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// This is mul/mbl/mbl_rvm_regression_builder.cxx
#include "mbl_rvm_regression_builder.h"
//:
// \file
// \brief Object to train Relevance Vector Machines for regression
// \author Tim Cootes
#include <vcl_cmath.h>
#include <vcl_algorithm.h>
#include <vnl/algo/vnl_svd.h>
#include <mbl/mbl_matxvec.h>
#include <mbl/mbl_matrix_products.h>
#include <vcl_iostream.h>
#include <vcl_cassert.h>
//=======================================================================
// Note on indexing
// index[i] gives the index (from 0..n-1) of the selected vectors
// The offset weight is always included.
// The alpha's thus only apply to the n vector weights, not the offset
//=======================================================================
// Dflt ctor
//=======================================================================
mbl_rvm_regression_builder::mbl_rvm_regression_builder()
{
}
//=======================================================================
// Destructor
//=======================================================================
mbl_rvm_regression_builder::~mbl_rvm_regression_builder()
{
}
//: Compute design matrix F from subset of elements in kernel matrix
void mbl_rvm_regression_builder::design_matrix(const vnl_matrix<double>& K,
const vcl_vector<int>& index,
vnl_matrix<double>& F)
{
unsigned n=index.size();
unsigned ns=K.rows();
F.set_size(ns,n+1);
for (unsigned i=0;i<ns;++i)
{
F(i,0)=1.0;
for (unsigned j=0;j<n;++j)
{
F(i,j+1)=K(i,index[j]);
}
}
}
//: Train RVM given a set of vectors and set of target values
// Uses gaussian kernel function with variance var
// \param data[i] training vectors
// \param targets[i] gives value at vector i
// \param index returns indices of selected vectors
// \param weights returns weights for selected vectors
// \param error_var returns variance term for gaussian kernel
void mbl_rvm_regression_builder::gauss_build(
mbl_data_wrapper<vnl_vector<double> >& data,
double var, const vnl_vector<double>& targets,
vcl_vector<int>& index,
vnl_vector<double>& weights,
double &error_var)
{
assert(data.size()==targets.size());
unsigned n = data.size();
vnl_matrix<double> K(n,n);
double k = -1.0/2*var;
// Construct kernel matrix
for (unsigned i=1;i<n;++i)
{
data.set_index(i);
vnl_vector<double> vi = data.current();
for (unsigned j=0;j<i;++j)
{
data.set_index(j);
double d = vcl_exp(k*vnl_vector_ssd(vi,data.current()));
K(i,j)=d; K(j,i)=d;
}
}
for (unsigned i=0;i<n;++i) K(i,i)=1.0;
build(K,targets,index,weights,error_var);
}
//: Perform one iteration of optimisation
bool mbl_rvm_regression_builder::update_step(const vnl_matrix<double>& F,
const vnl_vector<double>& targets,
const vcl_vector<int>& index0,
const vcl_vector<double>& alpha0,
double error_var0,
vcl_vector<int>& index,
vcl_vector<double>& alpha,
double &error_var)
{
unsigned n0 = alpha0.size();
assert(F.rows()==targets.size());
assert(F.cols()==n0+1);
vnl_matrix<double> K_inv;
mbl_matrix_product_at_b(K_inv,F,F); // K_inv=F'F
K_inv/=error_var0;
for (unsigned i=0;i<n0;++i) K_inv(i+1,i+1)+=alpha0[i];
// K_inv = F'F/var + diag(alpha0)
vnl_svd<double> svd(K_inv);
S_ = svd.inverse();
vnl_vector<double> t2(n0+1);
mbl_matxvec_prod_vm(targets,F,t2); // t2=F'targets (n+1)
mbl_matxvec_prod_mv(S_,t2,mean_wts_); // mean=S*t2 (n+1)
mean_wts_/=error_var0;
#if 0
// ---------------------
// Estimate p(t|alpha,var)
vnl_vector<double> a_inv(n0+1);
a_inv[0]=0.0;
for (unsigned i=0;i<n0;++i) a_inv[i+1]=1.0/alpha0[i];
vnl_matrix<double> FAF;
mbl_matrix_product_adb(FAF,F,a_inv,F.transpose());
for (unsigned i=0;i<FAF.rows();++i) FAF(i,i)+=1.0/error_var0;
vnl_svd<double> FAFsvd(FAF);
vnl_matrix<double> FAFinv=FAFsvd.inverse();
vnl_vector<double> Xt=FAFinv*targets;
double M = dot_product(Xt,targets);
double det=FAFsvd.determinant_magnitude();
vcl_cout<<"M="<<M<<" -log(p)="<<M+vcl_log(det)<<vcl_endl;
// ---------------------
#endif // 0
// Compute new alphas and eliminate very large values
alpha.resize(0);
index.resize(0);
double sum=0.0;
double change=0.0;
for (unsigned i=0;i<n0;++i)
{
double a=vcl_max(0.0,1.0-alpha0[i]*S_(i+1,i+1));
sum+=a;
if (vcl_fabs(mean_wts_[i+1])<1e-4) continue;
double mi2 = mean_wts_[i+1]*mean_wts_[i+1];
a/=mi2;
if (a>1e8) continue;
alpha.push_back(a);
index.push_back(index0[i]);
change+=vcl_fabs(a-alpha0[i]);
}
// Update estimate of error_var
vnl_vector<double> Fm;
mbl_matxvec_prod_mv(F,mean_wts_,Fm); // Fm=F*mean
double sum_sqr_error=vnl_vector_ssd(targets,Fm);
error_var = sum_sqr_error/(targets.size()-sum);
// vcl_cout<<"Sum sqr error = "<<sum_sqr_error<<vcl_endl;
change+=vcl_fabs(error_var-error_var0);
// Decide if optimisation completed
if (alpha.size()!=alpha0.size()) return true;
return change/n0 > 0.01;
}
//: Train RVM given a distance matrix and set of target values
// \param kernel_matrix (i,j) element gives kernel function between i and j training vectors
// \param targets[i] gives value at vector i
// \param index returns indices of selected vectors
// \param weights returns weights for selected vectors
// \param error_var returns variance term for gaussian kernel
void mbl_rvm_regression_builder::build(
const vnl_matrix<double>& kernel_matrix,
const vnl_vector<double>& targets,
vcl_vector<int>& index,
vnl_vector<double>& weights,
double &error_var)
{
assert(kernel_matrix.rows()==targets.size());
assert(kernel_matrix.cols()<=targets.size());
unsigned n0=kernel_matrix.cols();
// Initialise to use all n0 samples with equal weights
index.resize(n0);
vcl_vector<double> alpha(n0),new_alpha;
vcl_vector<int> new_index;
for (unsigned i=0;i<n0;++i) { index[i]=i; alpha[i]=1e-4; }
error_var = 0.01;
double new_error_var;
vnl_matrix<double> F;
design_matrix(kernel_matrix,index,F);
int max_its=500;
int n_its=0;
while (update_step(F,targets,index,alpha,error_var,
new_index,new_alpha,new_error_var) && n_its<max_its)
{
index = new_index;
alpha = new_alpha;
error_var= new_error_var;
design_matrix(kernel_matrix,index,F);
n_its++;
}
if (n_its>=max_its)
vcl_cerr<<"mbl_rvm_regression_builder::build() Too many iterations. Convergence failure.\n";
weights=mean_wts_;
}
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