paradiseo/eo/contrib/mathsym/regression/Scaling.cpp
2012-08-30 11:30:11 +02:00

417 lines
11 KiB
C++

/*
* Copyright (C) 2005 Maarten Keijzer
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of version 2 of the GNU General Public License as
* published by the Free Software Foundation.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "Scaling.h"
#include "TargetInfo.h"
using namespace std;
Scaling slope(const std::valarray<double>& x, const TargetInfo& targets) {
double xx = 0.0;
double xy = 0.0;
const valarray<double>& y = targets.targets();
for (unsigned i = 0; i < x.size(); ++i) {
xx += x[i] * x[i];
xy += x[i] * y[i];
}
if (xx < 1e-7) return Scaling(new LinearScaling(0.0,0.0));
double b = xy / xx;
return Scaling(new LinearScaling(0.0, b));
}
// Still needs proper testing with non-trivial lambda
Scaling regularized_least_squares(const std::valarray<double>& inputs, const TargetInfo& targets, double lambda) {
double n = inputs.size();
valarray<double> x = inputs;
double a,b,d;
a=b=d=0;
for (unsigned i = 0; i < n; ++i) {
a += 1 + lambda;
b += x[i];
d += x[i] * x[i] + lambda;
}
//invert
double ad_bc = a*d - b * b;
// if ad_bc equals zero there's a problem
if (ad_bc < 1e-17) return Scaling(new LinearScaling);
double ai = d/ad_bc;
double bi = -b/ad_bc;
double di = a/ad_bc;
double ci = bi;
// Now multiply this inverted covariance matrix (C^-1) with x' * t
std::valarray<double> ones = x;
// calculate C^-1 * x' )
for (unsigned i = 0; i < n; ++i)
{
ones[i] = (ai + bi * x[i]);
x[i] = (ci + di * x[i]);
}
// results are in [ones, x], now multiply with y
a = 0.0; // intercept
b = 0.0; // slope
const valarray<double>& t = targets.targets();
for (unsigned i = 0; i < n; ++i)
{
a += ones[i] * t[i];
b += x[i] * t[i];
}
return Scaling(new LinearScaling(a,b));
}
Scaling ols(const std::valarray<double>& y, const std::valarray<double>& t) {
double n = y.size();
double y_mean = y.sum() / n;
double t_mean = t.sum() / n;
std::valarray<double> y_var = (y - y_mean);
std::valarray<double> t_var = (t - t_mean);
std::valarray<double> cov = t_var * y_var;
y_var *= y_var;
t_var *= t_var;
double sumvar = y_var.sum();
if (sumvar == 0. || sumvar/n < 1e-7 || sumvar/n > 1e+7) // breakout when numerical problems are likely
return Scaling(new LinearScaling(t_mean,0.));
double b = cov.sum() / sumvar;
double a = t_mean - b * y_mean;
Scaling s = Scaling(new LinearScaling(a,b));
return s;
}
Scaling ols(const std::valarray<double>& y, const TargetInfo& targets) {
double n = y.size();
double y_mean = y.sum() / n;
std::valarray<double> y_var = (y - y_mean);
std::valarray<double> cov = targets.tcov_part() * y_var;
y_var *= y_var;
double sumvar = y_var.sum();
if (sumvar == 0. || sumvar/n < 1e-7 || sumvar/n > 1e+7) // breakout when numerical problems are likely
return Scaling(new LinearScaling(targets.tmean(),0.));
double b = cov.sum() / sumvar;
double a = targets.tmean() - b * y_mean;
if (!finite(b)) {
cout << a << ' ' << b << endl;
cout << sumvar << endl;
cout << y_mean << endl;
cout << cov.sum() << endl;
exit(1);
}
Scaling s = Scaling(new LinearScaling(a,b));
return s;
}
Scaling wls(const std::valarray<double>& inputs, const TargetInfo& targets) {
std::valarray<double> x = inputs;
const std::valarray<double>& w = targets.weights();
unsigned n = x.size();
// First calculate x'*W (as W is a diagonal matrix it's simply elementwise multiplication
std::valarray<double> wx = targets.weights() * x;
// Now x'*W is contained in [w,wx], calculate x' * W * x (the covariance)
double a,b,d;
a=b=d=0.0;
for (unsigned i = 0; i < n; ++i)
{
a += w[i];
b += wx[i];
d += x[i] * wx[i];
}
//invert
double ad_bc = a*d - b * b;
// if ad_bc equals zero there's a problem
if (ad_bc < 1e-17) return Scaling(new LinearScaling);
double ai = d/ad_bc;
double bi = -b/ad_bc;
double di = a/ad_bc;
double ci = bi;
// Now multiply this inverted covariance matrix (C^-1) with x' * W * y
// create alias to reuse the wx we do not need anymore
std::valarray<double>& ones = wx;
// calculate C^-1 * x' * W (using the fact that W is diagonal)
for (unsigned i = 0; i < n; ++i)
{
ones[i] = w[i]*(ai + bi * x[i]);
x[i] = w[i]*(ci + di * x[i]);
}
// results are in [ones, x], now multiply with y
a = 0.0; // intercept
b = 0.0; // slope
const valarray<double>& t = targets.targets();
for (unsigned i = 0; i < n; ++i)
{
a += ones[i] * t[i];
b += x[i] * t[i];
}
return Scaling(new LinearScaling(a,b));
}
//Scaling med(const std::valarray<double>& inputs, const TargetInfo& targets);
double mse(const std::valarray<double>& y, const TargetInfo& t) {
valarray<double> residuals = t.targets()-y;
residuals *= residuals;
double sz = residuals.size();
