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Copy pathML_reg_dcorr_ver1.h
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ML_reg_dcorr_ver1.h
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#ifndef ML_REG_DCORR_H_
#define ML_REG_DCORR_H_
#include <unistd.h>
#include <omp.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/lib/SGVector.h>
#include <shogun/mathematics/linalg/LinalgNamespace.h>
#include <shogun/mathematics/Statistics.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <nl_dgp.h>
#include<ShogunML/ml_reg_6_1_4.h>
#define CHUNK 1
using namespace std;
using namespace shogun;
using namespace shogun::linalg;
class ML_REG_DCORR {
public:
ML_REG_DCORR () { };//default constructor
~ML_REG_DCORR () { };//default destructor
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
a ML regression algorithm.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
static void reg ( SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X, const int L, const double expn,
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/);
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
a ML regression algorithm applied to model (2.15).
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
static void reg1( SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X,
const int L, /*maximum truncation lag*/
const double expn, /*exponent of distances*/
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/);
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
a ML regression algorithm with model (2.15).
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
static void reg1( SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X,
const int L, /*maximum truncation lag*/
const double expn, /*exponent of distances*/
const double expn_x, /*exponent of data*/
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/);
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
moving averages.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
static void reg(SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X,
const int L,
const double expn);
/* Calculate centered Euclidean distances by ML methods.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_U). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
static SGMatrix<double> var_U( const SGMatrix<double> &X, const int L, const double expn,
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/);
/* Calculate centered Euclidean distances by ML methods.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_U). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
static SGMatrix<double> var_U( const SGMatrix<double> &X,
const int L, /*maximum truncation lag*/
const double expn, /*exponent of distances*/
const double expn_x, /*exponent of data*/
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/);
/* Calculate centered Euclidean distances by moving averages.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_U). */
static SGMatrix<double> var_U( const SGMatrix<double> &X,
const int L,
const double expn);
};
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
a ML regression algorithm.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
void ML_REG_DCORR::reg (SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X, const int L, const double expn,
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/) {
auto T = X.num_rows, N = X.num_cols;
auto T0 = T - L;
ASSERT_(T0 == mat_reg_first.num_rows && T0 == mat_reg_first.num_cols && T0 == mat_breg.num_rows && T0 == mat_breg.num_cols);
mat_reg_first.zero(); // reset the output matrix
mat_reg_second.zero();
mat_breg.zero();
auto t = 0, s = 0, ell = 0, i = 0;
SGVector<double> labels(T0), new_labels(T0), row_vec(N);
SGMatrix<double> features(T0, N*L);
int opt_tree_max_depth = 0, opt_num_iters = 0, opt_num_rand_feats = 0., opt_num_bags = 0.;
double opt_learning_rate = 0, opt_subset_fraction = 0, label_mean = 0.;
/* 1. Estimate E[||x_t - x_s||^\kappa| lags of x_t] */
// do hyperparameter tuning
for (t = L; t < T; ++t) {
// construct labels
row_vec = add(X.get_row_vector(t), X.get_row_vector(L), 1., -1.);
labels[t-L] = std::pow(norm(row_vec), expn);
//row_vec.display_vector("row_vec");
//cout << "norm of row_vec = " << norm(row_vec) << endl;
// construct features
for (i = 0; i < N; ++i) {
for (ell = 0; ell < L; ++ell) {
features(t-L, i*L+ell) = X(t-ell-1, i);
}
}
