GaussianLikelihood.cpp

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/*
 * Copyright (c) The Shogun Machine Learning Toolbox
 * Written (W) 2013 Roman Votyakov
 * Written (W) 2012 Jacob Walker
 * All rights reserved.
 *
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 * modification, are permitted provided that the following conditions are met:
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 *    list of conditions and the following disclaimer.
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 *    this list of conditions and the following disclaimer in the documentation
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 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
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#include <shogun/machine/gp/GaussianLikelihood.h>


#include <shogun/labels/RegressionLabels.h>
#include <shogun/mathematics/eigen3.h>

using namespace shogun;
using namespace Eigen;

CGaussianLikelihood::CGaussianLikelihood() : CLikelihoodModel()
{
    init();
}

CGaussianLikelihood::CGaussianLikelihood(float64_t sigma) : CLikelihoodModel()
{
    init();
    set_sigma(sigma);
}

void CGaussianLikelihood::init()
{
    m_log_sigma=0.0;
    SG_ADD(&m_log_sigma, "log_sigma", "Observation noise in log domain", MS_AVAILABLE, GRADIENT_AVAILABLE);
}

CGaussianLikelihood::~CGaussianLikelihood()
{
}

CGaussianLikelihood* CGaussianLikelihood::obtain_from_generic(
        CLikelihoodModel* lik)
{
    ASSERT(lik!=NULL);

    if (lik->get_model_type()!=LT_GAUSSIAN)
        SG_SERROR("Provided likelihood is not of type CGaussianLikelihood!\n")

    SG_REF(lik);
    return (CGaussianLikelihood*)lik;
}

SGVector<float64_t> CGaussianLikelihood::get_predictive_means(
        SGVector<float64_t> mu, SGVector<float64_t> s2, const CLabels* lab) const
{
    return SGVector<float64_t>(mu);
}

SGVector<float64_t> CGaussianLikelihood::get_predictive_variances(
        SGVector<float64_t> mu, SGVector<float64_t> s2, const CLabels* lab) const
{
    SGVector<float64_t> result(s2);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    eigen_result=eigen_result.array()+CMath::exp(m_log_sigma*2.0);

    return result;
}

SGVector<float64_t> CGaussianLikelihood::get_log_probability_f(const CLabels* lab,
        SGVector<float64_t> func) const
{
    // check the parameters
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")
    REQUIRE(lab->get_num_labels()==func.vlen, "Number of labels must match "
            "length of the function vector\n")

    Map<VectorXd> eigen_f(func.vector, func.vlen);

    SGVector<float64_t> result(func.vlen);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    SGVector<float64_t> y=((CRegressionLabels*)lab)->get_labels();
    Map<VectorXd> eigen_y(y.vector, y.vlen);

    // compute log probability: lp=-(y-f).^2./sigma^2/2-log(2*pi*sigma^2)/2
    eigen_result=eigen_y-eigen_f;
    eigen_result=-eigen_result.cwiseProduct(eigen_result)/(2.0*CMath::exp(m_log_sigma*2.0))-
        VectorXd::Ones(result.vlen)*log(2.0*CMath::PI*CMath::exp(m_log_sigma*2.0))/2.0;

    return result;
}

SGVector<float64_t> CGaussianLikelihood::get_log_probability_derivative_f(
        const CLabels* lab, SGVector<float64_t> func, index_t i) const
{
    // check the parameters
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")
    REQUIRE(lab->get_num_labels()==func.vlen, "Number of labels must match "
            "length of the function vector\n")
    REQUIRE(i>=1 && i<=3, "Index for derivative should be 1, 2 or 3\n")

    Map<VectorXd> eigen_f(func.vector, func.vlen);

    SGVector<float64_t> result(func.vlen);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    SGVector<float64_t> y=((CRegressionLabels*)lab)->get_labels();
    Map<VectorXd> eigen_y(y.vector, y.vlen);

    // set result=y-f
    eigen_result=eigen_y-eigen_f;

    // compute derivatives of log probability wrt f
    if (i == 1)
        eigen_result/=CMath::exp(m_log_sigma*2.0);
    else if (i == 2)
        eigen_result=-VectorXd::Ones(result.vlen)/CMath::exp(m_log_sigma*2.0);
    else if (i == 3)
        eigen_result=VectorXd::Zero(result.vlen);

    return result;
}

SGVector<float64_t> CGaussianLikelihood::get_first_derivative(const CLabels* lab,
        SGVector<float64_t> func, const TParameter* param) const
{
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")
    REQUIRE(lab->get_num_labels()==func.vlen, "Number of labels must match "
            "length of the function vector\n")

    Map<VectorXd> eigen_f(func.vector, func.vlen);

    SGVector<float64_t> result(func.vlen);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    if (strcmp(param->m_name, "log_sigma"))
        return SGVector<float64_t>();

    SGVector<float64_t> y=((CRegressionLabels*)lab)->get_labels();
    Map<VectorXd> eigen_y(y.vector, y.vlen);

    // compute derivative of log probability wrt log_sigma:
    // dlp_dlogsigma
    // lp_dsigma=(y-f).^2/sigma^2-1
    eigen_result=eigen_y-eigen_f;
    eigen_result=eigen_result.cwiseProduct(eigen_result)/CMath::exp(m_log_sigma*2.0);
    eigen_result-=VectorXd::Ones(result.vlen);

    return result;
}

SGVector<float64_t> CGaussianLikelihood::get_second_derivative(const CLabels* lab,
        SGVector<float64_t> func, const TParameter* param) const
{
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")
    REQUIRE(lab->get_num_labels()==func.vlen, "Number of labels must match "
            "length of the function vector\n")

    if (strcmp(param->m_name, "log_sigma"))
        return SGVector<float64_t>();

