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maxent.cpp
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/*
* $Id: maxent.cpp,v 1.1.1.1 2007/05/15 08:30:35 kyoshida Exp $
*/
#include "maxent.h"
#include <vector>
#include <iostream>
#include <cmath>
#include <cstdio>
using namespace std;
namespace maxent {
double ME_Model::FunctionGradient(const vector<double>& x,
vector<double>& grad) {
assert((int)_fb.Size() == x.size());
for (size_t i = 0; i < x.size(); i++) {
_vl[i] = x[i];
}
double score = update_model_expectation();
if (_l2reg == 0) {
for (size_t i = 0; i < x.size(); i++) {
grad[i] = -(_vee[i] - _vme[i]);
}
} else {
const double c = _l2reg * 2;
for (size_t i = 0; i < x.size(); i++) {
grad[i] = -(_vee[i] - _vme[i] - c * _vl[i]);
}
}
return -score;
}
int ME_Model::perform_GIS(int C) {
cerr << "C = " << C << endl;
C = 1;
cerr << "performing AGIS" << endl;
vector<double> pre_v;
double pre_logl = -999999;
for (int iter = 0; iter < 200; iter++) {
double logl = update_model_expectation();
fprintf(stderr, "iter = %2d C = %d f = %10.7f train_err = %7.5f", iter,
C, logl, _train_error);
if (_heldout.size() > 0) {
double hlogl = heldout_likelihood();
fprintf(stderr, " heldout_logl(err) = %f (%6.4f)", hlogl,
_heldout_error);
}
cerr << endl;
if (logl < pre_logl) {
C += 1;
_vl = pre_v;
iter--;
continue;
}
if (C > 1 && iter % 10 == 0) C--;
pre_logl = logl;
pre_v = _vl;
for (int i = 0; i < _fb.Size(); i++) {
double coef = _vee[i] / _vme[i];
_vl[i] += log(coef) / C;
}
}
cerr << endl;
return 0;
}
int ME_Model::perform_QUASI_NEWTON() {
const int dim = _fb.Size();
vector<double> x0(dim);
for (int i = 0; i < dim; i++) {
x0[i] = _vl[i];
}
vector<double> x;
if (_l1reg > 0) {
cerr << "performing OWLQN" << endl;
x = perform_OWLQN(x0, _l1reg);
} else {
cerr << "performing LBFGS" << endl;
x = perform_LBFGS(x0);
}
for (int i = 0; i < dim; i++) {
_vl[i] = x[i];
}
return 0;
}
int ME_Model::conditional_probability(const Sample& s,
std::vector<double>& membp) const {
// int num_classes = membp.size();
double sum = 0;
int max_label = 0;
// double maxp = 0;
vector<double> powv(_num_classes, 0.0);
for (vector<int>::const_iterator j = s.positive_features.begin();
j != s.positive_features.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[*j].begin();
k != _feature2mef[*j].end(); k++) {
powv[_fb.Feature(*k).label()] += _vl[*k];
}
}
for (vector<pair<int, double> >::const_iterator j = s.rvfeatures.begin();
j != s.rvfeatures.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[j->first].begin();
k != _feature2mef[j->first].end(); k++) {
powv[_fb.Feature(*k).label()] += _vl[*k] * j->second;
}
}
std::vector<double>::const_iterator pmax =
max_element(powv.begin(), powv.end());
double offset = max(0.0, *pmax - 700); // to avoid overflow
for (int label = 0; label < _num_classes; label++) {
double pow = powv[label] - offset;
double prod = exp(pow);
// cout << pow << " " << prod << ", ";
// if (_ref_modelp != NULL) prod *= _train_refpd[n][label];
if (_ref_modelp != NULL) prod *= s.ref_pd[label];
assert(prod != 0);
membp[label] = prod;
sum += prod;
}
for (int label = 0; label < _num_classes; label++) {
membp[label] /= sum;
if (membp[label] > membp[max_label]) max_label = label;
}
return max_label;
}
int ME_Model::make_feature_bag(const int cutoff) {
int max_num_features = 0;
