// Copyright (C) 2016 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_ElASTIC_NET_Hh_
#define DLIB_ElASTIC_NET_Hh_
#include "../matrix.h"
#include "elastic_net_abstract.h"
namespace dlib
{
// ----------------------------------------------------------------------------------------
class elastic_net
{
public:
template <typename EXP>
explicit elastic_net(
const matrix_exp<EXP>& XX
) : eps(1e-5), max_iterations(50000), verbose(false)
{
// make sure requires clause is not broken
DLIB_ASSERT(XX.size() > 0 &&
XX.nr() == XX.nc(),
"\t elastic_net::elastic_net(XX)"
<< " \n\t XX must be a non-empty square matrix."
<< " \n\t XX.nr(): " << XX.nr()
<< " \n\t XX.nc(): " << XX.nc()
<< " \n\t this: " << this
);
// If the number of columns in X is big and in particular bigger than the number of
// rows then we can get rid of them by doing some SVD magic. Doing this doesn't
// make the final results of anything change but makes all the matrices have
// dimensions that are X.nr() in size, which can be much smaller.
matrix<double,0,1> s;
svd3(XX,u,eig_vals,eig_vects);
s = sqrt(eig_vals);
X = eig_vects*diagm(s);
u = eig_vects*inv(diagm(s));
samples.resize(X.nr()*2);
for (size_t i = 0; i < samples.size(); ++i)
index.push_back(i);
active_size = index.size();
// setup the training samples used in the SVM optimizer below
for (size_t i = 0; i < samples.size(); ++i)
{
auto& x = samples[i];
const long idx = i/2;
if (i%2 == 0)
x.label = +1;
else
x.label = -1;
x.r = idx%X.nr();
}
}
template <typename EXP1, typename EXP2>
elastic_net(
const matrix_exp<EXP1>& XX,
const matrix_exp<EXP2>& XY
) : elastic_net(XX)
{
// make sure requires clause is not broken
DLIB_ASSERT(XX.size() > 0 &&
XX.nr() == XX.nc() &&
is_col_vector(XY) &&
XX.nc() == XY.size() ,
"\t elastic_net::elastic_net(XX,XY)"
<< " \n\t Invalid inputs were given to this function."
<< " \n\t XX.size(): " << XX.size()
<< " \n\t is_col_vector(XY): " << is_col_vector(XY)
<< " \n\t XX.nr(): " << XX.nr()
<< " \n\t XX.nc(): " << XX.nc()
<< " \n\t XY.size(): " << XY.size()
<< " \n\t this: " << this
);
set_xy(XY);
}
long size (
) const { return u.nr(); }
template <typename EXP>
void set_xy(
const matrix_exp<EXP>& XY
)
{
// make sure requires clause is not broken
DLIB_ASSERT(is_col_vector(XY) &&
XY.size() == size(),
"\t void elastic_net::set_y(Y)"
<< " \n\t Invalid inputs were given to this function."
<< " \n\t is_col_vector(XY): " << is_col_vector(XY)
<< " \n\t size(): " << size()
<< " \n\t XY.size(): " << XY.size()
<< " \n\t this: " << this
);
Y = trans(u)*XY;
// We can use the ynorm after it has been projected because the only place Y
// appears in the algorithm is in terms of dot products with w and x vectors.
// But those vectors are always in the span of X and therefore we only see the
// part of the norm of Y that is in the span of X (and hence u since u and X
// have the same span by construction)
ynorm = length_squared(Y);
xdoty = X*Y;
eig_vects_xdoty = trans(eig_vects)*xdoty;
w.set_size(Y.size());
// zero out any memory of previous solutions
alpha.assign(X.nr()*2, 0);
}
bool have_target_values (
) const { return Y.size() != 0; }
void set_epsilon(
double eps_
)
{
// make sure requires clause is not broken
DLIB_ASSERT(eps_ > 0,
"\t void elastic_net::set_epsilon()"
<< " \n\t eps_ must be greater than 0"
<< " \n\t eps_: " << eps_
<< " \n\t this: " << this
);
eps = eps_;
}
unsigned long get_max_iterations (
) const { return max_iterations; }
void set_max_iterations (
unsigned long max_iter
)
{
max_iterations = max_iter;
}
void be_verbose (
)
{
verbose = true;
}
void be_quiet (
)
{
verbose = false;
}
double get_epsilon (
) const { return eps; }
matrix<double,0,1> operator() (
double ridge_lambda,
double lasso_budget = std::numeric_limits<double>::infinity()
)
{
// make sure requires clause is not broken
DLIB_ASSERT(have_target_values() &&
ridge_lambda > 0 &&
lasso_budget > 0 ,
"\t matrix<double,0,1> elastic_net::operator()()"
<< " \n\t Invalid inputs were given to this function."
