root/library/bdm/stat/emix.h @ 477

/*!
  \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 EMIX_H
#define EMIX_H

#define LOG2  0.69314718055995

#include "../shared_ptr.h"
#include "exp_family.h"

namespace bdm {

//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 evallogcond().
 */
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;
        //!datalink between conditional and nom
        datalink_m2e dl;
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 ( ), dl ( ) {
                // adjust rv and rvc
                rvc = nom0->_rv().subt ( rv );
                dimc = rvc._dsize();
                set_ep ( shared_ptr<epdf> ( new epdf ) );
                e()->set_parameters ( rv._dsize() );
                e()->set_rv ( rv );

                //prepare data structures
                if ( copy ) {
                        it_error ( "todo" );
                        destroynom = true;
                } else {
                        nom = nom0;
                        destroynom = false;
                }
                it_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" );

                // build denominator
                den = nom->marginal ( rvc );
                dl.set_connection ( rv, rvc, nom0->_rv() );
        };
        double evallogcond ( const vec &val, const vec &cond ) {
                double tmp;
                vec nom_val ( e()->dimension() + dimc );
                dl.pushup_cond ( nom_val, val, cond );
                tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) );
                it_assert_debug ( std::isfinite ( tmp ), "Infinite value" );
                return tmp;
        }
        //! 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 ( ) : epdf ( ) {};
        //! Set weights \c w and components \c Coms
        //!By default Coms are copied inside. Parameter \c 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 = false );

        vec sample() const;
        vec mean() const {
                int i;
                vec mu = zeros ( dim );
                for ( i = 0; i < w.length(); i++ ) {
                        mu += w ( i ) * Coms ( i )->mean();
                }
                return mu;
        }
        vec variance() const {
                //non-central moment
                vec mom2 = zeros ( dim );
                for ( int i = 0; i < w.length(); i++ ) {
                        mom2 += w ( i ) * ( Coms ( i )->variance() + pow ( Coms ( i )->mean(), 2 ) );
                }
                //central moment
                return mom2 - pow ( mean(), 2 );
        }
        double evallog ( const vec &val ) const {
                int i;
                double sum = 0.0;
                for ( i = 0; i < w.length(); i++ ) {
                        sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) );
                }
                if ( sum == 0.0 ) {
                        sum = std::numeric_limits<double>::epsilon();
                }
                double tmp = log ( sum );
                it_assert_debug ( std::isfinite ( tmp ), "Infinite" );
                return tmp;
        };
        vec evallog_m ( const mat &Val ) const {
                vec x = zeros ( Val.cols() );
                for ( int i = 0; i < w.length(); i++ ) {
                        x += w ( i ) * exp ( Coms ( i )->evallog_m ( Val ) );
                }
                return log ( x );
        };
        //! Auxiliary function that returns pdflog for each component
        mat evallog_M ( const mat &Val ) const {
                mat X ( w.length(), Val.cols() );
                for ( int i = 0; i < w.length(); i++ ) {
                        X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ) );
                }
                return 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;
        }

        //!access function
        epdf* _Coms ( int i ) {
                return Coms ( i );
        }
        void set_rv ( const RV &rv ) {
                epdf::set_rv ( rv );
                for ( int i = 0; i < Coms.length(); i++ ) {
                        Coms ( i )->set_rv ( rv );
                }
        }
};


/*!
* \brief Mixture of egiws

*/
class egiwmix : public egiw {
protected:
        //! weights of the components
        vec w;
        //! Component (epdfs)
        Array<egiw*> Coms;
        //!Flag if owning Coms
        bool destroyComs;
public:
        //!Default constructor
        egiwmix ( ) : egiw ( ) {};

        //! Set weights \c w and components \c Coms
        //!By default Coms are copied inside. Parameter \c 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<egiw*> &Coms, bool copy = false );

        //!return expected value
        vec mean() const;

        //!return a sample from the density
        vec sample() const;

        //!return the expected variance
        vec variance() const;

        // TODO!!! Defined to follow ANSI and/or for future development
        void mean_mat ( mat &M, mat&R ) const {};
        double evallog_nn ( const vec &val ) const {
                return 0;
        };
        double lognc () const {
                return 0;
        };
        emix* marginal ( const RV &rv ) const;

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

        //!access function
        egiw* _Coms ( int i ) {
                return Coms ( i );
        }

        void set_rv ( const RV &rv ) {
                egiw::set_rv ( rv );
                for ( int i = 0; i < Coms.length(); i++ ) {
                        Coms ( i )->set_rv ( rv );
                }
        }

        //! Approximation of a GiW mix by a single GiW pdf
        egiw* approx();
};

/*! \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().posterior()
        Array<epdf*> epdfs;
        //! Data link for each mpdfs
        Array<datalink_m2m*> dls;

