SubGradientLPM.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) 2007-2009 Soeren Sonnenburg
 * Written (W) 2007-2008 Vojtech Franc
 * Copyright (C) 2007-2009 Fraunhofer Institute FIRST and Max-Planck-Society
 */

#include <shogun/lib/config.h>

#ifdef USE_CPLEX

#include <shogun/mathematics/Math.h>
#include <shogun/lib/Signal.h>
#include <shogun/lib/Time.h>
#include <shogun/machine/LinearMachine.h>
#include <shogun/classifier/SubGradientLPM.h>
#include <shogun/classifier/svm/QPBSVMLib.h>
#include <shogun/features/DotFeatures.h>
#include <shogun/labels/Labels.h>

using namespace shogun;

#define DEBUG_SUBGRADIENTLPM

CSubGradientLPM::CSubGradientLPM()
: CLinearMachine(), C1(1), C2(1), epsilon(1e-5), qpsize(42),
    qpsize_max(2000), use_bias(false), delta_active(0), delta_bound(0)
{
}

CSubGradientLPM::CSubGradientLPM(
    float64_t C, CDotFeatures* traindat, CLabels* trainlab)
: CLinearMachine(), C1(C), C2(C), epsilon(1e-5), qpsize(42),
    qpsize_max(2000), use_bias(false), delta_active(0), delta_bound(0)
{
    CLinearMachine::features=traindat;
    CLinearMachine::m_labels=trainlab;
}


CSubGradientLPM::~CSubGradientLPM()
{
    cleanup();
}

int32_t CSubGradientLPM::find_active(
    int32_t num_feat, int32_t num_vec, int32_t& num_active, int32_t& num_bound)
{
    //delta_active=0;
    //num_active=0;
    //num_bound=0;

    //for (int32_t i=0; i<num_vec; i++)
    //{
    //  active[i]=0;

    //  //within margin/wrong side
    //  if (proj[i] < 1-work_epsilon)
    //  {
    //      idx_active[num_active++]=i;
    //      active[i]=1;
    //  }

    //  //on margin
    //  if (CMath::abs(proj[i]-1) <= work_epsilon)
    //  {
    //      idx_bound[num_bound++]=i;
    //      active[i]=2;
    //  }

    //  if (active[i]!=old_active[i])
    //      delta_active++;
    //}

    delta_bound=0;
    delta_active=0;
    num_active=0;
    num_bound=0;

    for (int32_t i=0; i<num_vec; i++)
    {
        active[i]=0;

        //within margin/wrong side
        if (proj[i] < 1-autoselected_epsilon)
        {
            idx_active[num_active++]=i;
            active[i]=1;
        }

        //on margin
        if (CMath::abs(proj[i]-1) <= autoselected_epsilon)
        {
            idx_bound[num_bound++]=i;
            active[i]=2;
        }

        if (active[i]!=old_active[i])
            delta_active++;

        if (active[i]==2 && old_active[i]==2)
            delta_bound++;
    }


    if (delta_active==0 && work_epsilon<=epsilon) //we converged
        return 0;
    else if (delta_active==0) //lets decrease work_epsilon
    {
        work_epsilon=CMath::min(work_epsilon/2, autoselected_epsilon);
        work_epsilon=CMath::max(work_epsilon, epsilon);
        num_bound=qpsize;
    }

    delta_bound=0;
    delta_active=0;
    num_active=0;
    num_bound=0;

    for (int32_t i=0; i<num_vec; i++)
    {
        tmp_proj[i]=CMath::abs(proj[i]-1);
        tmp_proj_idx[i]=i;
    }

    CMath::qsort_index(tmp_proj, tmp_proj_idx, num_vec);

    autoselected_epsilon=tmp_proj[CMath::min(qpsize,num_vec)];