// count the occurrences of features
#ifdef USE_HASH_MAP
typedef std::unordered_map<unsigned int, int> map_type;
#else
typedef std::map<unsigned int, int> map_type;
#endif
map_type count;
if (cutoff > 0) {
for (std::vector<Sample>::const_iterator i = _vs.begin(); i != _vs.end();
i++) {
for (std::vector<int>::const_iterator j = i->positive_features.begin();
j != i->positive_features.end(); j++) {
count[ME_Feature(i->label, *j).body()]++;
}
for (std::vector<pair<int, double> >::const_iterator j =
i->rvfeatures.begin();
j != i->rvfeatures.end(); j++) {
count[ME_Feature(i->label, j->first).body()]++;
}
}
}
int n = 0;
for (std::vector<Sample>::const_iterator i = _vs.begin(); i != _vs.end();
i++, n++) {
max_num_features =
max(max_num_features, (int)(i->positive_features.size()));
for (std::vector<int>::const_iterator j = i->positive_features.begin();
j != i->positive_features.end(); j++) {
const ME_Feature feature(i->label, *j);
// if (cutoff > 0 && count[feature.body()] < cutoff) continue;
if (cutoff > 0 && count[feature.body()] <= cutoff) continue;
_fb.Put(feature);
// cout << i->label << "\t" << *j << "\t" << id << endl;
// feature2sample[id].push_back(n);
}
for (std::vector<pair<int, double> >::const_iterator j =
i->rvfeatures.begin();
j != i->rvfeatures.end(); j++) {
const ME_Feature feature(i->label, j->first);
// if (cutoff > 0 && count[feature.body()] < cutoff) continue;
if (cutoff > 0 && count[feature.body()] <= cutoff) continue;
_fb.Put(feature);
}
}
count.clear();
// cerr << "num_classes = " << _num_classes << endl;
// cerr << "max_num_features = " << max_num_features << endl;
init_feature2mef();
return max_num_features;
}
double ME_Model::heldout_likelihood() {
double logl = 0;
int ncorrect = 0;
for (std::vector<Sample>::const_iterator i = _heldout.begin();
i != _heldout.end(); i++) {
vector<double> membp(_num_classes);
int l = classify(*i, membp);
logl += log(membp[i->label]);
if (l == i->label) ncorrect++;
}
_heldout_error = 1 - (double)ncorrect / _heldout.size();
return logl /= _heldout.size();
}
double ME_Model::update_model_expectation() {
double logl = 0;
int ncorrect = 0;
_vme.resize(_fb.Size());
for (int i = 0; i < _fb.Size(); i++) _vme[i] = 0;
int n = 0;
for (vector<Sample>::const_iterator i = _vs.begin(); i != _vs.end();
i++, n++) {
vector<double> membp(_num_classes);
int max_label = conditional_probability(*i, membp);
logl += log(membp[i->label]);
// cout << membp[*i] << " " << logl << " ";
if (max_label == i->label) ncorrect++;
// model_expectation
for (vector<int>::const_iterator j = i->positive_features.begin();
j != i->positive_features.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[*j].begin();
k != _feature2mef[*j].end(); k++) {
_vme[*k] += membp[_fb.Feature(*k).label()];
}
}
for (vector<pair<int, double> >::const_iterator j = i->rvfeatures.begin();
j != i->rvfeatures.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[j->first].begin();
k != _feature2mef[j->first].end(); k++) {
_vme[*k] += membp[_fb.Feature(*k).label()] * j->second;
}
}
}
for (int i = 0; i < _fb.Size(); i++) {
_vme[i] /= _vs.size();
}
_train_error = 1 - (double)ncorrect / _vs.size();
logl /= _vs.size();
if (_l2reg > 0) {
const double c = _l2reg;
for (int i = 0; i < _fb.Size(); i++) {
logl -= _vl[i] * _vl[i] * c;
}
}
// logl /= _vs.size();
