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-rw-r--r--utils/maxent.cpp427
1 files changed, 426 insertions, 1 deletions
diff --git a/utils/maxent.cpp b/utils/maxent.cpp
index 0f49ee9d..fd772e08 100644
--- a/utils/maxent.cpp
+++ b/utils/maxent.cpp
@@ -3,12 +3,15 @@
*/
#include "maxent.h"
+
+#include <vector>
+#include <iostream>
#include <cmath>
#include <cstdio>
-#include "lbfgs.h"
using namespace std;
+namespace maxent {
double ME_Model::FunctionGradient(const vector<double>& x,
vector<double>& grad) {
assert((int)_fb.Size() == x.size());
@@ -601,6 +604,428 @@ vector<double> ME_Model::classify(ME_Sample& mes) const {
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 << "
+ // ";
+ f -= l1param * l1;
+ int nonzero = 0;
+ for (int j = 0; j < d; j++)
+ if (_vl[j] != 0) nonzero++;
+ // cerr << " f = " << f << " l1 = " << l1 << " nonzero_features = "
+ // << nonzero << endl;
+ }
+ // fprintf(stderr, "%4d obj = %7.3f acc = %6.4f", iter+1, f,
+ // (double)ncorrect/ntotal);
+ // fprintf(stderr, "%4d obj = %f", iter+1, f);
+ fprintf(stderr, "%3d obj(err) = %f (%6.4f)", iter + 1, f,
+ 1 - (double)ncorrect / ntotal);
+
+ if (_nheldout > 0) {
+ double heldout_logl = heldout_likelihood();
+ // fprintf(stderr, " heldout_logl = %f acc = %6.4f\n",
+ // heldout_logl, 1 - _heldout_error);
+ fprintf(stderr, " heldout_logl(err) = %f (%6.4f)", heldout_logl,
+ _heldout_error);
+ }
+ fprintf(stderr, "\n");
+ }
+
+ return 0;
+}
+
+} // namespace maxent
+
/*
* $Log: maxent.cpp,v $
* Revision 1.1.1.1 2007/05/15 08:30:35 kyoshida