#ifdef DEBUG_SUBGRADIENTSVM
    //SG_PRINT("autoseleps: %15.15f\n", autoselected_epsilon);
#endif

    if (autoselected_epsilon>work_epsilon)
        autoselected_epsilon=work_epsilon;

    if (autoselected_epsilon<epsilon)
    {
        autoselected_epsilon=epsilon;

        int32_t i=0;
        while (i < num_vec && tmp_proj[i] <= autoselected_epsilon)
            i++;

        //SG_PRINT("lower bound on epsilon requires %d variables in qp\n", i);

        if (i>=qpsize_max && autoselected_epsilon>epsilon) //qpsize limit
        {
            SG_PRINT("qpsize limit (%d) reached\n", qpsize_max);
            int32_t num_in_qp=i;
            while (--i>=0 && num_in_qp>=qpsize_max)
            {
                if (tmp_proj[i] < autoselected_epsilon)
                {
                    autoselected_epsilon=tmp_proj[i];
                    num_in_qp--;
                }
            }

            //SG_PRINT("new qpsize will be %d, autoeps:%15.15f\n", num_in_qp, autoselected_epsilon);
        }
    }

    for (int32_t i=0; i<num_vec; i++)
    {
        active[i]=0;

        //within margin/wrong side
        if (proj[i] < 1-autoselected_epsilon)
        {
            idx_active[num_active++]=i;
            active[i]=1;
        }

        //on margin
        if (CMath::abs(proj[i]-1) <= autoselected_epsilon)
        {
            idx_bound[num_bound++]=i;
            active[i]=2;
        }

        if (active[i]!=old_active[i])
            delta_active++;

        if (active[i]==2 && old_active[i]==2)
            delta_bound++;
    }

    pos_idx=0;
    neg_idx=0;
    zero_idx=0;

    for (int32_t i=0; i<num_feat; i++)
    {
        if (w[i]>work_epsilon)
        {
            w_pos[pos_idx++]=i;
            grad_w[i]=1;
        }
        else if (w[i]<-work_epsilon)
        {
            w_neg[neg_idx++]=i;
            grad_w[i]=-1;
        }

        if (CMath::abs(w[i])<=work_epsilon)
        {
            w_zero[zero_idx++]=i;
            grad_w[i]=-1;
        }
    }

    return delta_active;
}


void CSubGradientLPM::update_active(int32_t num_feat, int32_t num_vec)
{
    for (int32_t i=0; i<num_vec; i++)
    {
        int32_t lab = ((CBinaryLabels*) m_labels)->get_int_label(i);
        if (active[i]==1 && old_active[i]!=1)
        {
            features->add_to_dense_vec(C1*lab, i, sum_CXy_active, num_feat);
            if (use_bias)
                sum_Cy_active+=C1*lab;
        }
        else if (old_active[i]==1 && active[i]!=1)
        {
            features->add_to_dense_vec(-C1*lab, i, sum_CXy_active, num_feat);
            if (use_bias)
                sum_Cy_active-=C1*lab;
        }
    }

    CMath::swap(active,old_active);
}

float64_t CSubGradientLPM::line_search(int32_t num_feat, int32_t num_vec)
{
    int32_t num_hinge=0;
    float64_t alpha=0;
    float64_t sgrad=0;

    float64_t* A=SG_MALLOC(float64_t, num_feat+num_vec);
    float64_t* B=SG_MALLOC(float64_t, num_feat+num_vec);
    float64_t* C=SG_MALLOC(float64_t, num_feat+num_vec);
    float64_t* D=SG_MALLOC(float64_t, num_feat+num_vec);

    for (int32_t i=0; i<num_feat+num_vec; i++)
    {
        if (i<num_feat)
        {
            A[i]=-grad_w[i];
            B[i]=w[i];
            C[i]=+grad_w[i];
            D[i]=-w[i];
        }
        else
        {
            float64_t p=get_label(i-num_feat)*(features->dense_dot(i-num_feat, grad_w, num_feat)+grad_b);
            grad_proj[i-num_feat]=p;