}
labels.add( -Statistics::mean(labels) ); // de-mean labels
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
//#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(s,t,i,ell) firstprivate(labels,row_vec,features,new_labels)
for (s = L; s < T; ++s) {
for (t = L; t < T; ++t) {
// construct labels
row_vec = add(X.get_row_vector(t), X.get_row_vector(s), 1., -1.);
labels[t-L] = std::pow(norm(row_vec), expn);
//row_vec.display_vector("row_vec");
//cout << "norm of row_vec = " << norm(row_vec) << endl;
// construct features
for (i = 0; i < N; ++i){
for (ell = 0; ell < L; ++ell){
features(t-L, i*L+ell) = X(t-ell-1, i);
}
}
}
label_mean = Statistics::mean(labels);
labels.add(-label_mean); // de-mean labels
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
//new_labels.add(label_mean); // add back the label mean
mat_reg_first.set_column(s-L, new_labels);
}
/* 2. Estimate E[||x_t - x_s||^\kappa| lags of x_s] */
mat_reg_second = transpose_matrix(mat_reg_first);
/*//#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(t,s,i,ell) firstprivate(labels,row_vec,features,new_labels)
for (t = L; t < T; ++t) {
for (s = L; s < T; ++s) {
// construct labels
row_vec = add(X.get_row_vector(s), X.get_row_vector(t), 1., -1.);
labels[s-L] = std::pow(norm(row_vec), expn);
//row_vec.display_vector("row_vec");
//cout << "norm of row_vec = " << norm(row_vec) << endl;
// construct features
for (i = 0; i < N; ++i){
for (ell = 0; ell < L; ++ell){
features(s-L, i*L+ell) = X(s-ell-1, i);
}
}
}
label_mean = Statistics::mean(labels);
labels.add(-label_mean); // de-mean labels
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
new_labels.add(label_mean); // add back the label mean
mat_reg_second.set_column(t-L, new_labels);
}*/
/* 3. Estimate E[||x_t - x_s||^\kappa| lags of x_t and x_s] */
// do hyperparameter tuning
for (s = 0; s < T0; ++s) {
// construct labels
labels[s] = mat_reg_first(0, s);
// construct features
for (i = 0; i < N; ++i){
for (ell = 0; ell < L; ++ell){
features(s, i*L+ell) = X(s+L-ell-1, i);
}
}
}
// call a ML hyperparamter tuner
labels.add( -Statistics::mean(labels) ); // de-mean labels
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
//#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(t,s,i,ell) firstprivate(labels,features,new_labels)
for(t = 0; t < T0; ++t) {
for (s = 0; s < T0; ++s) {
// construct labels
labels[s] = mat_reg_first(t, s);
// construct features
for (i = 0; i < N; ++i){
for (ell = 0; ell < L; ++ell){
features(s, i*L+ell) = X(s+L-ell-1, i);
}
}
}
label_mean = Statistics::mean(labels);
labels.add(-label_mean); // de-mean labels
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
new_labels.add(label_mean); // add back the label mean
mat_breg.set_column(t, new_labels);
}
mat_breg = transpose_matrix(mat_breg);
}
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
moving averages.
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
void ML_REG_DCORR::reg( SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X,
const int L,
const double expn) {
auto T = X.num_rows, N = X.num_cols;
auto T0 = T - L;
ASSERT_(T0 == mat_reg_first.num_rows && T0 == mat_reg_first.num_cols && T0 == mat_breg.num_rows && T0 == mat_breg.num_cols);
mat_reg_first.zero(); // reset the output matrix
mat_reg_second.zero();
mat_breg.zero();
SGVector<double> row_vec(N);
/* 1. Estimate E[||x_t - x_s||^\kappa| lags of x_t] */
for (int s = L; s < T; ++s) {
for (int t = L; t < T; ++t) {
for (int ell = 0; ell < t; ++ell) {
row_vec = add(X.get_row_vector(ell), X.get_row_vector(s), 1., -1.);
mat_reg_first(t-L, s-L) += std::pow(norm(row_vec), expn) / L;
}
}
}
/* 2. Estimate E[||x_t - x_s||^\kappa| lags of x_s] */
for (int t = L; t < T; ++t) {
for (int s = L; s < T; ++s) {
for (int ell = 0; ell < s; ++ell) {
row_vec = add(X.get_row_vector(t), X.get_row_vector(ell), 1., -1.);
mat_reg_second(s-L, t-L) += std::pow(norm(row_vec), expn) / L;
}
}
}
/* 3. Estimate E[||x_t - x_s||^\kappa| lags of x_t and x_s] */
for (int t = L; t < T; ++t) {
for (int s = L; s < T; ++s) {
for (int ell = 0; ell < t; ++ell) {
for (int k = 0; k < s; ++k) {
row_vec = add(X.get_row_vector(ell), X.get_row_vector(k), 1., -1.);
mat_breg(t-L, s-L) += std::pow(norm(row_vec), expn) / pow(L, 2.);
}
}
}
}
}
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
a ML regression algorithm applied to model (2.15).