// fprintf(stderr, "iter =%3d logl = %10.7f train_acc = %7.5f\n", iter,
// logl, (double)ncorrect/train.size());
// fprintf(stderr, "logl = %10.7f train_acc = %7.5f\n", logl,
// (double)ncorrect/_train.size());
return logl;
}
int ME_Model::train(const vector<ME_Sample>& vms) {
_vs.clear();
for (vector<ME_Sample>::const_iterator i = vms.begin(); i != vms.end(); i++) {
add_training_sample(*i);
}
return train();
}
void ME_Model::add_training_sample(const ME_Sample& mes) {
Sample s;
s.label = _label_bag.Put(mes.label);
if (s.label > ME_Feature::MAX_LABEL_TYPES) {
cerr << "error: too many types of labels." << endl;
exit(1);
}
for (vector<string>::const_iterator j = mes.features.begin();
j != mes.features.end(); j++) {
s.positive_features.push_back(_featurename_bag.Put(*j));
}
for (vector<pair<string, double> >::const_iterator j = mes.rvfeatures.begin();
j != mes.rvfeatures.end(); j++) {
s.rvfeatures.push_back(
pair<int, double>(_featurename_bag.Put(j->first), j->second));
}
if (_ref_modelp != NULL) {
ME_Sample tmp = mes;
;
s.ref_pd = _ref_modelp->classify(tmp);
}
// cout << s.label << "\t";
// for (vector<int>::const_iterator j = s.positive_features.begin(); j !=
// s.positive_features.end(); j++){
// cout << *j << " ";
// }
// cout << endl;
_vs.push_back(s);
}
int ME_Model::train() {
if (_l1reg > 0 && _l2reg > 0) {
cerr << "error: L1 and L2 regularizers cannot be used simultaneously."
<< endl;
return 0;
}
if (_vs.size() == 0) {
cerr << "error: no training data." << endl;
return 0;
}
if (_nheldout >= (int)_vs.size()) {
cerr << "error: too much heldout data. no training data is available."
<< endl;
return 0;
}
// if (_nheldout > 0) random_shuffle(_vs.begin(), _vs.end());
int max_label = 0;
for (std::vector<Sample>::const_iterator i = _vs.begin(); i != _vs.end();
i++) {
max_label = max(max_label, i->label);
}
_num_classes = max_label + 1;
if (_num_classes != _label_bag.Size()) {
cerr << "warning: _num_class != _label_bag.Size()" << endl;
}
if (_ref_modelp != NULL) {
cerr << "setting reference distribution...";
for (int i = 0; i < _ref_modelp->num_classes(); i++) {
_label_bag.Put(_ref_modelp->get_class_label(i));
}
_num_classes = _label_bag.Size();
for (vector<Sample>::iterator i = _vs.begin(); i != _vs.end(); i++) {
set_ref_dist(*i);
}
cerr << "done" << endl;
}
for (int i = 0; i < _nheldout; i++) {
_heldout.push_back(_vs.back());
_vs.pop_back();
}
sort(_vs.begin(), _vs.end());
int cutoff = 0;
if (cutoff > 0) cerr << "cutoff threshold = " << cutoff << endl;
if (_l1reg > 0) cerr << "L1 regularizer = " << _l1reg << endl;
if (_l2reg > 0) cerr << "L2 regularizer = " << _l2reg << endl;
// normalize
_l1reg /= _vs.size();
_l2reg /= _vs.size();
cerr << "preparing for estimation...";
make_feature_bag(cutoff);
// _vs.clear();
cerr << "done" << endl;
cerr << "number of samples = " << _vs.size() << endl;
cerr << "number of features = " << _fb.Size() << endl;
cerr << "calculating empirical expectation...";
_vee.resize(_fb.Size());
for (int i = 0; i < _fb.Size(); i++) {
_vee[i] = 0;
}
for (int n = 0; n < (int)_vs.size(); n++) {
const Sample* i = &_vs[n];
for (vector<int>::const_iterator j = i->positive_features.begin();
j != i->positive_features.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[*j].begin();
k != _feature2mef[*j].end(); k++) {
