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LeastAngleRegression.cpp
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LeastAngleRegression.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 Chiyuan Zhang
* Copyright (C) 2012 Chiyuan Zhang
*/
#include <shogun/lib/config.h>
#include <vector>
#include <limits>
#include <algorithm>
#include <shogun/features/DenseFeatures.h>
#include <shogun/mathematics/Math.h>
#include <shogun/regression/LeastAngleRegression.h>
#include <shogun/labels/RegressionLabels.h>
#include <shogun/mathematics/eigen3.h>
using namespace Eigen;
using namespace shogun;
using namespace std;
CLeastAngleRegression::CLeastAngleRegression(bool lasso) :
CLinearMachine(), m_lasso(lasso),
m_max_nonz(0), m_max_l1_norm(0)
{
m_epsilon = CMath::MACHINE_EPSILON;
SG_ADD(&m_epsilon, "epsilon", "Epsilon for early stopping", MS_AVAILABLE);
SG_ADD(&m_max_nonz, "max_nonz", "Max number of non-zero variables", MS_AVAILABLE);
SG_ADD(&m_max_l1_norm, "max_l1_norm", "Max l1-norm of estimator", MS_AVAILABLE);
}
CLeastAngleRegression::~CLeastAngleRegression()
{
}
template <typename ST>
void CLeastAngleRegression::find_max_abs(const std::vector<ST> &vec, const std::vector<bool> &ignore_mask,
int32_t &imax, ST& vmax)
{
imax = -1;
vmax = -1;
for (size_t i=0; i < vec.size(); ++i)
{
if (ignore_mask[i])
continue;
if (CMath::abs(vec[i]) > vmax)
{
vmax = CMath::abs(vec[i]);
imax = i;
}
}
}
template <typename ST>
void CLeastAngleRegression::plane_rot(ST x0, ST x1,
ST &y0, ST &y1, SGMatrix<ST> &G)
{
memset(G.matrix, 0, G.num_rows * G.num_cols * sizeof(ST));
if (x1 == 0)
{
G(0, 0) = G(1, 1) = 1;
y0 = x0;
y1 = x1;
}
else
{
ST r = CMath::sqrt(x0*x0+x1*x1) ;
ST sx0 = x0 / r;
ST sx1 = x1 / r;
G(0,0) = sx0;
G(1,0) = -sx1;
G(0,1) = sx1;
G(1,1) = sx0;
y0 = r;
y1 = 0;
}
}
bool CLeastAngleRegression::train_machine(CFeatures* data)
{
REQUIRE(m_labels->get_label_type() == LT_REGRESSION, "Provided labels (%s) are of type (%d) - they should be regression labels (%d) instead.\n"
, m_labels->get_name(), m_labels->get_label_type(), LT_REGRESSION, m_labels->get_label_type())
if (!data)
{
REQUIRE(features, "No features provided.\n")
REQUIRE(features->get_feature_class() == C_DENSE,
"Feature-class (%d) must be of type C_DENSE (%d)\n", features->get_feature_class(), C_DENSE)
data = features;
}
else
REQUIRE(data->get_feature_class() == C_DENSE,
"Feature-class must be of type C_DENSE (%d)\n", data->get_feature_class(), C_DENSE)
REQUIRE(data->get_num_vectors() == m_labels->get_num_labels(), "Number of training vectors (%d) does not match number of labels (%d)\n"
, data->get_num_vectors(), m_labels->get_num_labels())
//check for type of CFeatures, then call the appropriate template method
if(data->get_feature_type() == F_DREAL)
return CLeastAngleRegression::train_machine_templated((CDenseFeatures<float64_t> *) data);
else if(data->get_feature_type() == F_SHORTREAL)
return CLeastAngleRegression::train_machine_templated((CDenseFeatures<float32_t> *) data);
else if(data->get_feature_type() == F_LONGREAL)
return CLeastAngleRegression::train_machine_templated((CDenseFeatures<floatmax_t> *) data);
