// Copyright (C) 2017 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_UPPER_bOUND_FUNCTION_Hh_
#define DLIB_UPPER_bOUND_FUNCTION_Hh_
#include "upper_bound_function_abstract.h"
#include "../svm/svm_c_linear_dcd_trainer.h"
#include "../statistics.h"
#include <limits>
#include <utility>
namespace dlib
{
// ----------------------------------------------------------------------------------------
struct function_evaluation
{
function_evaluation() = default;
function_evaluation(const matrix<double,0,1>& x, double y) :x(x), y(y) {}
matrix<double,0,1> x;
double y = std::numeric_limits<double>::quiet_NaN();
};
// ----------------------------------------------------------------------------------------
class upper_bound_function
{
public:
upper_bound_function(
) = default;
upper_bound_function(
const double relative_noise_magnitude,
const double solver_eps
) : relative_noise_magnitude(relative_noise_magnitude), solver_eps(solver_eps)
{
DLIB_CASSERT(relative_noise_magnitude >= 0);
DLIB_CASSERT(solver_eps > 0);
}
explicit upper_bound_function(
const std::vector<function_evaluation>& _points,
const double relative_noise_magnitude = 0.001,
const double solver_eps = 0.0001
) : relative_noise_magnitude(relative_noise_magnitude), solver_eps(solver_eps), points(_points)
{
DLIB_CASSERT(relative_noise_magnitude >= 0);
DLIB_CASSERT(solver_eps > 0);
if (points.size() > 1)
{
DLIB_CASSERT(points[0].x.size() > 0, "The vectors can't be empty.");
const long dims = points[0].x.size();
for (auto& p : points)
DLIB_CASSERT(p.x.size() == dims, "All the vectors given to upper_bound_function must have the same dimensionality.");
learn_params();
}
}
void add (
const function_evaluation& point
)
{
DLIB_CASSERT(point.x.size() != 0, "The vectors can't be empty.");
if (points.size() == 0)
{
points.push_back(point);
return;
}
DLIB_CASSERT(point.x.size() == dimensionality(), "All the vectors given to upper_bound_function must have the same dimensionality.");
if (points.size() < 4)
{
points.push_back(point);
*this = upper_bound_function(points, relative_noise_magnitude, solver_eps);
return;
}
points.push_back(point);
// add constraints between the new point and the old points
for (size_t i = 0; i < points.size()-1; ++i)
active_constraints.push_back(std::make_pair(i,points.size()-1));
learn_params();
}
long num_points(
) const
{
return points.size();
}
long dimensionality(
) const
{
if (points.size() == 0)
return 0;
else
return points[0].x.size();
}
const std::vector<function_evaluation>& get_points(
) const
{
return points;
}
double operator() (
const matrix<double,0,1>& x
) const
{
DLIB_CASSERT(num_points() > 0);
DLIB_CASSERT(x.size() == dimensionality());
double upper_bound = std::numeric_limits<double>::infinity();
for (size_t i = 0; i < points.size(); ++i)
{
const double local_bound = points[i].y + std::sqrt(offsets[i] + dot(slopes, squared(x-points[i].x)));
upper_bound = std::min(upper_bound, local_bound);
}
return upper_bound;
}
private:
void learn_params (
)
{
const long dims = points[0].x.size();
using sample_type = std::vector<std::pair<size_t,double>>;
using kernel_type = sparse_linear_kernel<sample_type>;
std::vector<sample_type> x;
std::vector<double> y;
// We are going to normalize the data so the values aren't extreme. First, we
// collect statistics on our data.
std::vector<running_stats<double>> x_rs(dims);
running_stats<double> y_rs;
for (auto& v : points)
{
for (long i = 0; i < v.x.size(); ++i)
x_rs[i].add(v.x(i));
y_rs.add(v.y);
}
// compute normalization vectors for the data. The only reason we do this is
// to make the optimization well conditioned. In particular, scaling the y
// values will prevent numerical errors in the 1-diff*diff computation below that
// would otherwise result when diff is really big. Also, scaling the xvalues
// to be about 1 will similarly make the optimization more stable and it also
// has the added benefit of keeping the relative_noise_magnitude's scale
// constant regardless of the size of x values.
const double yscale = 1.0/y_rs.stddev();
std::vector<double> xscale(dims);
for (size_t i = 0; i < xscale.size(); ++i)
xscale[i] = 1.0/(x_rs[i].stddev()*yscale); // make it so that xscale[i]*yscale == 1/x_rs[i].stddev()
sample_type samp;
auto add_constraint = [&](long i, long j) {
samp.clear();
for (long k = 0; k < dims; ++k)
{
double temp = (points[i].x(k) - points[j].x(k))*xscale[k]*yscale;
samp.push_back(std::make_pair(k, temp*temp));
}
if (points[i].y > points[j].y)
samp.push_back(std::make_pair(dims + j, relative_noise_magnitude));
else
samp.push_back(std::make_pair(dims + i, relative_noise_magnitude));
const double diff = (points[i].y - points[j].y)*yscale;
samp.push_back(std::make_pair(dims + points.size(), 1-diff*diff));
x.push_back(samp);
y.push_back(1);
};
if (active_constraints.size() == 0)
{
x.reserve(points.size()*(points.size()-1)/2);
y.reserve(points.size()*(points.size()-1)/2);
for (size_t i = 0; i < points.size(); ++i)
{
for (size_t j = i+1; j < points.size(); ++j)
{
add_constraint(i,j);
}
}
}
else
{
for (auto& p : active_constraints)
add_constraint(p.first, p.second);
}
svm_c_linear_dcd_trainer<kernel_type> trainer;
trainer.set_c(std::numeric_limits<double>::infinity());
//trainer.be_verbose();
trainer.force_last_weight_to_1(true);
trainer.set_epsilon(solver_eps);
svm_c_linear_dcd_trainer<kernel_type>::optimizer_state state;
auto df = trainer.train(x,y, state);
// save the active constraints for later so we can use them inside add() to add
// new points efficiently.
if (active_constraints.size() == 0)
{
long k = 0;
for (size_t i = 0; i < points.size(); ++i)
{
for (size_t j = i+1; j < points.size(); ++j)
{
if (state.get_alpha()[k++] != 0)
active_constraints.push_back(std::make_pair(i,j));
}
}
}
else
{
DLIB_CASSERT(state.get_alpha().size() == active_constraints.size());
new_active_constraints.clear();
for (size_t i = 0; i < state.get_alpha().size(); ++i)
{
if (state.get_alpha()[i] != 0)
new_active_constraints.push_back(active_constraints[i]);
}
active_constraints.swap(new_active_constraints);
}
//std::cout << "points.size(): " << points.size() << std::endl;
//std::cout << "active_constraints.size(): " << active_constraints.size() << std::endl;
const auto& bv = df.basis_vectors(0);
slopes.set_size(dims);
for (long i = 0; i < dims; ++i)
slopes(i) = bv[i].second*xscale[i]*xscale[i];
//std::cout << "slopes:" << trans(slopes);
offsets.assign(points.size(),0);
for (size_t i = 0; i < points.size(); ++i)
{
offsets[i] += bv[slopes.size()+i].second*relative_noise_magnitude;
}
}
double relative_noise_magnitude = 0.001;
double solver_eps = 0.0001;
std::vector<std::pair<size_t,size_t>> active_constraints, new_active_constraints;
std::vector<function_evaluation> points;
std::vector<double> offsets; // offsets.size() == points.size()
matrix<double,0,1> slopes; // slopes.size() == points[0].first.size()
};
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_UPPER_bOUND_FUNCTION_Hh_