
        NULL, obj_prt, &lbfgs_param);

    return nlml_opt;
}

SGVector<float64_t> CKLInferenceMethod::get_derivative_wrt_inference_method(const TParameter* param)
{
    REQUIRE(!strcmp(param->m_name, "log_scale"), "Can't compute derivative of "
            "the nagative log marginal likelihood wrt %s.%s parameter\n",
            get_name(), param->m_name)

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

    SGVector<float64_t> result(1);

    result[0]=get_derivative_related_cov(m_ktrtr);
    result[0]*=CMath::exp(m_log_scale*2.0)*2.0;

    return result;
}

SGVector<float64_t> CKLInferenceMethod::get_derivative_wrt_kernel(const TParameter* param)
{
    REQUIRE(param, "Param not set\n");
    SGVector<float64_t> result;
    int64_t len=const_cast<TParameter *>(param)->m_datatype.get_num_elements();
    result=SGVector<float64_t>(len);

    for (index_t i=0; i<result.vlen; i++)
    {
        SGMatrix<float64_t> dK(m_mu.vlen, m_mu.vlen);

        //dK = feval(covfunc{:},hyper,x,j);
        if (result.vlen==1)
            dK=m_kernel->get_parameter_gradient(param);
        else
            dK=m_kernel->get_parameter_gradient(param, i);

        result[i]=get_derivative_related_cov(dK);
        result[i]*=CMath::exp(m_log_scale*2.0);
    }

    return result;
}

SGMatrix<float64_t> CKLInferenceMethod::get_cholesky()
{
    if (parameter_hash_changed())
        update();

    return SGMatrix<float64_t>(m_L);
}

} /* namespace shogun */

#endif /* HAVE_EIGEN3 */