    Map<VectorXd> eigen_f(func.vector, func.vlen);

    SGVector<float64_t> result(func.vlen);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    SGVector<float64_t> y=((CRegressionLabels*)lab)->get_labels();
    Map<VectorXd> eigen_y(y.vector, y.vlen);

    // compute derivative of (the first log_sigma derivative of log probability) wrt f:
    // d2lp_dlogsigma_df == d2lp_df_dlogsigma
    // dlp_dsigma=2*(f-y)/sigma^2
    eigen_result=2.0*(eigen_f-eigen_y)/CMath::exp(m_log_sigma*2.0);

    return result;
}

SGVector<float64_t> CGaussianLikelihood::get_third_derivative(const CLabels* lab,
        SGVector<float64_t> func, const TParameter* param) const
{
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")
    REQUIRE(lab->get_num_labels()==func.vlen, "Number of labels must match "
            "length of the function vector\n")

    if (strcmp(param->m_name, "log_sigma"))
        return SGVector<float64_t>();

    Map<VectorXd> eigen_f(func.vector, func.vlen);

    SGVector<float64_t> result(func.vlen);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    // compute derivative of (the derivative of the first log_sigma derivative of log probability) wrt f:
    // d3lp_dlogsigma_df_df == d3lp_df_df_dlogsigma
    // d2lp_dsigma=2/sigma^2
    eigen_result=2.0*VectorXd::Ones(result.vlen)/CMath::exp(m_log_sigma*2.0);

    return result;
}

SGVector<float64_t> CGaussianLikelihood::get_log_zeroth_moments(
        SGVector<float64_t> mu, SGVector<float64_t> s2, const CLabels *lab) const
{
    SGVector<float64_t> y;

    if (lab)
    {
        REQUIRE((mu.vlen==s2.vlen) && (mu.vlen==lab->get_num_labels()),
                "Length of the vector of means (%d), length of the vector of "
                "variances (%d) and number of labels (%d) should be the same\n",
                mu.vlen, s2.vlen, lab->get_num_labels())
        REQUIRE(lab->get_label_type()==LT_REGRESSION,
                "Labels must be type of CRegressionLabels\n")

        y=((CRegressionLabels*)lab)->get_labels();
    }
    else
    {
        REQUIRE(mu.vlen==s2.vlen, "Length of the vector of means (%d) and "
                "length of the vector of variances (%d) should be the same\n",
                mu.vlen, s2.vlen)

        y=SGVector<float64_t>(mu.vlen);
        y.set_const(1.0);
    }

    // create eigen representation of y, mu and s2
    Map<VectorXd> eigen_mu(mu.vector, mu.vlen);
    Map<VectorXd> eigen_s2(s2.vector, s2.vlen);
    Map<VectorXd> eigen_y(y.vector, y.vlen);

    SGVector<float64_t> result(mu.vlen);
    Map<VectorXd> eigen_result(result.vector, result.vlen);

    // compule lZ=-(y-mu).^2./(sn2+s2)/2-log(2*pi*(sn2+s2))/2
    eigen_s2=eigen_s2.array()+CMath::exp(m_log_sigma*2.0);
    eigen_result=-(eigen_y-eigen_mu).array().square()/(2.0*eigen_s2.array())-
        (2.0*CMath::PI*eigen_s2.array()).log()/2.0;

    return result;
}

float64_t CGaussianLikelihood::get_first_moment(SGVector<float64_t> mu,
        SGVector<float64_t> s2, const CLabels *lab, index_t i) const
{
    // check the parameters
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE((mu.vlen==s2.vlen) && (mu.vlen==lab->get_num_labels()),
            "Length of the vector of means (%d), length of the vector of "
            "variances (%d) and number of labels (%d) should be the same\n",
            mu.vlen, s2.vlen, lab->get_num_labels())
    REQUIRE(i>=0 && i<=mu.vlen, "Index (%d) out of bounds!\n", i)
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")

    SGVector<float64_t> y=((CRegressionLabels*)lab)->get_labels();

    // compute 1st moment
    float64_t Ex=mu[i]+s2[i]*(y[i]-mu[i])/(CMath::exp(m_log_sigma*2.0)+s2[i]);

    return Ex;
}

float64_t CGaussianLikelihood::get_second_moment(SGVector<float64_t> mu,
        SGVector<float64_t> s2, const CLabels *lab, index_t i) const
{
    // check the parameters
    REQUIRE(lab, "Labels are required (lab should not be NULL)\n")
    REQUIRE((mu.vlen==s2.vlen) && (mu.vlen==lab->get_num_labels()),
            "Length of the vector of means (%d), length of the vector of "
            "variances (%d) and number of labels (%d) should be the same\n",
            mu.vlen, s2.vlen, lab->get_num_labels())
    REQUIRE(i>=0 && i<=mu.vlen, "Index (%d) out of bounds!\n", i)
    REQUIRE(lab->get_label_type()==LT_REGRESSION,
            "Labels must be type of CRegressionLabels\n")

    // compute 2nd moment
    float64_t Var=s2[i]-CMath::sq(s2[i])/(CMath::exp(m_log_sigma*2.0)+s2[i]);

    return Var;
}