<< " \n\t have_target_values(): " << have_target_values()
<< " \n\t ridge_lambda: " << ridge_lambda
<< " \n\t lasso_budget: " << lasso_budget
<< " \n\t this: " << this
);
// First check if lasso_budget is so big that it isn't even active. We do this
// by doing just ridge regression and checking the result.
matrix<double,0,1> betas = eig_vects*tmp(inv(diagm(eig_vals + ridge_lambda))*eig_vects_xdoty);
if (sum(abs(betas)) <= lasso_budget)
return betas;
// Set w back to 0. We will compute the w corresponding to what is currently
// in alpha layer on. This way w and alpha are always in sync.
w = 0;
wy_mult = 0;
wdoty = 0;
// return dot(w,x)
auto dot = [&](const matrix<double,0,1>& w, const en_sample2& x)
{
const double xmul = -x.label*(1/lasso_budget);
// Do the base dot product but don't forget to add in the -(1/t)*y part from the svm reduction paper
double val = rowm(X,x.r)*w + xmul*wdoty + wy_mult*xdoty(x.r) + xmul*wy_mult*ynorm;
return val;
};
// perform w += scale*x;
auto add_to = [&](matrix<double,0,1>& w, double scale, const en_sample2& x)
{
const double xmul = -x.label*(1/lasso_budget);
wy_mult += scale*xmul;
wdoty += scale*xdoty(x.r);
w += scale*trans(rowm(X,x.r));
};
const double Dii = ridge_lambda;
// setup the training samples used in the SVM optimizer below
for (size_t i = 0; i < samples.size(); ++i)
{
auto& x = samples[i];
const double xmul = -x.label*(1/lasso_budget);
x.xdotx = xmul*xmul*ynorm;
for (long c = 0; c < X.nc(); ++c)
x.xdotx += std::pow(X(x.r,c)+xmul*Y(c), 2.0) - std::pow(xmul*Y(c),2.0);
// compute the correct w given whatever might be in alpha.
if (alpha[i] != 0)
add_to(w, x.label*alpha[i], samples[i]);
}
// Now run the optimizer
double PG_max_prev = std::numeric_limits<double>::infinity();
double PG_min_prev = -std::numeric_limits<double>::infinity();
unsigned int iter;
for (iter = 0; iter < max_iterations; ++iter)
{
// randomly shuffle the indices
for (unsigned long i = 0; i < active_size; ++i)
{
// pick a random index >= i
const long j = i + rnd.get_random_32bit_number()%(active_size-i);
std::swap(index[i], index[j]);
}
double PG_max = -std::numeric_limits<double>::infinity();
double PG_min = std::numeric_limits<double>::infinity();
for (size_t ii = 0; ii < active_size; ++ii)
{
const auto i = index[ii];
const auto& x = samples[i];
double G = x.label*dot(w, x) - 1 + Dii*alpha[i];
double PG = 0;
if (alpha[i] == 0)
{
if (G > PG_max_prev)
{
// shrink the active set of training examples
--active_size;
std::swap(index[ii], index[active_size]);
--ii;
continue;
}
if (G < 0)
PG = G;
}
else
{
PG = G;
}
if (PG > PG_max)
PG_max = PG;
if (PG < PG_min)
PG_min = PG;
// if PG != 0
if (std::abs(PG) > 1e-12)
{
const double alpha_old = alpha[i];
alpha[i] = std::max(alpha[i] - G/(x.xdotx+Dii), (double)0.0);
const double delta = (alpha[i]-alpha_old)*x.label;
add_to(w, delta, x);
}
}
if (verbose)
{
using namespace std;
cout << "gap: " << PG_max - PG_min << endl;
cout << "active_size: " << active_size << endl;
cout << "iter: " << iter << endl;
cout << endl;
}
if (PG_max - PG_min <= eps)
{
// stop if we are within eps tolerance and the last iteration
// was over all the samples
if (active_size == index.size())
break;
// Turn off shrinking on the next iteration. We will stop if the
// tolerance is still <= eps when shrinking is off.
active_size = index.size();
PG_max_prev = std::numeric_limits<double>::infinity();
PG_min_prev = -std::numeric_limits<double>::infinity();
}
else
{
PG_max_prev = PG_max;
PG_min_prev = PG_min;
if (PG_max_prev <= 0)
PG_max_prev = std::numeric_limits<double>::infinity();
if (PG_min_prev >= 0)
PG_min_prev = -std::numeric_limits<double>::infinity();
}
// recalculate wdoty every so often to avoid drift.
if (iter%100 == 0)
wdoty = dlib::dot(Y, w);
}
betas.set_size(alpha.size()/2);
for (long i = 0; i < betas.size(); ++i)
betas(i) = lasso_budget*(alpha[2*i] - alpha[2*i+1]);
betas /= sum(mat(alpha));
return betas;
}
private:
struct en_sample2
{
// X location
long r;
double label;
double xdotx;
};
std::vector<en_sample2> samples;
std::vector<double> alpha;
double ynorm;
matrix<double> X;
matrix<double,0,1> Y;
matrix<double,0,1> xdoty;
double wdoty;
double wy_mult; // logically, the real w is what is in the w vector + wy_mult*Y
matrix<double,0,1> w;
std::vector<long> index;
unsigned long active_size;
matrix<double,0,1> eig_vects_xdoty;
matrix<double,0,1> eig_vals;
matrix<double> eig_vects;
matrix<double> u;
dlib::rand rnd;
double eps;
unsigned long max_iterations;
bool verbose;
};
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_ElASTIC_NET_Hh_