else
SG_ERROR("Feature-type (%d) must be of type F_SHORTREAL (%d), F_DREAL (%d) or F_LONGREAL (%d).\n",
data->get_feature_type(), F_SHORTREAL, F_DREAL, F_LONGREAL)
return false;
}
template <typename ST>
bool CLeastAngleRegression::train_machine_templated(CDenseFeatures<ST> * data)
{
std::vector<std::vector<ST>> m_beta_path_t;
int32_t n_fea = data->get_num_features();
int32_t n_vec = data->get_num_vectors();
bool lasso_cond = false;
bool stop_cond = false;
// init facilities
m_beta_idx.clear();
m_beta_path_t.clear();
m_num_active = 0;
m_active_set.clear();
m_is_active.resize(n_fea);
fill(m_is_active.begin(), m_is_active.end(), false);
SGVector<ST> y = ((CRegressionLabels*) m_labels)->template get_labels_t<ST>();
typename SGVector<ST>::EigenVectorXtMap map_y(y.vector, y.size());
// transpose(X) is more convenient to work with since we care
// about features here. After transpose, each row will be a data
// point while each column corresponds to a feature
SGMatrix<ST> X (n_vec, n_fea);
typename SGMatrix<ST>::EigenMatrixXtMap map_Xr = data->get_feature_matrix();
typename SGMatrix<ST>::EigenMatrixXtMap map_X(X.matrix, n_vec, n_fea);
map_X = map_Xr.transpose();
SGMatrix<ST> X_active(n_vec, n_fea);
// beta is the estimator
vector<ST> beta(n_fea);
vector<ST> Xy(n_fea);
typename SGVector<ST>::EigenVectorXtMap map_Xy(&Xy[0], n_fea);
// Xy = X' * y
map_Xy=map_Xr*map_y;
// mu is the prediction
vector<ST> mu(n_vec);
// correlation
vector<ST> corr(n_fea);
// sign of correlation
vector<ST> corr_sign(n_fea);
// Cholesky factorization R'R = X'X, R is upper triangular
SGMatrix<ST> R;
ST max_corr = 1;
int32_t i_max_corr = 1;
// first entry: all coefficients are zero
m_beta_path_t.push_back(beta);
m_beta_idx.push_back(0);
//maximum allowed active variables at a time
int32_t max_active_allowed = CMath::min(n_vec-1, n_fea);
//========================================
// main loop
//========================================
int32_t nloop=0;
while (m_num_active < max_active_allowed && max_corr/n_vec > m_epsilon && !stop_cond)
{
// corr = X' * (y-mu) = - X'*mu + Xy
typename SGVector<ST>::EigenVectorXtMap map_corr(&corr[0], n_fea);
typename SGVector<ST>::EigenVectorXtMap map_mu(&mu[0], n_vec);
map_corr = map_Xy - (map_Xr*map_mu);
// corr_sign = sign(corr)
for (size_t i=0; i < corr.size(); ++i)
corr_sign[i] = CMath::sign(corr[i]);
// find max absolute correlation in inactive set
find_max_abs(corr, m_is_active, i_max_corr, max_corr);
if (!lasso_cond)
{
// update Cholesky factorization matrix
if (m_num_active == 0)
{
// R isn't allocated yet
R=SGMatrix<ST>(1,1);
ST diag_k = map_X.col(i_max_corr).dot(map_X.col(i_max_corr));
R(0,0) = CMath::sqrt( diag_k);
}
else
R=cholesky_insert(X, X_active, R, i_max_corr, m_num_active);
activate_variable(i_max_corr);
}
// Active variables
typename SGMatrix<ST>::EigenMatrixXtMap map_Xa(X_active.matrix, n_vec, m_num_active);
if (!lasso_cond)
map_Xa.col(m_num_active-1)=map_X.col(i_max_corr);
SGVector<ST> corr_sign_a(m_num_active);
for (index_t i=0; i < m_num_active; ++i)
corr_sign_a[i] = corr_sign[m_active_set[i]];
