contrib/mul/mbl/mbl_rvm_regression_builder.h

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// This is mul/mbl/mbl_rvm_regression_builder.h
#ifndef mbl_rvm_regression_builder_h_
#define mbl_rvm_regression_builder_h_
//:
// \file
// \brief Object to train Relevance Vector Machines for regression
// \author Tim Cootes

#include <vcl_vector.h>
#include <vnl/vnl_vector.h>
#include <vnl/vnl_matrix.h>
#include <mbl/mbl_data_wrapper.h>

//=======================================================================
//: Object to train Relevance Vector Machines for regression.
// Trains Relevance Vector Machines (see papers by Michael Tipping)
// for regression.
class mbl_rvm_regression_builder
{
 private:
  //: Record of mean weights
  vnl_vector<double> mean_wts_;

  //: Record of covariance in weights
  vnl_matrix<double> S_;

  //: Compute design matrix F from subset of elements in kernel matrix
  //  Uses gaussian distance expression with variance var
  void design_matrix(const vnl_matrix<double>& kernel_matrix,
                     const vcl_vector<int>& index,
                     vnl_matrix<double>& F);

  //: Perform one iteration of optimisation
  bool update_step(const vnl_matrix<double>& design_matrix,
                   const vnl_vector<double>& targets,
                   const vcl_vector<int>& index0,
                   const vcl_vector<double>& alpha0,
                   double sqr_width0,
                   vcl_vector<int>& index,
                   vcl_vector<double>& alpha,
                   double &error_var);
 public:
  //: Dflt ctor
  mbl_rvm_regression_builder();

  //: Destructor
  virtual ~mbl_rvm_regression_builder();

  //: Train RVM given a set of vectors and set of target values
  //  Resulting RVM has form f(x)=w[0]+sum w[i+1]K(x,data[index[i]])
  //  where K(x,y)=exp(-|x-y|^2/2var), and index.size() gives
  //  the number of the selected vectors.
  //  Note that on exit, weights.size()==index.size()+1
  //  weights[0] is the constant offset, and weights[i+1]
  //  corresponds to selected input vector index[i].
  // \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 estimated error variance for resulting function
  void 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);

  //: Train RVM given a distance matrix and set of target values
  //  Resulting RVM has form f(x)=w[0]+sum w[i+1]K(x,vec[index[i]])
  //  where K(x,y) is the kernel function, and index.size() gives
  //  the number of the selected vectors.
  //  Assuming the original data is vec[i], then on input we should
  //  have kernel_matrix(i,j)=K(vec[i],vec[j])
  //  Note that on exit, weights.size()==index.size()+1
  //  weights[0] is the constant offset, and weights[i+1]
  //  corresponds to selected input vector index[i].
  //
  // The algorithm involves inverting an (n+1)x(n+1) matrix,
  // where n is the number of vectors to consider as relevant
  // vectors.  This doesn't have to be all the samples.
  // For efficiency, one can provide the kernel matrix as an
  // m x n matrix, where m is the number of samples to test
  // against (targets.size()==m) but n<=m samples are to be
  // considered as potential relevant vectors (ie the first n).
  // \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 estimated error variance for resulting function
  void build(const vnl_matrix<double>& kernel_matrix,
             const vnl_vector<double>& targets,
             vcl_vector<int>& index,
             vnl_vector<double>& weights,
             double &error_var);
};

#endif