        //! dummy ep
        shared_ptr<epdf> dummy;

public:
        /*!\brief Constructor from list of mFacs,
        */
        mprod() : dummy ( new epdf() ) { }
        mprod ( Array<mpdf*> mFacs ) :
                        dummy ( new epdf() ) {
                set_elements ( mFacs );
        }

        void set_elements ( Array<mpdf*> mFacs , bool own = false ) {

                compositepdf::set_elements ( mFacs, own );
                dls.set_size ( mFacs.length() );
                epdfs.set_size ( mFacs.length() );

                set_ep ( dummy );
                RV rv = getrv ( true );
                set_rv ( rv );
                dummy->set_parameters ( rv._dsize() );
                setrvc ( e()->_rv(), rvc );
                // rv and rvc established = > we can link them with mpdfs
                for ( int i = 0; i < mpdfs.length(); i++ ) {
                        dls ( i ) = new datalink_m2m;
                        dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), _rv(), _rvc() );
                }

                for ( int i = 0; i < mpdfs.length(); i++ ) {
                        epdfs ( i ) = mpdfs ( i )->e();
                }
        };

        double evallogcond ( const vec &val, const vec &cond ) {
                int i;
                double res = 0.0;
                for ( i = mpdfs.length() - 1; i >= 0; i-- ) {
                        /*                      if ( mpdfs(i)->_rvc().count() >0) {
                                                        mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) );
                                                }
                                                // add logarithms
                                                res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/
                        res += mpdfs ( i )->evallogcond (
                                   dls ( i )->pushdown ( val ),
                                   dls ( i )->get_cond ( val, cond )
                               );
                }
                return res;
        }
        vec evallogcond_m ( const mat &Dt, const vec &cond ) {
                vec tmp ( Dt.cols() );
                for ( int i = 0; i < Dt.cols(); i++ ) {
                        tmp ( i ) = evallogcond ( Dt.get_col ( i ), cond );
                }
                return tmp;
        };
        vec evallogcond_m ( const Array<vec> &Dt, const vec &cond ) {
                vec tmp ( Dt.length() );
                for ( int i = 0; i < Dt.length(); i++ ) {
                        tmp ( i ) = evallogcond ( Dt ( i ), cond );
                }
                return tmp;
        };


        //TODO smarter...
        vec samplecond ( const vec &cond ) {
                //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely.
                vec smp = std::numeric_limits<double>::infinity() * ones ( e()->dimension() );
                vec smpi;
                // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated!
                for ( int i = ( mpdfs.length() - 1 ); i >= 0; i-- ) {
                        if ( mpdfs ( i )->dimensionc() ) {
                                mpdfs ( i )->condition ( dls ( i )->get_cond ( smp , cond ) ); // smp is val here!!
                        }
                        smpi = epdfs ( i )->sample();
                        // copy contribution of this pdf into smp
                        dls ( i )->pushup ( smp, smpi );
                        // add ith likelihood contribution
                }
                return smp;
        }
        mat samplecond ( const vec &cond,  int N ) {
                mat Smp ( dimension(), N );
                for ( int i = 0; i < N; i++ ) {
                        Smp.set_col ( i, samplecond ( cond ) );
                }
                return Smp;
        }

        ~mprod() {};
        //! Load from structure with elements:
        //!  \code
        //! { class='mprod';
        //!   mpdfs = (..., ...);     // list of mpdfs in the order of chain rule
        //! }
        //! \endcode
        //!@}
        void from_setting ( const Setting &set ) {
                Array<mpdf*> Atmp; //temporary Array
                UI::get ( Atmp, set, "mpdfs", UI::compulsory );
                set_elements ( Atmp, true );
        }

};
UIREGISTER ( 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<datalink*> dls;
public:
        eprod () : epdfs ( 0 ), dls ( 0 ) {};
        void set_parameters ( const Array<const epdf*> &epdfs0, bool named = true ) {
                epdfs = epdfs0;//.set_length ( epdfs0.length() );
                dls.set_length ( epdfs.length() );

                bool independent = true;
                if ( named ) {
                        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." );
                        }
                        dim = rv._dsize();
                } else {
                        dim = 0;
                        for ( int i = 0; i < epdfs.length(); i++ ) {
                                dim += epdfs ( i )->dimension();
                        }
                }
                //
                int cumdim = 0;
                int dimi = 0;
                int i;
                for ( i = 0; i < epdfs.length(); i++ ) {
                        dls ( i ) = new datalink;
                        if ( named ) {
                                dls ( i )->set_connection ( epdfs ( i )->_rv() , rv );
                        } else {
                                dimi = epdfs ( i )->dimension();
                                dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) );
                                cumdim += dimi;
                        }
                }
        }

        vec mean() const {
                vec tmp ( dim );
                for ( int i = 0; i < epdfs.length(); i++ ) {
                        vec pom = epdfs ( i )->mean();
                        dls ( i )->pushup ( tmp, pom );
                }
                return tmp;
        }
        vec variance() const {
                vec tmp ( dim ); //second moment
                for ( int i = 0; i < epdfs.length(); i++ ) {
                        vec pom = epdfs ( i )->mean();
                        dls ( i )->pushup ( tmp, pow ( pom, 2 ) );
                }
                return tmp - pow ( mean(), 2 );
        }
        vec sample() const {
                vec tmp ( dim );
                for ( int i = 0; i < epdfs.length(); i++ ) {
                        vec pom = epdfs ( i )->sample();
                        dls ( i )->pushup ( tmp, pom );
                }
                return tmp;
        }
        double evallog ( const vec &val ) const {
                double tmp = 0;
                for ( int i = 0; i < epdfs.length(); i++ ) {
                        tmp += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );
                }
                it_assert_debug ( std::isfinite ( tmp ), "Infinite" );
                return tmp;
        }
        //!access function
        const epdf* operator () ( int i ) const {
                it_assert_debug ( i < epdfs.length(), "wrong index" );
                return epdfs ( i );
        }

        //!Destructor
        ~eprod() {
                for ( int i = 0; i < epdfs.length(); i++ ) {
                        delete dls ( 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
        shared_ptr<emix> iepdf;

public:
        //!Default constructor
        mmix() : iepdf ( new emix() ) {
                set_ep ( iepdf );
        }

        //! 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 )->e();
                }

                iepdf->set_parameters ( w, Eps );
        }

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

}
#endif //MX_H