typename SGVector<ST>::EigenVectorXtMap map_corr_sign_a(corr_sign_a.vector, corr_sign_a.size());
typename SGMatrix<ST>::EigenMatrixXtMap map_R(R.matrix, R.num_rows, R.num_cols);
typename SGVector<ST>::EigenVectorXt solve = map_R.transpose().template triangularView<Lower>().template solve<OnTheLeft>(map_corr_sign_a);
typename SGVector<ST>::EigenVectorXt GA1 = map_R.template triangularView<Upper>().template solve<OnTheLeft>(solve);
// AA = 1/sqrt(GA1' * corr_sign_a)
ST AA = GA1.dot(map_corr_sign_a);
AA = 1/CMath::sqrt( AA);
typename SGVector<ST>::EigenVectorXt wA = AA*GA1;
// equiangular direction (unit vector)
vector<ST> u(n_vec);
typename SGVector<ST>::EigenVectorXtMap map_u(&u[0], n_vec);
map_u = map_Xa*wA;
ST gamma = max_corr / AA;
if (m_num_active < n_fea)
{
#pragma omp parallel for shared(gamma)
for (index_t i=0; i < n_fea; ++i)
{
if (m_is_active[i])
continue;
// correlation between X[:,i] and u
ST dir_corr = map_u.dot(map_X.col(i));
ST tmp1 = (max_corr-corr[i])/(AA-dir_corr);
ST tmp2 = (max_corr+corr[i])/(AA+dir_corr);
#pragma omp critical
{
if (tmp1 > CMath::MACHINE_EPSILON && tmp1 < gamma)
gamma = tmp1;
if (tmp2 > CMath::MACHINE_EPSILON && tmp2 < gamma)
gamma = tmp2;
}
}
}
int32_t i_kick=-1;
int32_t i_change=i_max_corr;
if (m_lasso)
{
// lasso modification to further refine gamma
lasso_cond = false;
ST lasso_bound = numeric_limits<ST>::max();
for (index_t i=0; i < m_num_active; ++i)
{
ST tmp = -beta[m_active_set[i]] / wA(i);
if (tmp > CMath::MACHINE_EPSILON && tmp < lasso_bound)
{
lasso_bound = tmp;
i_kick = i;
}
}
if (lasso_bound < gamma)
{
gamma = lasso_bound;
lasso_cond = true;
i_change = m_active_set[i_kick];
}
}
// update prediction: mu = mu + gamma * u
map_mu += gamma*map_u;
// update estimator
for (index_t i=0; i < m_num_active; ++i)
beta[m_active_set[i]] += gamma * wA(i);
// early stopping on max l1-norm
if (m_max_l1_norm > 0)
{
ST l1 = SGVector<ST>::onenorm(&beta[0], n_fea);
if (l1 > m_max_l1_norm)
{
// stopping with interpolated beta
stop_cond = true;
lasso_cond = false;
ST l1_prev = (ST) SGVector<ST>::onenorm(&m_beta_path_t[nloop][0], n_fea);
ST s = (m_max_l1_norm-l1_prev)/(l1-l1_prev);
typename SGVector<ST>::EigenVectorXtMap map_beta(&beta[0], n_fea);
typename SGVector<ST>::EigenVectorXtMap map_beta_prev(&m_beta_path_t[nloop][0], n_fea);
map_beta = (1-s)*map_beta_prev + s*map_beta;
}
}
// if lasso cond, drop the variable from active set
if (lasso_cond)
{
beta[i_change] = 0;
R=cholesky_delete(R, i_kick);
deactivate_variable(i_kick);
// Remove column from active set
int32_t numRows = map_Xa.rows();
int32_t numCols = map_Xa.cols()-1;
if( i_kick < numCols )
map_Xa.block(0, i_kick, numRows, numCols-i_kick) =
map_Xa.block(0, i_kick+1, numRows, numCols-i_kick).eval();
}
nloop++;
m_beta_path_t.push_back(beta);
if (size_t(m_num_active) >= m_beta_idx.size())
m_beta_idx.push_back(nloop);
else
m_beta_idx[m_num_active] = nloop;
// early stopping with max number of non-zero variables
if (m_max_nonz > 0 && m_num_active >= m_max_nonz)
stop_cond = true;
SG_DEBUG("Added : %d , Dropped %d, Active set size %d max_corr %.17f \n", i_max_corr, i_kick, m_num_active, max_corr);
