root/library/bdm/stat/merger.h @ 507

/*!
  \file
  \brief Mergers for combination of pdfs
  \author Vaclav Smidl.

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

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

#ifndef MERGER_H
#define MERGER_H


#include "../estim/mixtures.h"

namespace bdm {
using std::string;

//!Merging methods
enum MERGER_METHOD {ARITHMETIC = 1, GEOMETRIC = 2, LOGNORMAL = 3};

/*!
@brief Base class for general combination of pdfs on discrete support

Mixtures of Gaussian densities are used internally. Switching to other densities should be trivial.

The merged pdfs are expected to be of the form:
 \f[ f(x_i|y_i),  i=1..n \f]
where the resulting merger is a density on \f$ \cup [x_i,y_i] \f$ .
Note that all variables will be joined.

As a result of this feature, each source must be extended to common support
\f[ f(z_i|y_i,x_i) f(x_i|y_i) f(y_i)  i=1..n \f]
where \f$ z_i \f$ accumulate variables that were not in the original source.
These extensions are calculated on-the-fly.

However, these operations can not be performed in general. Hence, this class merges only sources on common support, \f$ y_i={}, z_i={}, \forall i \f$.
For merging of more general cases, use offsprings merger_mix and merger_grid.
*/

class merger_base : public epdf {
protected:
        //! Elements of composition
        Array<shared_ptr<mpdf> > mpdfs;

        //! Data link for each mpdf in mpdfs
        Array<datalink_m2e*> dls;

        //! Array of rvs that are not modelled by mpdfs at all, \f$ z_i \f$
        Array<RV> rvzs;

        //! Data Links for extension \f$ f(z_i|x_i,y_i) \f$
        Array<datalink_m2e*> zdls;

        //! number of support points
        int Npoints;

        //! number of sources
        int Nsources;

        //! switch of the methoh used for merging
        MERGER_METHOD METHOD;
        //! Default for METHOD
        static const MERGER_METHOD DFLT_METHOD;

        //!Prior on the log-normal merging model
        double beta;
        //! default for beta
        static const double DFLT_beta;

        //! Projection to empirical density (could also be piece-wise linear)
        eEmp eSmp;

        //! debug or not debug
        bool DBG;

        //! debugging file
        it_file* dbg_file;
public:
        //! \name Constructors
        //! @{

        //! Default constructor
        merger_base () : Npoints(0), Nsources(0), DBG(false), dbg_file(0) {
        }

        //!Constructor from sources
        merger_base ( const Array<shared_ptr<mpdf> > &S );

        //! Function setting the main internal structures
        void set_sources ( const Array<shared_ptr<mpdf> > &Sources ) {
                mpdfs = Sources;
                Nsources = mpdfs.length();
                //set sizes
                dls.set_size ( Sources.length() );
                rvzs.set_size ( Sources.length() );
                zdls.set_size ( Sources.length() );

                rv = get_composite_rv ( mpdfs, /* checkoverlap = */ false );

                RV rvc;
                // Extend rv by rvc!
                for ( int i = 0; i < mpdfs.length(); i++ ) {
                        RV rvx = mpdfs ( i )->_rvc().subt ( rv );
                        rvc.add ( rvx ); // add rv to common rvc
                }

                // join rv and rvc - see descriprion
                rv.add ( rvc );
                // get dimension
                dim = rv._dsize();

                // create links between sources and common rv
                RV xytmp;
                for ( int i = 0; i < mpdfs.length(); i++ ) {
                        //Establich connection between mpdfs and merger
                        dls ( i ) = new datalink_m2e;
                        dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), rv );

