malsar_low_rank.cpp

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/*
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or
 * (at your option) any later version.
 *
 * Written (W) 2012 Sergey Lisitsyn
 * Copyright (C) 2012 Jiayu Zhou and Jieping Ye
 */

#include <shogun/lib/malsar/malsar_low_rank.h>
#ifdef HAVE_EIGEN3
#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/Math.h>
#include <iostream>

using namespace Eigen;

namespace shogun
{

malsar_result_t malsar_low_rank(
        CDotFeatures* features,
        double* y,
        double rho,
        const malsar_options& options)
{
    int task;
    int n_feats = features->get_dim_feature_space();
    SG_SDEBUG("n feats = %d\n", n_feats)
    int n_vecs = features->get_num_vectors();
    SG_SDEBUG("n vecs = %d\n", n_vecs)
    int n_tasks = options.n_tasks;
    SG_SDEBUG("n tasks = %d\n", n_tasks)

    int iter = 0;

    // initialize weight vector and bias for each task
    MatrixXd Ws = MatrixXd::Zero(n_feats, n_tasks);
    VectorXd Cs = VectorXd::Zero(n_tasks);
    MatrixXd Wz=Ws, Wzp=Ws, Wz_old=Ws, delta_Wzp=Ws, gWs=Ws;
    VectorXd Cz=Cs, Czp=Cs, Cz_old=Cs, delta_Czp=Cs, gCs=Cs;

    double t=1, t_old=0;
    double gamma=1, gamma_inc=2;
    double obj=0.0, obj_old=0.0;

    double rho_L2 = 0.0;

    //internal::set_is_malloc_allowed(false);
    bool done = false;
    while (!done && iter <= options.max_iter)
    {
        double alpha = double(t_old - 1)/t;

        // compute search point
        Ws = (1+alpha)*Wz - alpha*Wz_old;
        Cs = (1+alpha)*Cz - alpha*Cz_old;

        // zero gradient
        gWs.setZero();
        gCs.setZero();

        // compute gradient and objective at search point
        double Fs = 0;
        for (task=0; task<n_tasks; task++)
        {
            SGVector<index_t> task_idx = options.tasks_indices[task];
            int n_task_vecs = task_idx.vlen;
            for (int i=0; i<n_task_vecs; i++)
            {
                double aa = -y[task_idx[i]]*(features->dense_dot(task_idx[i], Ws.col(task).data(), n_feats)+Cs[task]);
                double bb = CMath::max(aa,0.0);

                // avoid underflow when computing exponential loss
                Fs += (CMath::log(CMath::exp(-bb) + CMath::exp(aa-bb)) + bb)/n_task_vecs;
                double b = -y[task_idx[i]]*(1 - 1/(1+CMath::exp(aa)))/n_task_vecs;

                gCs[task] += b;
                features->add_to_dense_vec(b, task_idx[i], gWs.col(task).data(), n_feats);
            }
        }
        gWs.noalias() += 2*rho_L2*Ws;
        //SG_SDEBUG("gWs=%f\n",gWs.squaredNorm())

        // add regularizer
        Fs += rho_L2*Ws.squaredNorm();

        double Fzp = 0.0;

        int inner_iter = 0;
        // line search, Armijo-Goldstein scheme
        while (inner_iter <= 1000)
        {
            // compute trace projection of Ws - gWs/gamma with 2*rho/gamma
            //internal::set_is_malloc_allowed(true);
            Wzp.setZero();
            JacobiSVD<MatrixXd> svd((Ws - gWs/gamma).transpose(),ComputeThinU | ComputeThinV);
            for (int i=0; i<svd.singularValues().size(); i++)
            {
                if (svd.singularValues()[i] > rho/gamma)
                    Wzp += (svd.matrixU().col(i)*
                           svd.singularValues()[i]*
                           svd.matrixV().col(i).transpose()).transpose();
            }
            //internal::set_is_malloc_allowed(false);
            // walk in direction of antigradient
            Czp = Cs - gCs/gamma;

            // compute objective at line search point
            Fzp = 0.0;
            for (task=0; task<n_tasks; task++)
            {
                SGVector<index_t> task_idx = options.tasks_indices[task];
                int n_task_vecs = task_idx.vlen;
                for (int i=0; i<n_task_vecs; i++)
                {
                    double aa = -y[task_idx[i]]*(features->dense_dot(task_idx[i], Wzp.col(task).data(), n_feats)+Czp[task]);
                    double bb = CMath::max(aa,0.0);

                    Fzp += (CMath::log(CMath::exp(-bb) + CMath::exp(aa-bb)) + bb)/n_task_vecs;
                }
            }
            Fzp += rho_L2*Wzp.squaredNorm();

            // compute delta between line search point and search point
            delta_Wzp = Wzp - Ws;
            delta_Czp = Czp - Cs;

            // norms of delta
            double nrm_delta_Wzp = delta_Wzp.squaredNorm();
            double nrm_delta_Czp = delta_Czp.squaredNorm();

            double r_sum = (nrm_delta_Wzp + nrm_delta_Czp)/2;

            double Fzp_gamma = Fs + (delta_Wzp.transpose()*gWs).trace() +
                (delta_Czp.transpose()*gCs).trace() +
                (gamma/2)*nrm_delta_Wzp +
                (gamma/2)*nrm_delta_Czp;

            // break if delta is getting too small
            if (r_sum <= 1e-20)
            {
                done = true;
                break;
            }

            // break if objective at line search point is smaller than Fzp_gamma
            if (Fzp <= Fzp_gamma)
                break;
            else
                gamma *= gamma_inc;
        }

        Wz_old = Wz;
        Cz_old = Cz;
        Wz = Wzp;
        Cz = Czp;

        // compute objective value
        obj_old = obj;
        obj = Fzp;
        //internal::set_is_malloc_allowed(true);
        JacobiSVD<MatrixXd> svd(Wzp, EigenvaluesOnly);
        obj += rho*svd.singularValues().sum();
        //internal::set_is_malloc_allowed(false);


        // check if process should be terminated
        switch (options.termination)
        {
            case 0:
                if (iter>=2)
                {
                    if ( CMath::abs(obj-obj_old) <= options.tolerance )
                        done = true;
                }
            break;
            case 1:
                if (iter>=2)
                {
                    if ( CMath::abs(obj-obj_old) <= options.tolerance*CMath::abs(obj_old))
                        done = true;
                }
            break;
            case 2:
                if (CMath::abs(obj) <= options.tolerance)
                    done = true;
            break;
            case 3:
                if (iter>=options.max_iter)
                    done = true;
            break;
        }

        iter++;
        t_old = t;
        t = 0.5 * (1 + CMath::sqrt(1.0 + 4*t*t));
    }
    //internal::set_is_malloc_allowed(true);
    SG_SDEBUG("%d iteration passed, objective = %f\n",iter,obj)

    SGMatrix<float64_t> tasks_w(n_feats, n_tasks);
    for (int i=0; i<n_feats; i++)
    {
        for (task=0; task<n_tasks; task++)
            tasks_w(i,task) = Wzp(i,task);
    }
    SGVector<float64_t> tasks_c(n_tasks);
    for (int i=0; i<n_tasks; i++) tasks_c[i] = Czp[i];
    return malsar_result_t(tasks_w, tasks_c);
};
};
#endif