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
void ML_REG_DCORR::reg1(SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X,
const int L, /*maximum truncation lag*/
const double expn, /*exponent of distances*/
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/) {
auto T = X.num_rows, N = X.num_cols;
auto T0 = T - L;
ASSERT_(T0 == mat_reg_first.num_rows && T0 == mat_reg_first.num_cols && T0 == mat_breg.num_rows && T0 == mat_breg.num_cols);
mat_reg_first.zero(); // reset the output matrix
mat_reg_second.zero();
mat_breg.zero();
if (N == 1) {
int t = 0, s = 0, tau = 0, ell = 0;
double row = 0.;
SGVector<double> labels(T0);
SGMatrix<double> features(T0, L);
int opt_tree_max_depth = 0, opt_num_iters = 0, opt_num_rand_feats = 0., opt_num_bags = 0.;
double opt_learning_rate = 0, opt_subset_fraction = 0, label_mean = 0.;
/* 1. Estimate E[x_t | lags of x_t] */
SGVector<double> mu(T0);
for (int t = L; t < T; ++t) {
labels[t-L] = X(t,0);
for (int ell = 0; ell < L; ++ell) {
features(t-L, ell) = X(t-ell-1,0);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
mu = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
/* 2. Estimate Var[x_t | lags of x_t] */
SGVector<double> var(T0);
var.set_const(1.);
for (int t = L; t < T; ++t) {
labels[t-L] = std::pow(X(t,0) - mu[t-L], 2.);
for (int ell = 0; ell < L; ++ell) {
features(t-L, ell) = X(t-ell-1,0);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
var = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
/* 3. Compute residuals of a univariate model */
SGVector<double> resid(T0);
for (t = 0; t < T0; ++t) {
resid[t] = (X(t+L,0) - mu[t]) / sqrt(var[t]);
}
/* 4. Estimate E[||x_t - x_s||^\kappa| lags of x_t] */
for (t = 0; t < T0; ++t) {
for (s = 0; s < T0; ++s) {
for (tau = 0; tau < T0; ++tau) {
row = mu[t] + sqrt(var[t])*resid[tau] - X(s+L,0);
mat_reg_first(t, s) += std::pow(fabs(row), expn) / T0;
}
}
}
/* 5. Estimate E[||x_t - x_s||^\kappa| lags of x_s] */
mat_reg_second = transpose_matrix(mat_reg_first);
/* 6. Estimate E[||x_t - x_s||^\kappa| lags of x_t and x_s] */
int tau1 = 0, tau2 = 0;
#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(t,s,tau1,tau2) firstprivate(row)
for (t = 0; t < T0; ++t) {
for (s = t; s < T0; ++s) {
if (T0 <= 400) {
for (tau1 = 0; tau1 < T0; ++tau1) {
for (tau2 = 0; tau2 < T0; ++tau2) {
row = mu[t] + sqrt(var[t])*resid[tau1] - (mu[s] + sqrt(var[s])*resid[tau2]);
//#pragma omp atomic
mat_breg(t,s) += std::pow(fabs(row), expn) / pow(T0, 2.);
}
}
}
else {
for (tau1 = 0; tau1 < T0; ++tau1) {
row = mu[t] + sqrt(var[t])*resid[tau1] - (mu[s] + sqrt(var[s])*resid[tau1]);
//#pragma omp atomic
mat_breg(t,s) += std::pow(fabs(row), expn) / T0;
}
}
mat_breg(s, t) = mat_breg(t,s);
}
}
}
else {
auto t = 0, s = 0, tau = 0, ell = 0, i = 0, j = 0;
SGVector<double> labels(T0), new_labels(T0), row_vec(N);
SGMatrix<double> features(T0, L);
int opt_tree_max_depth = 0, opt_num_iters = 0, opt_num_rand_feats = 0., opt_num_bags = 0.;
double opt_learning_rate = 0, opt_subset_fraction = 0, label_mean = 0.;
/* 1. Estimate E[x_t | lags of x_t] */
SGMatrix<double> mu(T0, N);
for (int i = 0; i < N; ++i) {
for (int t = L; t < T; ++t) {
labels[t-L] = X(t,i);
for (int ell = 0; ell < L; ++ell) {
features(t-L, ell) = X(t-ell-1,i);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
mu.set_column(i, new_labels);
}
/* 2. Estimate Var[x_t | lags of x_t] */
SGMatrix<double> var(T0, N);
var.set_const(1.);
for (int i = 0; i < N; ++i) {