            A[i]=0;
            B[i]=0;
            C[i]=C1*p;
            D[i]=C1*(1-proj[i-num_feat]);
        }

        if (A[i]==C[i] && B[i]>D[i])
            sgrad+=A[i]+C[i];
        else if (A[i]==C[i] && B[i]==D[i])
            sgrad+=CMath::max(A[i],C[i]);
        else if (A[i]!=C[i])
        {
            hinge_point[num_hinge]=(D[i]-B[i])/(A[i]-C[i]);
            hinge_idx[num_hinge]=i; // index into A,B,C,D arrays
            num_hinge++;

            if (A[i]>C[i])
                sgrad+=C[i];
            if (A[i]<C[i])
                sgrad+=A[i];
        }
    }

    //SG_PRINT("sgrad:%f\n", sgrad);
    //CMath::display_vector(A, num_feat+num_vec, "A");
    //CMath::display_vector(B, num_feat+num_vec, "B");
    //CMath::display_vector(C, num_feat+num_vec, "C");
    //CMath::display_vector(D, num_feat+num_vec, "D");
    //CMath::display_vector(hinge_point, num_feat+num_vec, "hinge_point");
    //CMath::display_vector(hinge_idx, num_feat+num_vec, "hinge_idx");
    //ASSERT(0);

    CMath::qsort_index(hinge_point, hinge_idx, num_hinge);
    //CMath::display_vector(hinge_point, num_feat+num_vec, "hinge_point_sorted");


    int32_t i=-1;
    while (i < num_hinge-1 && sgrad < 0)
    {
        i+=1;

        if (A[hinge_idx[i]] > C[hinge_idx[i]])
            sgrad += A[hinge_idx[i]] - C[hinge_idx[i]];
        else
            sgrad += C[hinge_idx[i]] - A[hinge_idx[i]];
    }

    alpha = hinge_point[i];

    SG_FREE(D);
    SG_FREE(C);
    SG_FREE(B);
    SG_FREE(A);

    //SG_PRINT("alpha=%f\n", alpha);
    return alpha;
}

float64_t CSubGradientLPM::compute_min_subgradient(
    int32_t num_feat, int32_t num_vec, int32_t num_active, int32_t num_bound)
{
    float64_t dir_deriv=0;
    solver->init(E_QP);

    if (zero_idx+num_bound > 0)
    {
        //SG_PRINT("num_var:%d (zero:%d, bound:%d) num_feat:%d\n", zero_idx+num_bound, zero_idx,num_bound, num_feat);
        //CMath::display_vector(grad_w, num_feat+1, "grad_w");
        CMath::add(grad_w, 1.0, grad_w, -1.0, sum_CXy_active, num_feat);
        grad_w[num_feat]= -sum_Cy_active;

        grad_b = -sum_Cy_active;

        //CMath::display_vector(sum_CXy_active, num_feat, "sum_CXy_active");
        //SG_PRINT("sum_Cy_active=%10.10f\n", sum_Cy_active);

        //CMath::display_vector(grad_w, num_feat+1, "grad_w");

        solver->setup_subgradientlpm_QP(C1, m_labels, (CSparseFeatures<float64_t>*) features, idx_bound, num_bound,
                w_zero, zero_idx,
                grad_w, num_feat+1,
                use_bias);

        solver->optimize(beta);
        //CMath::display_vector(beta, num_feat+1, "v");

        //compute dir_deriv here, variable grad_w constains still 'v' and beta
        //contains the future gradient
        dir_deriv = CMath::dot(beta, grad_w, num_feat);
        dir_deriv-=beta[num_feat]*sum_Cy_active;

        for (int32_t i=0; i<num_bound; i++)
        {
            float64_t val= C1*get_label(idx_bound[i])*(features->dense_dot(idx_bound[i], beta, num_feat)+ beta[num_feat]);
            dir_deriv += CMath::max(0.0, val);
        }

        for (int32_t i=0; i<num_feat; i++)
            grad_w[i]=beta[i];

        if (use_bias)
            grad_b=beta[num_feat];