if (_fb.Feature(*k).label() == i->label) _vee[*k] += 1.0;
}
}
for (vector<pair<int, double> >::const_iterator j = i->rvfeatures.begin();
j != i->rvfeatures.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[j->first].begin();
k != _feature2mef[j->first].end(); k++) {
if (_fb.Feature(*k).label() == i->label) _vee[*k] += j->second;
}
}
}
for (int i = 0; i < _fb.Size(); i++) {
_vee[i] /= _vs.size();
}
cerr << "done" << endl;
_vl.resize(_fb.Size());
for (int i = 0; i < _fb.Size(); i++) _vl[i] = 0.0;
if (_optimization_method == SGD) {
perform_SGD();
} else {
perform_QUASI_NEWTON();
}
int num_active = 0;
for (int i = 0; i < _fb.Size(); i++) {
if (_vl[i] != 0) num_active++;
}
cerr << "number of active features = " << num_active << endl;
return 0;
}
void ME_Model::get_features(list<pair<pair<string, string>, double> >& fl) {
fl.clear();
// for (int i = 0; i < _fb.Size(); i++) {
// ME_Feature f = _fb.Feature(i);
// fl.push_back( make_pair(make_pair(_label_bag.Str(f.label()),
// _featurename_bag.Str(f.feature())), _vl[i]));
// }
for (MiniStringBag::map_type::const_iterator i = _featurename_bag.begin();
i != _featurename_bag.end(); i++) {
for (int j = 0; j < _label_bag.Size(); j++) {
string label = _label_bag.Str(j);
string history = i->first;
int id = _fb.Id(ME_Feature(j, i->second));
if (id < 0) continue;
fl.push_back(make_pair(make_pair(label, history), _vl[id]));
}
}
}
void ME_Model::clear() {
_vl.clear();
_label_bag.Clear();
_featurename_bag.Clear();
_fb.Clear();
_feature2mef.clear();
_vee.clear();
_vme.clear();
_vs.clear();
_heldout.clear();
}
bool ME_Model::load_from_file(const string& filename) {
FILE* fp = fopen(filename.c_str(), "r");
if (!fp) {
cerr << "error: cannot open " << filename << "!" << endl;
return false;
}
_vl.clear();
_label_bag.Clear();
_featurename_bag.Clear();
_fb.Clear();
char buf[1024];
while (fgets(buf, 1024, fp)) {
string line(buf);
string::size_type t1 = line.find_first_of('\t');
string::size_type t2 = line.find_last_of('\t');
string classname = line.substr(0, t1);
string featurename = line.substr(t1 + 1, t2 - (t1 + 1));
float lambda;
string w = line.substr(t2 + 1);
sscanf(w.c_str(), "%f", &lambda);
int label = _label_bag.Put(classname);
int feature = _featurename_bag.Put(featurename);
_fb.Put(ME_Feature(label, feature));
_vl.push_back(lambda);
}
_num_classes = _label_bag.Size();
init_feature2mef();
fclose(fp);
return true;
}
void ME_Model::init_feature2mef() {
_feature2mef.clear();
for (int i = 0; i < _featurename_bag.Size(); i++) {
vector<int> vi;
for (int k = 0; k < _num_classes; k++) {
int id = _fb.Id(ME_Feature(k, i));
if (id >= 0) vi.push_back(id);
}
_feature2mef.push_back(vi);
}
}
bool ME_Model::load_from_array(const ME_Model_Data data[]) {
_vl.clear();
for (int i = 0;; i++) {
if (string(data[i].label) == "///") break;
int label = _label_bag.Put(data[i].label);
int feature = _featurename_bag.Put(data[i].feature);
_fb.Put(ME_Feature(label, feature));
_vl.push_back(data[i].weight);
}
_num_classes = _label_bag.Size();
init_feature2mef();
return true;
}
bool ME_Model::save_to_file(const string& filename, const double th) const {
FILE* fp = fopen(filename.c_str(), "w");
if (!fp) {
cerr << "error: cannot open " << filename << "!" << endl;
return false;
}
// for (int i = 0; i < _fb.Size(); i++) {