for (int t = L; t < T; ++t) {
labels[t-L] = std::pow(X(t,i) - mu(t-L,i), 2.);
for (int ell = 0; ell < L; ++ell) {
features(t-L, ell) = X(t-ell-1,i);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
var.set_column(i, new_labels);
}
/* 3. Estimate Cov[x_it, x_jt | lags of x_it and x_jt] */
SGMatrix<double> cov(T0, N*(N-1)/2), features_c(T0, 2*L);
cov.set_const(0.); // zero out all covariances
int counter = 0;
for (int i = 0; i < N; ++i) {
for (int j = i+1; j < N; ++j) {
for (int t = L; t < T; ++t) {
labels[t-L] = ( X(t,i) - mu(t-L,i) ) * ( X(t,j) - mu(t-L,j) );
for (int ell = 0; ell < L; ++ell) {
features_c(t-L, ell) = X(t-ell-1,i);
features_c(t-L, L+ell) = X(t-ell-1,j);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features_c, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
new_labels = ML_reg(features_c, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
cov.set_column(counter, new_labels);
counter++;
}
}
/* 4. Compute residuals of a multivariate model */
SGMatrix<double> cov_mat(N, N), cov_mat_sqrt_inv(N, N), resid(N, T0);
for (t = 0; t < T0; ++t) {
counter = 0; // reset counter
for (i = 0; i < N; ++i) {
cov_mat(i, i) = var(t,i);
for (j = i+1; j < N; ++j) {
cov_mat(i, j) = cov(t,counter);
cov_mat(j, i) = cov_mat(i, j);
//#pragma omp atomic
counter += 1;
}
}
cov_mat_sqrt_inv = inv_sqrt_mat(cov_mat);
row_vec = matrix_prod( cov_mat_sqrt_inv, add(X.get_row_vector(t+L), mu.get_row_vector(t), 1., -1.) );
resid.set_column(t, row_vec);
}
SGMatrix<double> resid1 = transpose_matrix(resid); // transpose the residual matrix
/* 5. Estimate E[||x_t - x_s||^\kappa| lags of x_t] */
SGMatrix<double> cov_mat_sqrt(N, N);
//#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(t,i,j,s,tau) firstprivate(counter,cov_mat,cov_mat_sqrt,row_vec)
for (t = 0; t < T0; ++t) {
counter = 0; // reset counter
for (i = 0; i < N; ++i) {
cov_mat(i, i) = var(t,i);
for (j = i+1; j < N; ++j) {
cov_mat(i, j) = cov(t,counter);
cov_mat(j, i) = cov_mat(i, j);
//#pragma omp atomic
counter += 1;
}
}
cov_mat_sqrt = sqrt_mat(cov_mat);
for (s = 0; s < T0; ++s) {
for (tau = 0; tau < T0; ++tau) {
row_vec = add(add(mu.get_row_vector(t), matrix_prod( cov_mat_sqrt, resid1.get_row_vector(tau) ), 1., 1.), X.get_row_vector(s+L), 1., -1.);
//#pragma omp atomic
mat_reg_first(t, s) += std::pow(norm(row_vec), expn) / T0;
}
}
}
/* 6. Estimate E[||x_t - x_s||^\kappa| lags of x_s] */
mat_reg_second = transpose_matrix(mat_reg_first);
/* 7. Estimate E[||x_t - x_s||^\kappa| lags of x_t and x_s] */
//SGMatrix<double> cov_mat_t(N, N), cov_mat_s(N, N), cov_mat_sqrt_t(N, N), cov_mat_sqrt_s(N, N);
int i1 = 0, j1 = 0, i2 = 0, j2 = 0, counter_t = 0, counter_s = 0, tau1 = 0, tau2 = 0;
#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(t,s,i1,j1,i2,j2,tau1,tau2) firstprivate(counter_t,counter_s)
for (t = 0; t < T0; ++t) {
SGMatrix<double> cov_mat_t(N, N), cov_mat_sqrt_t(N, N), cov_mat_s(N, N), cov_mat_sqrt_s(N, N);
SGVector<double> row_vec(N);
//#pragma omp critical
{
counter_t = 0; // reset counter
for (i1 = 0; i1 < N; ++i1) {
cov_mat_t(i1, i1) = var(t, i1);
for (j1 = i1+1; j1 < N; ++j1) {
cov_mat_t(i1, j1) = cov(t, counter_t);
cov_mat_t(j1, i1) = cov_mat_t(i1, j1);
//#pragma omp atomic
counter_t += 1;
}
}
}
cov_mat_sqrt_t = sqrt_mat(cov_mat_t);
for (s = t; s < T0; ++s) {
//#pragma omp critical
{
counter_s = 0; // reset counter
for (i2 = 0; i2 < N; ++i2) {
cov_mat_s(i2, i2) = var(s,i2);
for (j2 = i2+1; j2 < N; ++j2) {