if (t.has_weights()) {
residuals *= t.weights();
sz = 1.0;
}
return residuals.sum() / sz;
}
double rms(const std::valarray<double>& y, const TargetInfo& t) {
return sqrt(mse(y,t));
}
double mae(const std::valarray<double>& y, const TargetInfo& t) {
valarray<double> residuals = abs(t.targets()-y);
if (t.has_weights()) residuals *= t.weights();
return residuals.sum() / residuals.size();
}
/*
double standard_error(const std::valarray<double>& y, const std::pair<double,double>& scaling) {
double a = scaling.first;
double b = scaling.second;
double n = y.size();
double se = sqrt( pow(a+b*y-current_set->targets,2.0).sum() / (n-2));
double mean_y = y.sum() / n;
double sxx = pow( y - mean_y, 2.0).sum();
return se / sqrt(sxx);
}
double scaled_mse(const std::valarray<double>& y){
std::pair<double,double> scaling;
return scaled_mse(y,scaling);
}
double scaled_mse(const std::valarray<double>& y, std::pair<double, double>& scaling)
{
scaling = scale(y);
double a = scaling.first;
double b = scaling.second;
std::valarray<double> tmp = current_set->targets - a - b * y;
tmp *= tmp;
if (weights.size())
return (weights * tmp).sum();
return tmp.sum() / tmp.size();
}
double robust_mse(const std::valarray<double>& ny, std::pair<double, double>& scaling) {
double smse = scaled_mse(ny,scaling);
std::valarray<double> y = ny;
// find maximum covariance case
double n = y.size();
int largest = 0;
{
double y_mean = y.sum() / n;
std::valarray<double> y_var = (y - y_mean);
std::valarray<double> cov = tcov * y_var;
std::valarray<bool> maxcov = cov == cov.max();
for (unsigned i = 0; i < maxcov.size(); ++i) {
if (maxcov[i]) {
largest = i;
break;
}
}
}
double y_mean = (y.sum() - y[largest]) / (n-1);
y[largest] = y_mean; // dissappears from covariance calculation
std::valarray<double> y_var = (y - y_mean);
std::valarray<double> cov = tcov * y_var;
y_var *= y_var;
double sumvar = y_var.sum();
if (sumvar == 0. || sumvar/n < 1e-7 || sumvar/n > 1e+7) // breakout when numerical problems are likely
return worst_performance();
double b = cov.sum() / sumvar;
double a = tmean - b * y_mean;
std::valarray<double> tmp = current_set->targets - a - b * y;
tmp[largest] = 0.0;
tmp *= tmp;
double smse2 = tmp.sum() / (tmp.size()-1);
static std::ofstream os("smse.txt");
os << smse << ' ' << smse2 << '\n';
if (smse2 > smse) {
return worst_performance();
//std::cerr << "overfit? " << smse << ' ' << smse2 << '\n';
}
scaling.first = a;
scaling.second = b;
return smse2;
}
class Sorter {
const std::valarray<double>& scores;
public:
Sorter(const std::valarray<double>& _scores) : scores(_scores) {}
bool operator()(unsigned i, unsigned j) const {
return scores[i] < scores[j];
}
};
double coc(const std::valarray<double>& y) {
std::vector<unsigned> indices(y.size());
for (unsigned i = 0; i < y.size(); ++i) indices[i] = i;
std::sort(indices.begin(), indices.end(), Sorter(y));
const std::valarray<double>& targets = current_set->targets;
double neg = 1.0 - targets[indices[0]];
double pos = targets[indices[0]];
double cumpos = 0;
double cumneg = 0;
double sum=0;
double last_score = y[indices[0]];
for(unsigned i = 1; i < targets.size(); ++i) {
if (fabs(y[indices[i]] - last_score) < 1e-9) { // we call it tied
pos += targets[indices[i]];
neg += 1.0 - targets[indices[i]];
if (i < targets.size()-1)
continue;
}
sum += pos * cumneg + (pos * neg) * 0.5;
cumneg += neg;
cumpos += pos;
pos = targets[indices[i]];
neg = 1.0 - targets[indices[i]];
last_score = y[indices[i]];
}
return sum / (cumneg * cumpos);
}
// iterative re-weighted least squares (for parameters.classification)
double irls(const std::valarray<double>& scores, std::pair<double,double>& scaling) {
const std::valarray<double>& t = current_set->targets;
std::valarray<double> e(scores.size());
std::valarray<double> u(scores.size());
std::valarray<double> w(scores.size());
std::valarray<double> z(scores.size());
parameters.use_irls = false; parameters.classification=false;
scaling = scale(scores);
parameters.use_irls=true;parameters.classification=true;
if (scaling.second == 0.0) return worst_performance();
for (unsigned i = 0; i < 10; ++i) {
e = exp(scaling.first + scaling.second*scores);
u = e / (e + exp(-(scaling.first + scaling.second * scores)));
w = u*(1.-u);
z = (t-u)/w;
scaling = wls(scores, u, w);
//double ll = (log(u)*t + (1.-log(u))*(1.-t)).sum();
//std::cout << "Scale " << i << ' ' << scaling.first << " " << scaling.second << " LL " << 2*ll << std::endl;
}
// log-likelihood
u = exp(scaling.first + scaling.second*scores) / (1 + exp(scaling.first + scaling.second*scores));
double ll = (log(u)*t + (1.-log(u))*(1.-t)).sum();
return 2*ll;
}
*/