// if (_vl[i] == 0) continue; // ignore zero-weight features
// ME_Feature f = _fb.Feature(i);
// fprintf(fp, "%s\t%s\t%f\n", _label_bag.Str(f.label()).c_str(),
// _featurename_bag.Str(f.feature()).c_str(), _vl[i]);
// }
for (MiniStringBag::map_type::const_iterator i = _featurename_bag.begin();
i != _featurename_bag.end(); i++) {
for (int j = 0; j < _label_bag.Size(); j++) {
string label = _label_bag.Str(j);
string history = i->first;
int id = _fb.Id(ME_Feature(j, i->second));
if (id < 0) continue;
if (_vl[id] == 0) continue; // ignore zero-weight features
if (fabs(_vl[id]) < th) continue; // cut off low-weight features
fprintf(fp, "%s\t%s\t%f\n", label.c_str(), history.c_str(), _vl[id]);
}
}
fclose(fp);
return true;
}
void ME_Model::set_ref_dist(Sample& s) const {
vector<double> v0 = s.ref_pd;
vector<double> v(_num_classes);
for (unsigned int i = 0; i < v.size(); i++) {
v[i] = 0;
string label = get_class_label(i);
int id_ref = _ref_modelp->get_class_id(label);
if (id_ref != -1) {
v[i] = v0[id_ref];
}
if (v[i] == 0) v[i] = 0.001; // to avoid -inf logl
}
s.ref_pd = v;
}
int ME_Model::classify(const Sample& nbs, vector<double>& membp) const {
// vector<double> membp(_num_classes);
assert(_num_classes == (int)membp.size());
conditional_probability(nbs, membp);
int max_label = 0;
double max = 0.0;
for (int i = 0; i < (int)membp.size(); i++) {
// cout << membp[i] << " ";
if (membp[i] > max) {
max_label = i;
max = membp[i];
}
}
// cout << endl;
return max_label;
}
vector<double> ME_Model::classify(ME_Sample& mes) const {
Sample s;
for (vector<string>::const_iterator j = mes.features.begin();
j != mes.features.end(); j++) {
int id = _featurename_bag.Id(*j);
if (id >= 0) s.positive_features.push_back(id);
}
for (vector<pair<string, double> >::const_iterator j = mes.rvfeatures.begin();
j != mes.rvfeatures.end(); j++) {
int id = _featurename_bag.Id(j->first);
if (id >= 0) {
s.rvfeatures.push_back(pair<int, double>(id, j->second));
}
}
if (_ref_modelp != NULL) {
s.ref_pd = _ref_modelp->classify(mes);
set_ref_dist(s);
}
vector<double> vp(_num_classes);
int label = classify(s, vp);
mes.label = get_class_label(label);
return vp;
}
// template<class FuncGrad>
// std::vector<double>
// perform_LBFGS(FuncGrad func_grad, const std::vector<double> & x0);
std::vector<double> perform_LBFGS(
double (*func_grad)(const std::vector<double> &, std::vector<double> &),
const std::vector<double> &x0);
std::vector<double> perform_OWLQN(
double (*func_grad)(const std::vector<double> &, std::vector<double> &),
const std::vector<double> &x0, const double C);
const int LBFGS_M = 10;
const static int M = LBFGS_M;
const static double LINE_SEARCH_ALPHA = 0.1;
const static double LINE_SEARCH_BETA = 0.5;
// stopping criteria
int LBFGS_MAX_ITER = 300;
const static double MIN_GRAD_NORM = 0.0001;
// LBFGS
double ME_Model::backtracking_line_search(const Vec& x0, const Vec& grad0,
const double f0, const Vec& dx,
Vec& x, Vec& grad1) {
double t = 1.0 / LINE_SEARCH_BETA;
double f;
do {
t *= LINE_SEARCH_BETA;
x = x0 + t * dx;
f = FunctionGradient(x.STLVec(), grad1.STLVec());
// cout << "*";
} while (f > f0 + LINE_SEARCH_ALPHA * t * dot_product(dx, grad0));
return f;
}
//
// Jorge Nocedal, "Updating Quasi-Newton Matrices With Limited Storage",
// Mathematics of Computation, Vol. 35, No. 151, pp. 773-782, 1980.