cov_mat_s(i2, j2) = cov(s, counter_s);
cov_mat_s(j2, i2) = cov_mat_s(i2, j2);
//#pragma omp atomic
counter_s += 1;
}
}
}
cov_mat_sqrt_s = sqrt_mat(cov_mat_s);
if (T0 <= 400) {
for (tau1 = 0; tau1 < T0; ++tau1) {
for (tau2 = 0; tau2 < T0; ++tau2) {
row_vec = add(add(mu.get_row_vector(t), matrix_prod( cov_mat_sqrt_t, resid1.get_row_vector(tau1) ), 1., 1.), \
add(mu.get_row_vector(s), matrix_prod( cov_mat_sqrt_s, resid1.get_row_vector(tau2) ), 1., 1.), 1., -1.);
//#pragma omp atomic
mat_breg(t,s) += std::pow(norm(row_vec), expn) / pow(T0, 2.);
}
}
}
else {
for (tau1 = 0; tau1 < T0; ++tau1) {
row_vec = add(add(mu.get_row_vector(t), matrix_prod( cov_mat_sqrt_t, resid1.get_row_vector(tau1) ), 1., 1.), \
add(mu.get_row_vector(s), matrix_prod( cov_mat_sqrt_s, resid1.get_row_vector(tau1) ), 1., 1.), 1., -1.);
//#pragma omp atomic
mat_breg(t,s) += std::pow(norm(row_vec), expn) / T0;
}
}
mat_breg(s, t) = mat_breg(t,s);
}
}
}
}
/* Calculate the conditional expectations of ||x_t - x_s||^\alpha (conditioning on 'L' lags of x_t or/and x_s) for t = 1, ..., T0 and s = 1, ..., T0 by
a ML regression algorithm applied to model (2.15).
INPUT: T by N matrix of data (X), a number of lags (L), and an exponent of the distance correlation (expn).
OUTPUT: a T0 = T-L by T-L matrix (mat_reg_first, mat_reg_second, mat_breg). */
template<std::tuple<int, int, double, double, int, int> ML_cv( const SGMatrix<double> &, /*columns are features*/
const SGVector<double> &, /*train labels*/
int, /*number of subsets for TSCV*/
int, /*minimum subset size for TSCV*/
SGVector<int>, /*list of tree max depths (for GBM)*/
SGVector<int>, /*list of numbers of iterations (for GBM)*/
SGVector<double>, /*list of learning rates (for GBM)*/
SGVector<double>, /*list of subset fractions (for GBM)*/
SGVector<int>, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int>, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/),
SGVector<double> ML_reg(const SGMatrix<double> &,
const SGVector<double> &,
int, /*tree max depth*/
int, /*number of iterations*/
double, /*learning rate*/
double, /*subset fraction*/
int, /*number of random features used for bagging (for RF)*/
int, /*number of bags (for RF)*/
int /*seed for the random number generator*/)>
void ML_REG_DCORR::reg1(SGMatrix<double> &mat_reg_first, /*E[||x_t - x_s||^\kappa| lags of x_t]*/
SGMatrix<double> &mat_reg_second, /*E[||x_t - x_s||^\kappa| lags of x_s]*/
SGMatrix<double> &mat_breg, /*E[||x_t - x_s||^\kappa| lags of x_t and x_s]*/
const SGMatrix<double> &X,
const int L, /*maximum truncation lag*/
const double expn, /*exponent of distances*/
const double expn_x, /*exponent of data*/
int num_subsets, /*number of subsets for TSCV*/
int min_subset_size, /*minimum subset size for TSCV*/
SGVector<int> tree_max_depths_list, /*list of tree max depths (for GBM)*/
SGVector<int> num_iters_list, /*list of numbers of iterations (for GBM)*/
SGVector<double> learning_rates_list, /*list of learning rates (for GBM)*/
SGVector<double> subset_fractions_list, /*list of subset fractions (for GBM)*/
SGVector<int> num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
SGVector<int> num_bags_list, /*list of number of bags (for RF)*/
int seed /*seed for random number generator*/) {
auto T = X.num_rows, N = X.num_cols;
auto T0 = T - L;
ASSERT_(T0 == mat_reg_first.num_rows && T0 == mat_reg_first.num_cols && T0 == mat_breg.num_rows && T0 == mat_breg.num_cols);