}
//copy m_beta_path_t (of type ST) into m_beta_path
for(size_t i = 0; i < m_beta_path_t.size(); ++i)
{
std::vector<float64_t> va;
for(size_t p = 0; p < m_beta_path_t[i].size(); ++p){
va.push_back((float64_t) m_beta_path_t[i][p]);
}
m_beta_path.push_back(va);
}
// assign default estimator
w.vlen = n_fea;
switch_w(m_beta_idx.size()-1);
return true;
}
template <typename ST>
SGMatrix<ST> CLeastAngleRegression::cholesky_insert(const SGMatrix<ST>& X,
const SGMatrix<ST>& X_active, SGMatrix<ST>& R, int32_t i_max_corr, int32_t num_active)
{
typename SGMatrix<ST>::EigenMatrixXtMap map_X(X.matrix, X.num_rows, X.num_cols);
typename SGMatrix<ST>::EigenMatrixXtMap map_X_active(X_active.matrix, X.num_rows, num_active);
ST diag_k = map_X.col(i_max_corr).dot(map_X.col(i_max_corr));
// col_k is the k-th column of (X'X)
typename SGVector<ST>::EigenVectorXtMap map_i_max(X.get_column_vector(i_max_corr), X.num_rows);
typename SGVector<ST>::EigenVectorXt R_k = map_X_active.transpose()*map_i_max;
typename SGMatrix<ST>::EigenMatrixXtMap map_R(R.matrix, R.num_rows, R.num_cols);
// R' * R_k = (X' * X)_k = col_k, solving to get R_k
map_R.transpose().template triangularView<Lower>().template solveInPlace<OnTheLeft>(R_k);
ST R_kk = CMath::sqrt(diag_k - R_k.dot(R_k));
SGMatrix<ST> R_new(num_active+1, num_active+1);
typename SGMatrix<ST>::EigenMatrixXtMap map_R_new(R_new.matrix, R_new.num_rows, R_new.num_cols);
map_R_new.block(0, 0, num_active, num_active) = map_R;
memcpy(R_new.matrix+num_active*(num_active+1), R_k.data(), sizeof(ST)*(num_active));
map_R_new.row(num_active).setZero();
map_R_new(num_active, num_active) = R_kk;
return R_new;
}
template <typename ST>
SGMatrix<ST> CLeastAngleRegression::cholesky_delete(SGMatrix<ST>& R, int32_t i_kick)
{
if (i_kick != m_num_active-1)
{
// remove i_kick-th column
for (index_t j=i_kick; j < m_num_active-1; ++j)
for (index_t i=0; i < m_num_active; ++i)
R(i,j) = R(i,j+1);
SGMatrix<ST> G(2,2);
for (index_t i=i_kick; i < m_num_active-1; ++i)
{
plane_rot(R(i,i),R(i+1,i), R(i,i), R(i+1,i), G);
if (i < m_num_active-2)
{
for (index_t k=i+1; k < m_num_active-1; ++k)
{
// R[i:i+1, k] = G*R[i:i+1, k]
ST Rik = R(i,k), Ri1k = R(i+1,k);
R(i,k) = G(0,0)*Rik + G(0,1)*Ri1k;
R(i+1,k) = G(1,0)*Rik+G(1,1)*Ri1k;
}
}
}
}
SGMatrix<ST> nR(m_num_active-1, m_num_active-1);
for (index_t i=0; i < m_num_active-1; ++i)
for (index_t j=0; j < m_num_active-1; ++j)
nR(i,j) = R(i,j);
return nR;
}
template bool CLeastAngleRegression::train_machine_templated<float64_t>(CDenseFeatures<float64_t> * data);
template bool CLeastAngleRegression::train_machine_templated<float32_t>(CDenseFeatures<float32_t> * data);
template SGMatrix<float32_t> CLeastAngleRegression::cholesky_insert(const SGMatrix<float32_t>& X, const SGMatrix<float32_t>& X_active, SGMatrix<float32_t>& R, int32_t i_max_corr, int32_t num_active);
template SGMatrix<float64_t> CLeastAngleRegression::cholesky_insert(const SGMatrix<float64_t>& X, const SGMatrix<float64_t>& X_active, SGMatrix<float64_t>& R, int32_t i_max_corr, int32_t num_active);