root/bdm/stat/emix.h @ 182

/*!
  \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;

//this comes first because it is used inside emix!

/*! \brief Class representing ratio of two densities
which arise e.g. by applying the Bayes rule.
It represents density in the form:
\f[
f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)}
\f]
where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$.

In particular this type of arise by conditioning of a mixture model.

At present the only supported operation is evalcond().
 */
class mratio: public mpdf {
        protected:
        //! Nominator in the form of mpdf
                const epdf* nom;
        //!Denominator in the form of epdf
                epdf* den;
        //!flag for destructor 
                bool destroynom;
        public:
        //!Default constructor. By default, the given epdf is not copied! 
        //! It is assumed that this function will be used only temporarily.
                mratio(const epdf* nom0, const RV &rv, bool copy=false):mpdf(rv,RV()){
                        if (copy){
//                      nom = nom0->_copy_();
                                destroynom=true;
                        } else {
                                nom = nom0;
                                destroynom = false;
                        }
                        rvc = nom->_rv().subt(rv);
                        it_assert_debug(rvc.length()>0,"Makes no sense to use this object!");
                        den = nom->marginal(rvc);
                };
                double evalcond(const vec &val, const vec &cond) const {
                        return exp(nom->evalpdflog(concat(val,cond)) - den->evalpdflog(cond));
                }
        //! Object takes ownership of nom and will destroy it
                void ownnom(){destroynom=true;}
        //! Default destructor
                ~mratio(){delete den; if (destroynom) {delete nom;}}
};

/*!
* \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;
        //!Flag if owning Coms
        bool destroyComs;
public:
        //!Default constructor
        emix ( const RV &rv ) : epdf ( rv ) {};
        //! Set weights \c w and components \c Coms
        //!By default Coms are copied inside. \param copy can be set to false if Coms live externally. Use method ownComs() if Coms should be destroyed by the destructor.
        void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy=true );

        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 );
        };
        vec evalpdflog_m ( const mat &Val ) const {
                vec x=ones(Val.cols());
                vec y(Val.cols());
                for (int i = 0; i < w.length(); i++ ) {
                        y = w ( i )*exp(Coms ( i )->evalpdflog_m ( Val ) );
                        elem_mult_inplace(y,x); //result is in x
                }
                return log(x);
        };

        emix* marginal ( const RV &rv ) const;
        mratio* condition ( const RV &rv ) const; //why not mratio!!

//Access methods
        //! returns a pointer to the internal mean value. Use with Care!
        vec& _w() {return w;}
        virtual ~emix() {if ( destroyComs ) {for ( int i=0;i<Coms.length();i++ ) {delete Coms ( i );}}}
        //! Auxiliary function for taking ownership of the Coms()
        void ownComs() {destroyComs=true;}
};

/*! \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 compositepdf, public mpdf {
protected:
        //! pointers to epdfs - shortcut to mpdfs()._epdf()
        Array<epdf*> epdfs;
        //! Indeces of rvc in common rvc
        Array<ivec> irvcs_rvc;
        //! Indeces of common rvc in rvcs
        Array<ivec> irvc_rvcs;
public:
        /*!\brief Constructor from list of mFacs,
        */
        mprod ( Array<mpdf*> mFacs ) : compositepdf ( mFacs ), mpdf ( getrv ( true ),RV() ), epdfs ( n ), irvcs_rvc ( n ), irvc_rvcs ( n ) {
                setrvc ( rv,rvc );
                setindices ( rv );
                for ( int i = 0;i < n;i++ ) {
                        // establish link between rvc and rvcs
                        rvc.dataind ( mpdfs ( i )->_rvc(), irvc_rvcs ( i ), irvcs_rvc ( i ) );
                }

                for ( int i=0;i<n;i++ ) {
                        epdfs ( i ) =& ( mpdfs ( i )->_epdf() );
                }
        };

        double evalcond ( const vec &val, const vec &cond ) {
                int i;
                double res = 0.0;
                vec condi;
                for ( i = n - 1;i >= 0;i-- ) {
                        if ( ( irvcs_rvc ( i ).length() > 0 ) || ( irvcs_rv ( i ).length() > 0 ) ) {
                                condi = zeros ( irvcs_rvc ( i ).length() +irvcs_rv ( i ).length() );
                                //copy part of the rvc into condi
                                set_subvector ( condi, irvcs_rvc ( i ), get_vec ( cond,irvc_rvcs ( i ) ) );
                                //copy part of the rv into condi
                                set_subvector ( condi, irvcs_rv ( i ), get_vec ( val,irv_rvcs ( i ) ) );
                                mpdfs ( i )->condition ( condi );
                        }
                        // add logarithms
                        res += epdfs ( i )->evalpdflog ( val ( rvsinrv ( i ) ) );
                }
                return exp ( 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 ( ( irvcs_rvc ( i ).length() > 0 ) || ( irvcs_rv ( i ).length() > 0 ) ) {
                                condi = zeros ( irvcs_rv ( i ).length() + irvcs_rvc ( i ).length() );
                                // copy data in condition
                                set_subvector ( condi,irvcs_rvc ( i ), get_vec ( cond, irvc_rvcs ( i ) ) );
                                // copy data in already generated sample
                                set_subvector ( condi,irvcs_rv ( i ), get_vec ( smp,irv_rvcs ( i ) ) );

                                mpdfs ( i )->condition ( condi );
                        }
                        smpi = epdfs ( i )->sample();
                        // copy contribution of this pdf into smp
                        set_subvector ( smp,rvsinrv ( 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<const epdf*> epdfs;
        //! Array of indeces
        Array<ivec> rvinds;
public:
        eprod ( const Array<const 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;
        }
        //!access function
        const epdf* operator () ( int i ) const {it_assert_debug ( i<epdfs.length(),"wrong index" );return epdfs ( i );}
};


/*! \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