                        // find out what is missing in each mpdf
                        xytmp = mpdfs ( i )->_rv();
                        xytmp.add ( mpdfs ( i )->_rvc() );
                        // z_i = common_rv-xy
                        rvzs ( i ) = rv.subt ( xytmp );
                        //establish connection between extension (z_i|x,y)s and common rv
                        zdls ( i ) = new datalink_m2e;
                        zdls ( i )->set_connection ( rvzs ( i ), xytmp, rv ) ;
                };
        }
        //! Rectangular support  each vector of XYZ specifies (begining-end) interval for each dimension. Same number of points, \c dimsize, in each dimension.
        void set_support ( const Array<vec> &XYZ, const int dimsize ) {
                set_support ( XYZ, dimsize*ones_i ( XYZ.length() ) );
        }
        //! Rectangular support  each vector of XYZ specifies (begining-end) interval for each dimension. \c gridsize specifies number of points is each dimension.
        void set_support ( const Array<vec> &XYZ, const ivec &gridsize ) {
                int dim = XYZ.length();  //check with internal dim!!
                Npoints = prod ( gridsize );
                eSmp.set_parameters ( Npoints, false );
                Array<vec> &samples = eSmp._samples();
                eSmp._w() = ones ( Npoints ) / Npoints; //unifrom size of bins
                //set samples
                ivec ind = zeros_i ( dim );    //indeces of dimensions in for cycle;
                vec smpi ( dim );          // ith sample
                vec steps = zeros ( dim );        // ith sample
                // first corner
                for ( int j = 0; j < dim; j++ ) {
                        smpi ( j ) = XYZ ( j ) ( 0 ); /* beginning of the interval*/
                        it_assert ( gridsize ( j ) != 0.0, "Zeros in gridsize!" );
                        steps ( j ) = ( XYZ ( j ) ( 1 ) - smpi ( j ) ) / gridsize ( j );
                }
                // fill samples
                for ( int i = 0; i < Npoints; i++ ) {
                        // copy
                        samples ( i ) = smpi;
                        // go through all dimensions
                        for ( int j = 0; j < dim; j++ ) {
                                if ( ind ( j ) == gridsize ( j ) - 1 ) { //j-th index is full
                                        ind ( j ) = 0; //shift back
                                        smpi ( j ) = XYZ ( j ) ( 0 );

                                        if ( i < Npoints - 1 ) {
                                                ind ( j + 1 ) ++; //increase the next dimension;
                                                smpi ( j + 1 ) += steps ( j + 1 );
                                                break;
                                        }

                                } else {
                                        ind ( j ) ++;
                                        smpi ( j ) += steps ( j );
                                        break;
                                }
                        }
                }
        }
        //! set debug file
        void set_debug_file ( const string fname ) {
                if ( DBG ) delete dbg_file;
                dbg_file = new it_file ( fname );
                if ( dbg_file ) DBG = true;
        }
        //! Set internal parameters used in approximation
        void set_method ( MERGER_METHOD MTH = DFLT_METHOD, double beta0 = DFLT_beta ) {
                METHOD = MTH;
                beta = beta0;
        }
        //! Set support points from a pdf by drawing N samples
        void set_support ( const epdf &overall, int N ) {
                eSmp.set_statistics ( overall, N );
                Npoints = N;
        }

        //! Destructor
        virtual ~merger_base() {
                for ( int i = 0; i < Nsources; i++ ) {
                        delete dls ( i );
                        delete zdls ( i );
                }
                if ( DBG ) delete dbg_file;
        };
        //!@}

        //! \name Mathematical operations
        //!@{

        //!Merge given sources in given points
        virtual void merge () {
                validate();

                //check if sources overlap:
                bool OK = true;
                for ( int i = 0; i < mpdfs.length(); i++ ) {
                        OK &= ( rvzs ( i )._dsize() == 0 ); // z_i is empty
                        OK &= ( mpdfs ( i )->_rvc()._dsize() == 0 ); // y_i is empty
                }

                if ( OK ) {
                        mat lW = zeros ( mpdfs.length(), eSmp._w().length() );

                        vec emptyvec ( 0 );
                        for ( int i = 0; i < mpdfs.length(); i++ ) {
                                for ( int j = 0; j < eSmp._w().length(); j++ ) {
                                        lW ( i, j ) = mpdfs ( i )->evallogcond ( eSmp._samples() ( j ), emptyvec );
                                }
                        }

                        vec w_nn = merge_points ( lW );
                        vec wtmp = exp ( w_nn - max ( w_nn ) );
                        //renormalize
                        eSmp._w() = wtmp / sum ( wtmp );
                } else {
                        it_error ( "Sources are not compatible - use merger_mix" );
                }
        };


        //! Merge log-likelihood values in points using method specified by parameter METHOD
        vec merge_points ( mat &lW );


        //! sample from merged density
//! weight w is a
        vec mean() const {
                const Vec<double> &w = eSmp._w();
                const Array<vec> &S = eSmp._samples();
                vec tmp = zeros ( dim );
                for ( int i = 0; i < Npoints; i++ ) {
                        tmp += w ( i ) * S ( i );
                }
                return tmp;
        }
        mat covariance() const {
                const vec &w = eSmp._w();
                const Array<vec> &S = eSmp._samples();

                vec mea = mean();