mat_reg_first.zero(); // reset the output matrix
mat_reg_second.zero();
mat_breg.zero();
auto t = 0, s = 0, tau = 0, ell = 0, i = 0, j = 0;
SGVector<double> labels(T0), new_labels(T0), row_vec(N);
SGMatrix<double> features(T0, L);
int opt_tree_max_depth = 0, opt_num_iters = 0, opt_num_rand_feats = 0., opt_num_bags = 0.;
double opt_learning_rate = 0, opt_subset_fraction = 0, label_mean = 0.;
/* 1. Estimate E[x_t | lags of x_t] */
SGMatrix<double> mu(T0, N);
for (int i = 0; i < N; ++i) {
for (int t = L; t < T; ++t) {
labels[t-L] = X(t,i);
for (int ell = 0; ell < L; ++ell) {
features(t-L, ell) = X(t-ell-1,i);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
mu.set_column(i, new_labels);
}
/* 2. Estimate Var[x_t | lags of x_t] */
SGMatrix<double> var(T0, N);
for (int i = 0; i < N; ++i) {
for (int t = L; t < T; ++t) {
labels[t-L] = std::pow(X(t,i) - mu(t-L,i), 2.);
for (int ell = 0; ell < L; ++ell) {
features(t-L, ell) = X(t-ell-1,i);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
new_labels = ML_reg(features, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
var.set_column(i, new_labels);
}
/* 3. Estimate Cov[x_it, x_jt | lags of x_it and x_jt] */
SGMatrix<double> cov(T0, N*(N-1)/2), features_c(T0, 2*L);
int counter = 0;
for (int i = 0; i < N; ++i) {
for (int j = i+1; j < N; ++j) {
for (int t = L; t < T; ++t) {
labels[t-L] = ( X(t,i) - mu(t-L,i) ) * ( X(t,j) - mu(t-L,j) );
for (int ell = 0; ell < L; ++ell) {
features_c(t-L, ell) = X(t-ell-1,i);
features_c(t-L, L+ell) = X(t-ell-1,j);
}
}
// do hyperparameter tuning
std::tie(opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, opt_num_rand_feats, opt_num_bags) =
ML_cv( features_c, labels, num_subsets, min_subset_size, tree_max_depths_list, num_iters_list, \
learning_rates_list, subset_fractions_list, num_rand_feats_list, num_bags_list, seed);
// estimate conditional expectations
new_labels = ML_reg(features_c, labels, opt_tree_max_depth, opt_num_iters, opt_learning_rate, opt_subset_fraction, \
opt_num_rand_feats, opt_num_bags, seed);
cov.set_column(counter, new_labels);
counter++;
}
}
/* 4. Compute residuals of a multivariate model */
SGMatrix<double> cov_mat(N, N), cov_mat_sqrt_inv(N, N), resid(N, T0);
for (t = 0; t < T0; ++t) {
counter = 0; // reset counter
for (i = 0; i < N; ++i) {
cov_mat(i, i) = var(t,i);
for (j = i+1; j < N; ++j) {
cov_mat(i, j) = cov(t,counter);
cov_mat(j, i) = cov_mat(i, j);
//#pragma omp atomic
counter += 1;
}
}
cov_mat_sqrt_inv = inv_sqrt_mat(cov_mat);
row_vec = matrix_prod( cov_mat_sqrt_inv, add(X.get_row_vector(t+L), mu.get_row_vector(t), 1., -1.) );
resid.set_column(t, row_vec);
}
SGMatrix<double> resid1 = transpose_matrix(resid); // transpose the residual matrix
/* 5. Estimate E[||x_t - x_s||^\kappa| lags of x_t] */
SGMatrix<double> cov_mat_sqrt(N, N);
//#pragma omp parallel for default(shared) schedule(dynamic,CHUNK) private(t,i,j,s,tau) firstprivate(counter,cov_mat,cov_mat_sqrt,row_vec)
for (t = 0; t < T0; ++t) {
counter = 0; // reset counter
for (i = 0; i < N; ++i) {
cov_mat(i, i) = var(t,i);
for (j = i+1; j < N; ++j) {
cov_mat(i, j) = cov(t,counter);
cov_mat(j, i) = cov_mat(i, j);
//#pragma omp atomic
counter += 1;
}
}
cov_mat_sqrt = sqrt_mat(cov_mat);
for (s = 0; s < T0; ++s) {
for (tau = 0; tau < T0; ++tau) {
row_vec = add(pow_vec(add(mu.get_row_vector(t), matrix_prod( cov_mat_sqrt, resid1.get_row_vector(tau) ), 1., 1.), expn_x), \
pow_vec(X.get_row_vector(s+L), expn_x), 1., -1.);