//
Vec approximate_Hg(const int iter, const Vec& grad, const Vec s[],
const Vec y[], const double z[]) {
int offset, bound;
if (iter <= M) {
offset = 0;
bound = iter;
} else {
offset = iter - M;
bound = M;
}
Vec q = grad;
double alpha[M], beta[M];
for (int i = bound - 1; i >= 0; i--) {
const int j = (i + offset) % M;
alpha[i] = z[j] * dot_product(s[j], q);
q += -alpha[i] * y[j];
}
if (iter > 0) {
const int j = (iter - 1) % M;
const double gamma = ((1.0 / z[j]) / dot_product(y[j], y[j]));
// static double gamma;
// if (gamma == 0) gamma = ((1.0 / z[j]) / dot_product(y[j], y[j]));
q *= gamma;
}
for (int i = 0; i <= bound - 1; i++) {
const int j = (i + offset) % M;
beta[i] = z[j] * dot_product(y[j], q);
q += s[j] * (alpha[i] - beta[i]);
}
return q;
}
vector<double> ME_Model::perform_LBFGS(const vector<double>& x0) {
const size_t dim = x0.size();
Vec x = x0;
Vec grad(dim), dx(dim);
double f = FunctionGradient(x.STLVec(), grad.STLVec());
Vec s[M], y[M];
double z[M]; // rho
for (int iter = 0; iter < LBFGS_MAX_ITER; iter++) {
fprintf(stderr, "%3d obj(err) = %f (%6.4f)", iter + 1, -f, _train_error);
if (_nheldout > 0) {
const double heldout_logl = heldout_likelihood();
fprintf(stderr, " heldout_logl(err) = %f (%6.4f)", heldout_logl,
_heldout_error);
}
fprintf(stderr, "\n");
if (sqrt(dot_product(grad, grad)) < MIN_GRAD_NORM) break;
dx = -1 * approximate_Hg(iter, grad, s, y, z);
Vec x1(dim), grad1(dim);
f = backtracking_line_search(x, grad, f, dx, x1, grad1);
s[iter % M] = x1 - x;
y[iter % M] = grad1 - grad;
z[iter % M] = 1.0 / dot_product(y[iter % M], s[iter % M]);
x = x1;
grad = grad1;
}
return x.STLVec();
}
// OWLQN
// stopping criteria
int OWLQN_MAX_ITER = 300;
Vec approximate_Hg(const int iter, const Vec& grad, const Vec s[],
const Vec y[], const double z[]);
inline int sign(double x) {
if (x > 0) return 1;
if (x < 0) return -1;
return 0;
};
static Vec pseudo_gradient(const Vec& x, const Vec& grad0, const double C) {
Vec grad = grad0;
for (size_t i = 0; i < x.Size(); i++) {
if (x[i] != 0) {
grad[i] += C * sign(x[i]);
continue;
}
const double gm = grad0[i] - C;
if (gm > 0) {
grad[i] = gm;
continue;
}
const double gp = grad0[i] + C;
if (gp < 0) {
grad[i] = gp;
continue;
}
grad[i] = 0;
}
return grad;
}
double ME_Model::regularized_func_grad(const double C, const Vec& x,
Vec& grad) {
double f = FunctionGradient(x.STLVec(), grad.STLVec());
for (size_t i = 0; i < x.Size(); i++) {
f += C * fabs(x[i]);
}
return f;
}
double ME_Model::constrained_line_search(double C, const Vec& x0,
const Vec& grad0, const double f0,