//                      cout << sum (w) << "," << w*w << endl;

                mat Tmp = zeros ( dim, dim );
                for ( int i = 0; i < Npoints; i++ ) {
                        Tmp += w ( i ) * outer_product ( S ( i ), S ( i ) );
                }
                return Tmp - outer_product ( mea, mea );
        }
        vec variance() const {
                const vec &w = eSmp._w();
                const Array<vec> &S = eSmp._samples();

                vec tmp = zeros ( dim );
                for ( int i = 0; i < Nsources; i++ ) {
                        tmp += w ( i ) * pow ( S ( i ), 2 );
                }
                return tmp - pow ( mean(), 2 );
        }
        //!@}

        //! \name Access to attributes
        //! @{

        //! Access function
        eEmp& _Smp() {
                return eSmp;
        }

        //! load from setting
        void from_setting ( const Setting& set ) {
                // get support
                // find which method to use
                string meth_str;
                UI::get<string> ( meth_str, set, "method", UI::compulsory );
                if ( !strcmp ( meth_str.c_str(), "arithmetic" ) )
                        set_method ( ARITHMETIC );
                else {
                        if ( !strcmp ( meth_str.c_str(), "geometric" ) )
                                set_method ( GEOMETRIC );
                        else if ( !strcmp ( meth_str.c_str(), "lognormal" ) ) {
                                set_method ( LOGNORMAL );
                                set.lookupValue ( "beta", beta );
                        }
                }
                string dbg_file;
                if ( UI::get ( dbg_file, set, "dbg_file" ) )
                        set_debug_file ( dbg_file );
                //validate() - not used
        }

        void validate() {
                it_assert ( eSmp._w().length() > 0, "Empty support, use set_support()." );
                it_assert ( dim == eSmp._samples() ( 0 ).length(), "Support points and rv are not compatible!" );
                it_assert ( isnamed(), "mergers must be named" );
        }
        //!@}
};
UIREGISTER ( merger_base );

class merger_mix : public merger_base {
protected:
        //!Internal mixture of EF models
        MixEF Mix;
        //!Number of components in a mixture
        int Ncoms;
        //! coefficient of resampling [0,1]
        double effss_coef;
        //! stop after niter iterations
        int stop_niter;

        //! default value for Ncoms
        static const int DFLT_Ncoms;
        //! default value for efss_coef;
        static const double DFLT_effss_coef;

public:
        //!\name Constructors
        //!@{
        merger_mix ():Ncoms(0), effss_coef(0), stop_niter(0) { }

        merger_mix ( const Array<shared_ptr<mpdf> > &S ):
                Ncoms(0), effss_coef(0), stop_niter(0) {
                set_sources ( S );
        }

        //! Set sources and prepare all internal structures
        void set_sources ( const Array<shared_ptr<mpdf> > &S ) {
                merger_base::set_sources ( S );
                Nsources = S.length();
        }

        //! Set internal parameters used in approximation
        void set_parameters ( int Ncoms0 = DFLT_Ncoms, double effss_coef0 = DFLT_effss_coef ) {
                Ncoms = Ncoms0;
                effss_coef = effss_coef0;
        }
        //!@}

        //! \name Mathematical operations
        //!@{

        //!Merge values using mixture approximation
        void merge ();

        //! sample from the approximating mixture
        vec sample () const {
                return Mix.posterior().sample();
        }
        //! loglikelihood computed on mixture models
        double evallog ( const vec &dt ) const {
                vec dtf = ones ( dt.length() + 1 );
                dtf.set_subvector ( 0, dt );
                return Mix.logpred ( dtf );
        }
        //!@}

        //!\name Access functions
        //!@{
//! Access function
        MixEF& _Mix() {
                return Mix;
        }
        //! Access function
        emix* proposal() {
                emix* tmp = Mix.epredictor();
                tmp->set_rv ( rv );
                return tmp;
        }
        //! from_settings
        void from_setting ( const Setting& set ) {
                merger_base::from_setting ( set );
                set.lookupValue ( "ncoms", Ncoms );
                set.lookupValue ( "effss_coef", effss_coef );
                set.lookupValue ( "stop_niter", stop_niter );
        }

        //! @}

};
UIREGISTER ( merger_mix );

}

#endif // MER_H