LogitLikelihood.cpp

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/*
 * Copyright (c) The Shogun Machine Learning Toolbox
 * Written (W) 2013 Roman Votyakov
 * 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.
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 * either expressed or implied, of the Shogun Development Team.
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 */
#include <shogun/machine/gp/LogitLikelihood.h>


#include <shogun/mathematics/Function.h>
#include <shogun/mathematics/Integration.h>
#include <shogun/labels/BinaryLabels.h>
#include <shogun/mathematics/eigen3.h>

using namespace shogun;
using namespace Eigen;

namespace shogun
{

#ifndef DOXYGEN_SHOULD_SKIP_THIS

class CNormalPDF : public CFunction
{
public:
    CNormalPDF()
    {
        m_mu=0.0;
        m_sigma=1.0;
    }

    CNormalPDF(float64_t mu, float64_t sigma)
    {
        m_mu=mu;
        m_sigma=sigma;
    }

    void set_mu(float64_t mu) { m_mu=mu; }

    void set_sigma(float64_t sigma) { m_sigma=sigma; }

    virtual float64_t operator() (float64_t x)
    {
        return (1.0/(CMath::sqrt(2*CMath::PI)*m_sigma))*
            CMath::exp(-CMath::sq(x-m_mu)/(2.0*CMath::sq(m_sigma)));
    }

private:
    /* mean */
    float64_t m_mu;

    /* standard deviation */
    float64_t m_sigma;
};

class CSigmoidFunction : public CFunction
{
public:
    CSigmoidFunction()
    {
        m_a=0.0;
    }

    CSigmoidFunction(float64_t a)
    {
        m_a=a;
    }

    void set_a(float64_t a) { m_a=a; }

    virtual float64_t operator() (float64_t x)
    {
        return 1.0/(1.0+CMath::exp(-m_a*x));
    }

private:
    float64_t m_a;
};

class CProductFunction : public CFunction
{
public:
    CProductFunction(CFunction* f, CFunction* g)
    {
        SG_REF(f);
        SG_REF(g);
        m_f=f;
        m_g=g;
    }

    virtual ~CProductFunction()
    {
        SG_UNREF(m_f);
        SG_UNREF(m_g);
    }

    virtual float64_t operator() (float64_t x)
    {
        return (*m_f)(x)*(*m_g)(x);
    }

private:
    CFunction* m_f;
    CFunction* m_g;
};

class CLinearFunction : public CFunction
{
public:
    CLinearFunction() { }

    virtual ~CLinearFunction() { }

    virtual float64_t operator() (float64_t x)
    {
        return x;
    }
};

class CQuadraticFunction : public CFunction
{
public:
    CQuadraticFunction() { }

    virtual ~CQuadraticFunction() { }

    virtual float64_t operator() (float64_t x)
    {
        return CMath::sq(x);
    }
};

#endif /* DOXYGEN_SHOULD_SKIP_THIS */

CLogitLikelihood::CLogitLikelihood() : CLikelihoodModel()
{
}

CLogitLikelihood::~CLogitLikelihood()
{
}

SGVector<float64_t> CLogitLikelihood::get_predictive_means(
        SGVector<float64_t> mu, SGVector<float64_t> s2, const CLabels* lab) const
{
    SGVector<float64_t> lp=get_log_zeroth_moments(mu, s2, lab);
    Map<VectorXd> eigen_lp(lp.vector, lp.vlen);

    SGVector<float64_t> r(lp.vlen);
    Map<VectorXd> eigen_r(r.vector, r.vlen);

    // evaluate predictive mean: ymu=2*p-1
    // Note that the distribution is Bernoulli distribution with p(x=1)=p and
    // p(x=-1)=(1-p)
    // the mean of the Bernoulli distribution is 2*p-1
    eigen_r=2.0*eigen_lp.array().exp()-1.0;

    return r;
}

SGVector<float64_t> CLogitLikelihood::get_predictive_variances(
        SGVector<float64_t> mu, SGVector<float64_t> s2, const CLabels* lab) const
{
    SGVector<float64_t> lp=get_log_zeroth_moments(mu, s2, lab);
    Map<VectorXd> eigen_lp(lp.vector, lp.vlen);

    SGVector<float64_t> r(lp.vlen);
    Map<VectorXd> eigen_r(r.vector, r.vlen);

    // evaluate predictive variance: ys2=1-(2*p-1).^2
    // Note that the distribution is Bernoulli distribution with p(x=1)=p and
    // p(x=-1)=(1-p)
    // the variance of the Bernoulli distribution is 1-(2*p-1).^2
    eigen_r=1-(2.0*eigen_lp.array().exp()-1.0).square();

    return r;
}

SGVector<float64_t> CLogitLikelihood::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_BINARY,
            "Labels must be type of CBinaryLabels\n")
    REQUIRE(lab->get_num_labels()==func.vlen, "Number of labels must match "
            "length of the function vector\n")

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

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

    SGVector<float64_t> r(func.vlen);
    Map<VectorXd> eigen_r(r.vector, r.vlen);

    // compute log probability: -log(1+exp(-f.*y))
    eigen_r=-(1.0+(-eigen_y.array()*eigen_f.array()).exp()).log();

    return r;
}

SGVector<float64_t> CLogitLikelihood::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_BINARY,
            "Labels must be type of CBinaryLabels\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")

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

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

    SGVector<float64_t> r(func.vlen);
    Map<VectorXd> eigen_r(r.vector, r.vlen);

    // compute s(f)=1./(1+exp(-f))
    VectorXd eigen_s=(VectorXd::Ones(func.vlen)).cwiseQuotient((1.0+
        (-eigen_f).array().exp()).matrix());