        //for (int32_t i=0; i<zero_idx+num_bound; i++)
        //  beta[i]=beta[i+num_feat+1];

        //CMath::display_vector(beta, zero_idx+num_bound, "beta");
        //SG_PRINT("beta[0]=%10.16f\n", beta[0]);
        //ASSERT(0);

        //for (int32_t i=0; i<zero_idx+num_bound; i++)
        //{
        //  if (i<zero_idx)
        //      grad_w[w_zero[i]]+=beta[w_zero[i]];
        //  else
        //  {
        //      features->add_to_dense_vec(-C1*beta[i]*get_label(idx_bound[i-zero_idx]), idx_bound[i-zero_idx], grad_w, num_feat);
        //      if (use_bias)
        //          grad_b -=  C1 * get_label(idx_bound[i-zero_idx])*beta[i-zero_idx];
        //  }
        //}

        //CMath::display_vector(w_zero, zero_idx, "w_zero");
        //CMath::display_vector(grad_w, num_feat, "grad_w");
        //SG_PRINT("grad_b=%f\n", grad_b);
        //
    }
    else
    {
        CMath::add(grad_w, 1.0, w, -1.0, sum_CXy_active, num_feat);
        grad_b = -sum_Cy_active;

        dir_deriv = CMath::dot(grad_w, grad_w, num_feat)+ grad_b*grad_b;
    }

    solver->cleanup();


    //SG_PRINT("Gradient   : |subgrad_W|^2=%f, |subgrad_b|^2=%f\n",
    //      CMath::dot(grad_w, grad_w, num_feat), grad_b*grad_b);

    return dir_deriv;
}

float64_t CSubGradientLPM::compute_objective(int32_t num_feat, int32_t num_vec)
{
    float64_t result= CMath::sum_abs(w, num_feat);

    for (int32_t i=0; i<num_vec; i++)
    {
        if (proj[i]<1.0)
            result += C1 * (1.0-proj[i]);
    }

    return result;
}

void CSubGradientLPM::compute_projection(int32_t num_feat, int32_t num_vec)
{
    for (int32_t i=0; i<num_vec; i++)
        proj[i]=get_label(i)*(features->dense_dot(i, w, num_feat) + bias);
}

void CSubGradientLPM::update_projection(float64_t alpha, int32_t num_vec)
{
    CMath::vec1_plus_scalar_times_vec2(proj,-alpha, grad_proj, num_vec);
}

void CSubGradientLPM::init(int32_t num_vec, int32_t num_feat)
{
    // alloc normal and bias inited with 0
    SG_FREE(w);
    w=SG_MALLOC(float64_t, num_feat);
    w_dim=num_feat;
    for (int32_t i=0; i<num_feat; i++)
        w[i]=1.0;
    //CMath::random_vector(w, num_feat, -1.0, 1.0);
    bias=0;
    num_it_noimprovement=0;
    grad_b=0;

    w_pos=SG_MALLOC(int32_t, num_feat);
    memset(w_pos,0,sizeof(int32_t)*num_feat);

    w_zero=SG_MALLOC(int32_t, num_feat);
    memset(w_zero,0,sizeof(int32_t)*num_feat);

    w_neg=SG_MALLOC(int32_t, num_feat);
    memset(w_neg,0,sizeof(int32_t)*num_feat);

    grad_w=SG_MALLOC(float64_t, num_feat+1);
    memset(grad_w,0,sizeof(float64_t)*(num_feat+1));

    sum_CXy_active=SG_MALLOC(float64_t, num_feat);
    memset(sum_CXy_active,0,sizeof(float64_t)*num_feat);

    sum_Cy_active=0;

    proj=SG_MALLOC(float64_t, num_vec);
    memset(proj,0,sizeof(float64_t)*num_vec);

