dlib C++ Library - krr_regression_ex.cpp

// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
/*
 This is an example illustrating the use of the kernel ridge regression 
 object from the dlib C++ Library.
 This example will train on data from the sinc function.
*/
#include <iostream>
#include <vector>
#include <dlib/svm.h>
using namespace std;
using namespace dlib;
// Here is the sinc function we will be trying to learn with kernel ridge regression 
double sinc(double x)
{
 if (x == 0)
 return 1;
 return sin(x)/x;
}
int main()
{
 // Here we declare that our samples will be 1 dimensional column vectors. 
 typedef matrix<double,1,1> sample_type;
 // Now sample some points from the sinc() function
 sample_type m;
 std::vector<sample_type> samples;
 std::vector<double> labels;
 for (double x = -10; x <= 4; x += 1)
 {
 m(0) = x;
 samples.push_back(m);
 labels.push_back(sinc(x));
 }
 // Now we are making a typedef for the kind of kernel we want to use. I picked the
 // radial basis kernel because it only has one parameter and generally gives good
 // results without much fiddling.
 typedef radial_basis_kernel<sample_type> kernel_type;
 // Here we declare an instance of the krr_trainer object. This is the
 // object that we will later use to do the training.
 krr_trainer<kernel_type> trainer;
 // Here we set the kernel we want to use for training. The radial_basis_kernel 
 // has a parameter called gamma that we need to determine. As a rule of thumb, a good 
 // gamma to try is 1.0/(mean squared distance between your sample points). So 
 // below we are using a similar value computed from at most 2000 randomly selected
 // samples.
 const double gamma = 3.0/compute_mean_squared_distance(randomly_subsample(samples, 2000));
 cout << "using gamma of " << gamma << endl;
 trainer.set_kernel(kernel_type(gamma));
 // now train a function based on our sample points
 decision_function<kernel_type> test = trainer.train(samples, labels);
 // now we output the value of the sinc function for a few test points as well as the 
 // value predicted by our regression.
 m(0) = 2.5; cout << sinc(m(0)) << " " << test(m) << endl;
 m(0) = 0.1; cout << sinc(m(0)) << " " << test(m) << endl;
 m(0) = -4; cout << sinc(m(0)) << " " << test(m) << endl;
 m(0) = 5.0; cout << sinc(m(0)) << " " << test(m) << endl;
 // The output is as follows:
 //using gamma of 0.075
 // 0.239389 0.239389
 // 0.998334 0.998362
 // -0.189201 -0.189254
 // -0.191785 -0.186618
 // The first column is the true value of the sinc function and the second
 // column is the output from the krr estimate. 
 // Note that the krr_trainer has the ability to tell us the leave-one-out predictions
 // for each sample. 
 std::vector<double> loo_values;
 trainer.train(samples, labels, loo_values);
 cout << "mean squared LOO error: " << mean_squared_error(labels,loo_values) << endl;
 cout << "R^2 LOO value: " << r_squared(labels,loo_values) << endl;
 // Which outputs the following:
 // mean squared LOO error: 8.29575e-07
 // R^2 LOO value: 0.999995
 // Another thing that is worth knowing is that just about everything in dlib is serializable.
 // So for example, you can save the test object to disk and recall it later like so:
 serialize("saved_function.dat") << test;
 // Now let's open that file back up and load the function object it contains.
 deserialize("saved_function.dat") >> test;
}