    // compute derivatives of log probability wrt f
    if (i == 1)
    {
        // compute the first derivative: dlp=(y+1)/2-s(f)
        eigen_r=(eigen_y.array()+1.0)/2.0-eigen_s.array();
    }
    else if (i == 2)
    {
        // compute the second derivative: d2lp=-s(f).*(1-s(f))
        eigen_r=-eigen_s.array()*(1.0-eigen_s.array());
    }
    else if (i == 3)
    {
        // compute the third derivative: d2lp=-s(f).*(1-s(f)).*(1-2*s(f))
        eigen_r=-eigen_s.array()*(1.0-eigen_s.array())*(1.0-2.0*eigen_s.array());
    }
    else
    {
        SG_ERROR("Invalid index for derivative\n")
    }

    return r;
}

SGVector<float64_t> CLogitLikelihood::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_BINARY,
                "Labels must be type of CBinaryLabels\n")

        y=((CBinaryLabels*)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 an object of normal pdf function
    CNormalPDF* f=new CNormalPDF();

    // create an object of sigmoid function
    CSigmoidFunction* g=new CSigmoidFunction();

    // create an object of product of sigmoid and normal pdf functions
    CProductFunction* h=new CProductFunction(f, g);
    SG_REF(h);

    // compute probabilities using numerical integration
    SGVector<float64_t> r(mu.vlen);

    for (index_t i=0; i<mu.vlen; i++)
    {
        // set normal pdf parameters
        f->set_mu(mu[i]);
        f->set_sigma(CMath::sqrt(s2[i]));

        // set sigmoid parameters
        g->set_a(y[i]);

        // evaluate integral on (-inf, inf)
        r[i]=CIntegration::integrate_quadgk(h, -CMath::INFTY, mu[i])+
            CIntegration::integrate_quadgk(h, mu[i], CMath::INFTY);
    }

    SG_UNREF(h);

    for (index_t i=0; i<r.vlen; i++)
        r[i]=CMath::log(r[i]);

    return r;
}

float64_t CLogitLikelihood::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_BINARY,
            "Labels must be type of CBinaryLabels\n")

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

    // create an object of f(x)=N(x|mu,sigma^2)
    CNormalPDF* f=new CNormalPDF(mu[i], CMath::sqrt(s2[i]));

    // create an object of g(x)=sigmoid(x)
    CSigmoidFunction* g=new CSigmoidFunction(y[i]);

    // create an object of h(x)=N(x|mu,sigma^2)*sigmoid(x)
    CProductFunction* h=new CProductFunction(f, g);

    // create an object of l(x)=x
    CLinearFunction* l=new CLinearFunction();

    // create an object of k(x)=x*N(x|mu,sigma^2)*sigmoid(x)
    CProductFunction* k=new CProductFunction(l, h);
    SG_REF(k);

    // compute Z = \int N(x|mu,sigma)*sigmoid(a*x) dx
    float64_t Z=CIntegration::integrate_quadgk(h, -CMath::INFTY, mu[i])+
        CIntegration::integrate_quadgk(h, mu[i], CMath::INFTY);

    // compute 1st moment: E[x] = Z^-1 * \int x*N(x|mu,sigma)*sigmoid(a*x)dx
    float64_t Ex=(CIntegration::integrate_quadgk(k, -CMath::INFTY, mu[i])+
            CIntegration::integrate_quadgk(k, mu[i], CMath::INFTY))/Z;

    SG_UNREF(k);

    return Ex;
}

float64_t CLogitLikelihood::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_BINARY,
            "Labels must be type of CBinaryLabels\n")

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

    // create an object of f(x)=N(x|mu,sigma^2)
    CNormalPDF* f=new CNormalPDF(mu[i], CMath::sqrt(s2[i]));

    // create an object of g(x)=sigmoid(a*x)
    CSigmoidFunction* g=new CSigmoidFunction(y[i]);

    // create an object of h(x)=N(x|mu,sigma^2)*sigmoid(a*x)
    CProductFunction* h=new CProductFunction(f, g);

    // create an object of l(x)=x
    CLinearFunction* l=new CLinearFunction();

    // create an object of k(x)=x*N(x|mu,sigma^2)*sigmoid(a*x)
    CProductFunction* k=new CProductFunction(l, h);
    SG_REF(k);

    // create an object of q(x)=x^2
    CQuadraticFunction* q=new CQuadraticFunction();

    // create an object of p(x)=x^2*N(x|mu,sigma^2)*sigmoid(x)
    CProductFunction* p=new CProductFunction(q, h);
    SG_REF(p);

    // compute Z = \int N(x|mu,sigma)*sigmoid(a*x) dx
    float64_t Z=CIntegration::integrate_quadgk(h, -CMath::INFTY, mu[i])+
        CIntegration::integrate_quadgk(h, mu[i], CMath::INFTY);

    // compute 1st moment: E[x] = Z^-1 * \int x*N(x|mu,sigma)*sigmoid(a*x)dx
    float64_t Ex=(CIntegration::integrate_quadgk(k, -CMath::INFTY, mu[i])+
            CIntegration::integrate_quadgk(k, mu[i], CMath::INFTY))/Z;

    // compute E[x^2] = Z^-1 * \int x^2*N(x|mu,sigma)*sigmoid(a*x)dx
    float64_t Ex2=(CIntegration::integrate_quadgk(p, -CMath::INFTY, mu[i])+
            CIntegration::integrate_quadgk(p, mu[i], CMath::INFTY))/Z;

    SG_UNREF(k);
    SG_UNREF(p);

    // return 2nd moment: Var[x]=E[x^2]-E[x]^2
    return Ex2-CMath::sq(Ex);;
}
}