    tmp_proj=SG_MALLOC(float64_t, num_vec);
    memset(proj,0,sizeof(float64_t)*num_vec);

    tmp_proj_idx=SG_MALLOC(int32_t, num_vec);
    memset(tmp_proj_idx,0,sizeof(int32_t)*num_vec);

    grad_proj=SG_MALLOC(float64_t, num_vec);
    memset(grad_proj,0,sizeof(float64_t)*num_vec);

    hinge_point=SG_MALLOC(float64_t, num_vec+num_feat);
    memset(hinge_point,0,sizeof(float64_t)*(num_vec+num_feat));

    hinge_idx=SG_MALLOC(int32_t, num_vec+num_feat);
    memset(hinge_idx,0,sizeof(int32_t)*(num_vec+num_feat));

    active=SG_MALLOC(uint8_t, num_vec);
    memset(active,0,sizeof(uint8_t)*num_vec);

    old_active=SG_MALLOC(uint8_t, num_vec);
    memset(old_active,0,sizeof(uint8_t)*num_vec);

    idx_bound=SG_MALLOC(int32_t, num_vec);
    memset(idx_bound,0,sizeof(int32_t)*num_vec);

    idx_active=SG_MALLOC(int32_t, num_vec);
    memset(idx_active,0,sizeof(int32_t)*num_vec);

    beta=SG_MALLOC(float64_t, num_feat+1+num_feat+num_vec);
    memset(beta,0,sizeof(float64_t)*num_feat+1+num_feat+num_vec);

    solver=new CCplex();
}

void CSubGradientLPM::cleanup()
{
    SG_FREE(hinge_idx);
    SG_FREE(hinge_point);
    SG_FREE(grad_proj);
    SG_FREE(proj);
    SG_FREE(tmp_proj);
    SG_FREE(tmp_proj_idx);
    SG_FREE(active);
    SG_FREE(old_active);
    SG_FREE(idx_bound);
    SG_FREE(idx_active);
    SG_FREE(sum_CXy_active);
    SG_FREE(w_pos);
    SG_FREE(w_zero);
    SG_FREE(w_neg);
    SG_FREE(grad_w);
    SG_FREE(beta);

    hinge_idx=NULL;
    hinge_point=NULL;
    grad_proj=NULL;
    proj=NULL;
    tmp_proj=NULL;
    tmp_proj_idx=NULL;
    active=NULL;
    old_active=NULL;
    idx_bound=NULL;
    idx_active=NULL;
    sum_CXy_active=NULL;
    w_pos=NULL;
    w_zero=NULL;
    w_neg=NULL;
    grad_w=NULL;
    beta=NULL;

    delete solver;
    solver=NULL;
}

bool CSubGradientLPM::train_machine(CFeatures* data)
{
    lpmtim=0;
    SG_INFO("C=%f epsilon=%f\n", C1, epsilon);
    ASSERT(m_labels);
    if (data)
    {
        if (!data->has_property(FP_DOT))
            SG_ERROR("Specified features are not of type CDotFeatures\n");
        set_features((CDotFeatures*) data);
    }
    ASSERT(features);

    int32_t num_iterations=0;
    int32_t num_train_labels=m_labels->get_num_labels();
    int32_t num_feat=features->get_dim_feature_space();
    int32_t num_vec=features->get_num_vectors();

    ASSERT(num_vec==num_train_labels);

    init(num_vec, num_feat);

    int32_t num_active=0;
    int32_t num_bound=0;
    float64_t alpha=0;
    float64_t dir_deriv=0;
    float64_t obj=0;
    delta_active=num_vec;
    last_it_noimprovement=-1;

    work_epsilon=0.99;
    autoselected_epsilon=work_epsilon;

    compute_projection(num_feat, num_vec);

