root/bdm/stat/emix.h @ 168

/*!
  \file
  \brief Probability distributions for Mixtures of pdfs
  \author Vaclav Smidl.

  -----------------------------------
  BDM++ - C++ library for Bayesian Decision Making under Uncertainty

  Using IT++ for numerical operations
  -----------------------------------
*/

#ifndef MX_H
#define MX_H

#include "libBM.h"
#include "libEF.h"
//#include <std>

using namespace itpp;

/*!
* \brief Mixture of epdfs

Density function:
\f[
f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1.
\f]
where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component,

*/
class emix : public epdf {
protected:
        //! weights of the components
        vec w;
        //! Component (epdfs)
        Array<epdf*> Coms;
public:
        //!Default constructor
        emix ( RV &rv ) : epdf ( rv ) {};
        //! Set weights \c w and components \c R
        void set_parameters ( const vec &w, const Array<epdf*> &Coms );

        vec sample() const;
        vec mean() const {
                int i; vec mu = zeros ( rv.count() );
                for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); }
                return mu;
        }
        double evalpdflog ( const vec &val ) const {
                int i;
                double sum = 0.0;
                for ( i = 0;i < w.length();i++ ) {sum += w ( i ) * Coms ( i )->evalpdflog ( val );}
                return log ( sum );
        };

//Access methods
        //! returns a pointer to the internal mean value. Use with Care!
        vec& _w() {return w;}
};

/*! \brief Chain rule decomposition of epdf

Probability density in the form of Chain-rule decomposition:
\[
f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3)
\]
Note that
*/
class mprod: public mpdf {
protected:
        //
        int n;
        // pointers to epdfs
        Array<epdf*> epdfs;
        Array<mpdf*> mpdfs;
        //
        //! Indeces of rvs in common rv
        Array<ivec> rvinds;
        //! Indeces of rvc in common rv
        Array<ivec> rvcinrv;
        //! Indeces of rvc in common rvc
        Array<ivec> rvcinds;
//      //! Indicate independence of its factors
//      bool independent;
//      //! Indicate internal creation of mpdfs which must be destroyed
//      bool intermpdfs;
public:
        /*!\brief Constructor from list of mFacs,
        Additional parameter overlap is left for future use. Do not set to true for mprod.
        */
        mprod ( Array<mpdf*> mFacs, bool overlap=false );

        double evalpdflog ( const vec &val ) const {
                int i;
                double res = 0.0;
                for ( i = n - 1;i > 0;i++ ) {
                        if ( rvcinds ( i ).length() > 0 )
                                {mpdfs ( i )->condition ( val ( rvcinds ( i ) ) );}
                        // add logarithms
                        res += epdfs ( i )->evalpdflog ( val ( rvinds ( i ) ) );
                }
                return res;
        }
        vec samplecond ( const vec &cond, double &ll ) {
                vec smp=zeros ( rv.count() );
                vec condi;
                vec smpi;
                ll = 0;
                for ( int i = ( n - 1 );i >= 0;i-- ) {
                        if ( rvcinds ( i ).length() > 0 ) {
                                condi = zeros ( rvcinrv.length() + rvcinds.length() );
                                // copy data in condition
                                set_subvector ( condi,rvcinds ( i ), cond );
                                // copy data in already generated sample
                                set_subvector ( condi,rvcinrv ( i ), smp );

                                mpdfs ( i )->condition ( condi );
                        }
                        smpi = epdfs ( i )->sample();
                        // copy contribution of this pdf into smp
                        set_subvector ( smp,rvinds ( i ), smpi );
                        // add ith likelihood contribution
                        ll+=epdfs ( i )->evalpdflog ( smpi );
                }
                return smp;
        }
        mat samplecond ( const vec &cond, vec &ll, int N ) {
                mat Smp ( rv.count(),N );
                for ( int i=0;i<N;i++ ) {Smp.set_col ( i,samplecond ( cond,ll ( i ) ) );}
                return Smp;
        }

        ~mprod() {};
};

//! Product of independent epdfs. For dependent pdfs, use mprod.
class eprod: public epdf {
protected:
        //! Components (epdfs)
        Array<epdf*> epdfs;
        //! Array of indeces
        Array<ivec> rvinds;
public:
        eprod ( const Array<epdf*> epdfs0 ) : epdf ( RV() ),epdfs ( epdfs0 ),rvinds ( epdfs.length() ) {
                bool independent=true;
                for ( int i=0;i<epdfs.length();i++ ) {
                        independent=rv.add ( epdfs ( i )->_rv() );
                        it_assert_debug ( independent==true, "eprod:: given components are not independent ." );
                        rvinds ( i ) = ( epdfs ( i )->_rv() ).dataind ( rv );
                }
        }

        vec mean() const {
                vec tmp ( rv.count() );
                for ( int i=0;i<epdfs.length();i++ ) {
                        vec pom = epdfs ( i )->mean();
                        set_subvector ( tmp,rvinds ( i ), pom );
                }
                return tmp;
        }
        vec sample() const {
                vec tmp ( rv.count() );
                for ( int i=0;i<epdfs.length();i++ ) {
                        vec pom = epdfs ( i )->sample();
                        set_subvector ( tmp,rvinds ( i ), pom );
                }
                return tmp;
        }
        double evalpdflog ( const vec &val ) const {
                double tmp=0;
                for ( int i=0;i<epdfs.length();i++ ) {
                        tmp+=epdfs(i)->evalpdflog(val(rvinds(i)));
                }
                return tmp;
        }
};


/*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type

*/
class mmix : public mpdf {
protected:
        //! Component (epdfs)
        Array<mpdf*> Coms;
        //!Internal epdf
        emix Epdf;
public:
        //!Default constructor
        mmix ( RV &rv, RV &rvc ) : mpdf ( rv, rvc ), Epdf ( rv ) {ep = &Epdf;};
        //! Set weights \c w and components \c R
        void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) {
                Array<epdf*> Eps ( Coms.length() );

                for ( int i = 0;i < Coms.length();i++ ) {
                        Eps ( i ) = & ( Coms ( i )->_epdf() );
                }
                Epdf.set_parameters ( w, Eps );
        };

        void condition ( const vec &cond ) {
                for ( int i = 0;i < Coms.length();i++ ) {Coms ( i )->condition ( cond );}
        };
};
#endif //MX_H