const Vec& dx, Vec& x, Vec& grad1) {
// compute the orthant to explore
Vec orthant = x0;
for (size_t i = 0; i < orthant.Size(); i++) {
if (orthant[i] == 0) orthant[i] = -grad0[i];
}
double t = 1.0 / LINE_SEARCH_BETA;
double f;
do {
t *= LINE_SEARCH_BETA;
x = x0 + t * dx;
x.Project(orthant);
// for (size_t i = 0; i < x.Size(); i++) {
// if (x0[i] != 0 && sign(x[i]) != sign(x0[i])) x[i] = 0;
// }
f = regularized_func_grad(C, x, grad1);
// cout << "*";
} while (f > f0 + LINE_SEARCH_ALPHA * dot_product(x - x0, grad0));
return f;
}
vector<double> ME_Model::perform_OWLQN(const vector<double>& x0,
const double C) {
const size_t dim = x0.size();
Vec x = x0;
Vec grad(dim), dx(dim);
double f = regularized_func_grad(C, x, grad);
Vec s[M], y[M];
double z[M]; // rho
for (int iter = 0; iter < OWLQN_MAX_ITER; iter++) {
Vec pg = pseudo_gradient(x, grad, C);
fprintf(stderr, "%3d obj(err) = %f (%6.4f)", iter + 1, -f, _train_error);
if (_nheldout > 0) {
const double heldout_logl = heldout_likelihood();
fprintf(stderr, " heldout_logl(err) = %f (%6.4f)", heldout_logl,
_heldout_error);
}
fprintf(stderr, "\n");
if (sqrt(dot_product(pg, pg)) < MIN_GRAD_NORM) break;
dx = -1 * approximate_Hg(iter, pg, s, y, z);
if (dot_product(dx, pg) >= 0) dx.Project(-1 * pg);
Vec x1(dim), grad1(dim);
f = constrained_line_search(C, x, pg, f, dx, x1, grad1);
s[iter % M] = x1 - x;
y[iter % M] = grad1 - grad;
z[iter % M] = 1.0 / dot_product(y[iter % M], s[iter % M]);
x = x1;
grad = grad1;
}
return x.STLVec();
}
// SGD
// const double SGD_ETA0 = 1;
// const double SGD_ITER = 30;
// const double SGD_ALPHA = 0.85;
//#define FOLOS_NAIVE
//#define FOLOS_LAZY
#define SGD_CP
inline void apply_l1_penalty(const int i, const double u, vector<double>& _vl,
vector<double>& q) {
double& w = _vl[i];
const double z = w;
double& qi = q[i];
if (w > 0) {
w = max(0.0, w - (u + qi));
} else if (w < 0) {
w = min(0.0, w + (u - qi));
}
qi += w - z;
}
static double l1norm(const vector<double>& v) {
double sum = 0;
for (size_t i = 0; i < v.size(); i++) sum += abs(v[i]);
return sum;
}
inline void update_folos_lazy(const int iter_sample, const int k,
vector<double>& _vl,
const vector<double>& sum_eta,
vector<int>& last_updated) {
const double penalty = sum_eta[iter_sample] - sum_eta[last_updated[k]];
double& x = _vl[k];
if (x > 0)
x = max(0.0, x - penalty);
else
x = min(0.0, x + penalty);
last_updated[k] = iter_sample;
}
int ME_Model::perform_SGD() {
if (_l2reg > 0) {
cerr << "error: L2 regularization is currently not supported in SGD mode."