    CTime time;
    float64_t loop_time=0;
    while (!(CSignal::cancel_computations()))
    {
        CTime t;
        delta_active=find_active(num_feat, num_vec, num_active, num_bound);

        update_active(num_feat, num_vec);

#ifdef DEBUG_SUBGRADIENTLPM
        SG_PRINT("==================================================\niteration: %d ", num_iterations);
        obj=compute_objective(num_feat, num_vec);
        SG_PRINT("objective:%.10f alpha: %.10f dir_deriv: %f num_bound: %d num_active: %d work_eps: %10.10f eps: %10.10f auto_eps: %10.10f time:%f\n",
                obj, alpha, dir_deriv, num_bound, num_active, work_epsilon, epsilon, autoselected_epsilon, loop_time);
#else
      SG_ABS_PROGRESS(work_epsilon, -CMath::log10(work_epsilon), -CMath::log10(0.99999999), -CMath::log10(epsilon), 6);
#endif
        //CMath::display_vector(w, w_dim, "w");
        //SG_PRINT("bias: %f\n", bias);
        //CMath::display_vector(proj, num_vec, "proj");
        //CMath::display_vector(idx_active, num_active, "idx_active");
        //SG_PRINT("num_active: %d\n", num_active);
        //CMath::display_vector(idx_bound, num_bound, "idx_bound");
        //SG_PRINT("num_bound: %d\n", num_bound);
        //CMath::display_vector(sum_CXy_active, num_feat, "sum_CXy_active");
        //SG_PRINT("sum_Cy_active: %f\n", sum_Cy_active);
        //CMath::display_vector(grad_w, num_feat, "grad_w");
        //SG_PRINT("grad_b:%f\n", grad_b);

        dir_deriv=compute_min_subgradient(num_feat, num_vec, num_active, num_bound);

        alpha=line_search(num_feat, num_vec);

        if (num_it_noimprovement==10 || num_bound<qpsize_max)
        {
            float64_t norm_grad=CMath::dot(grad_w, grad_w, num_feat) +
                grad_b*grad_b;

            SG_PRINT("CHECKING OPTIMALITY CONDITIONS: "
                    "work_epsilon: %10.10f delta_active:%d alpha: %10.10f norm_grad: %10.10f a*norm_grad:%10.16f\n",
                    work_epsilon, delta_active, alpha, norm_grad, CMath::abs(alpha*norm_grad));

            if (work_epsilon<=epsilon && delta_active==0 && CMath::abs(alpha*norm_grad)<1e-6)
                break;
            else
                num_it_noimprovement=0;
        }

        //if (work_epsilon<=epsilon && delta_active==0 && num_it_noimprovement)
        if ((dir_deriv<0 || alpha==0) && (work_epsilon<=epsilon && delta_active==0))
        {
            if (last_it_noimprovement==num_iterations-1)
            {
                SG_PRINT("no improvement...\n");
                num_it_noimprovement++;
            }
            else
                num_it_noimprovement=0;

            last_it_noimprovement=num_iterations;
        }

        CMath::vec1_plus_scalar_times_vec2(w, -alpha, grad_w, num_feat);
        bias-=alpha*grad_b;

        update_projection(alpha, num_vec);

        t.stop();
        loop_time=t.time_diff_sec();
        num_iterations++;

        if (get_max_train_time()>0 && time.cur_time_diff()>get_max_train_time())
            break;
    }

    SG_INFO("converged after %d iterations\n", num_iterations);

    obj=compute_objective(num_feat, num_vec);
    SG_INFO("objective: %f alpha: %f dir_deriv: %f num_bound: %d num_active: %d\n",
            obj, alpha, dir_deriv, num_bound, num_active);

#ifdef DEBUG_SUBGRADIENTLPM
    CMath::display_vector(w, w_dim, "w");
    SG_PRINT("bias: %f\n", bias);
#endif
    SG_PRINT("solver time:%f s\n", lpmtim);

    cleanup();

    return true;
}
#endif //USE_CPLEX