<< endl;
exit(1);
}
cerr << "performing SGD" << endl;
const double l1param = _l1reg;
const int d = _fb.Size();
vector<int> ri(_vs.size());
for (size_t i = 0; i < ri.size(); i++) ri[i] = i;
vector<double> grad(d);
int iter_sample = 0;
const double eta0 = SGD_ETA0;
// cerr << "l1param = " << l1param << endl;
cerr << "eta0 = " << eta0 << " alpha = " << SGD_ALPHA << endl;
double u = 0;
vector<double> q(d, 0);
vector<int> last_updated(d, 0);
vector<double> sum_eta;
sum_eta.push_back(0);
for (int iter = 0; iter < SGD_ITER; iter++) {
random_shuffle(ri.begin(), ri.end());
double logl = 0;
int ncorrect = 0, ntotal = 0;
for (size_t i = 0; i < _vs.size(); i++, ntotal++, iter_sample++) {
const Sample& s = _vs[ri[i]];
#ifdef FOLOS_LAZY
for (vector<int>::const_iterator j = s.positive_features.begin();
j != s.positive_features.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[*j].begin();
k != _feature2mef[*j].end(); k++) {
update_folos_lazy(iter_sample, *k, _vl, sum_eta, last_updated);
}
}
#endif
vector<double> membp(_num_classes);
const int max_label = conditional_probability(s, membp);
const double eta =
eta0 * pow(SGD_ALPHA,
(double)iter_sample / _vs.size()); // exponential decay
// const double eta = eta0 / (1.0 + (double)iter_sample /
// _vs.size());
// if (iter_sample % _vs.size() == 0) cerr << "eta = " << eta <<
// endl;
u += eta * l1param;
sum_eta.push_back(sum_eta.back() + eta * l1param);
logl += log(membp[s.label]);
if (max_label == s.label) ncorrect++;
// binary features
for (vector<int>::const_iterator j = s.positive_features.begin();
j != s.positive_features.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[*j].begin();
k != _feature2mef[*j].end(); k++) {
const double me = membp[_fb.Feature(*k).label()];
const double ee = (_fb.Feature(*k).label() == s.label ? 1.0 : 0);
const double grad = (me - ee);
_vl[*k] -= eta * grad;
#ifdef SGD_CP
apply_l1_penalty(*k, u, _vl, q);
#endif
}
}
// real-valued features
for (vector<pair<int, double> >::const_iterator j = s.rvfeatures.begin();
j != s.rvfeatures.end(); j++) {
for (vector<int>::const_iterator k = _feature2mef[j->first].begin();
k != _feature2mef[j->first].end(); k++) {
const double me = membp[_fb.Feature(*k).label()];
const double ee = (_fb.Feature(*k).label() == s.label ? 1.0 : 0);
const double grad = (me - ee) * j->second;
_vl[*k] -= eta * grad;
#ifdef SGD_CP
apply_l1_penalty(*k, u, _vl, q);
#endif
}
}
#ifdef FOLOS_NAIVE
for (size_t j = 0; j < d; j++) {
double& x = _vl[j];
if (x > 0)
x = max(0.0, x - eta * l1param);
else
x = min(0.0, x + eta * l1param);
}
#endif
}
logl /= _vs.size();
// fprintf(stderr, "%4d logl = %8.3f acc = %6.4f ", iter, logl,
// (double)ncorrect / ntotal);
#ifdef FOLOS_LAZY
if (l1param > 0) {
for (size_t j = 0; j < d; j++)
update_folos_lazy(iter_sample, j, _vl, sum_eta, last_updated);
}
#endif
double f = logl;
if (l1param > 0) {
const double l1 =
l1norm(_vl); // this is not accurate when lazy update is used
// cerr << "f0 = " << update_model_expectation() - l1param * l1 << "
// ";