root/library/bdm/estim/mixtures.h @ 1014

/*!
  \file
  \brief Bayesian Filtering for mixtures of exponential family (EF) members
  \author Vaclav Smidl.

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

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

#ifndef MIXTURES_H
#define MIXTURES_H


#include "../math/functions.h"
#include "../stat/exp_family.h"
#include "../stat/emix.h"
#include "arx.h"

namespace bdm {

//! enum switch for internal approximation used in MixEF
enum MixEF_METHOD { EM = 0, QB = 1};

/*!
* \brief Mixture of Exponential Family Densities

An approximate estimation method for models with latent discrete variable, such as
mixture models of the following kind:
\f[
f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i)
\f]
where  \f$\psi\f$ is a known function of past outputs, \f$w=[w_1,\ldots,w_n]\f$ are component weights, and component parameters \f$\theta_i\f$ are assumed to be mutually independent. \f$\Theta\f$ is an aggregation af all component parameters and weights, i.e. \f$\Theta = [\theta_1,\ldots,\theta_n,w]\f$.

The characteristic feature of this model is that if the exact values of the latent variable were known, estimation of the parameters can be handled by a single model. For example, for the case of mixture models, posterior density for each component parameters would be a BayesianModel from Exponential Family.

This class uses EM-style type algorithms for estimation of its parameters. Under this simplification, the posterior density is a product of exponential family members, hence under EM-style approximate estimation this class itself belongs to the exponential family.

Two methods are provided:
 - QB where the probability of being from one component is computed using predictors,
 - EM where the data is assigned to component with the highest likelihood (winner takes all)

These methods are stored in attribute options:
 - method: ["EM","QB"] estimation method as mentioned above, QB is default
 - max_niter: maximum of iterations in bayes_batch()

*/
class MixEF: public BMEF {
protected:
        //! Models for Components of \f$\theta_i\f$
        Array<BMEF*> Coms;
        //! Statistics for weights
        multiBM weights;
        //aux
        friend class eprod_mix;
        //!Posterior on component parameters
        class eprod_mix: public eprod_base {
                protected:
                const MixEF &mix; // pointer to parent.n
                public:
                eprod_mix(const MixEF &m):mix(m){}
                const epdf* factor(int i) const {return (i==(mix.Coms.length()-1)) ? &mix.weights.posterior() : &mix.Coms(i)->posterior();}
                const int no_factors()const {return mix.Coms.length()+1;}
        } est;
        ////!indices of component rvc in common rvc

        class MixEF_options: public root{
                public:
                //! Flag for a method that is used in the inference
                MixEF_METHOD method;

                //! maximum number of iterations
                int max_niter;
        
        MixEF_options():method(QB),max_niter(10){};
                
                void from_setting(const Setting &set){
                        string meth;
                        UI::get(meth,set,"method",UI::optional);
                        if (meth=="EM") {method=EM;}
                        max_niter =10;
                        UI::get(max_niter,set,"max_niter",UI::optional);
                };
                void to_setting(Setting &set)const{
                        string meth=(method==EM ? "EM" : "QB");
                        UI::save(meth,set,"method");
                        UI::save(max_niter,set,"max_niter");
                };
        };
        
        MixEF_options options;
public:
        //! Full constructor
        MixEF ( const Array<BMEF*> &Coms0, const vec &alpha0 ) :
                        BMEF ( ), Coms ( Coms0.length() ),
                        weights (), est(*this), options() {
                for ( int i = 0; i < Coms0.length(); i++ ) {
                        Coms ( i ) = ( BMEF* ) Coms0 ( i )->_copy();
                }
                weights.set_parameters(alpha0);
                weights.validate();
        }

        //! Constructor of empty mixture
        MixEF () :
                        BMEF ( ), Coms ( 0 ),
                        weights (), est(*this), options() {
        }
        //! Copy constructor
        MixEF ( const MixEF &M2 ) : BMEF ( ),  Coms ( M2.Coms.length() ),
                        weights ( M2.weights ), est(*this), options(M2.options) {
                for ( int i = 0; i < M2.Coms.length(); i++ ) {
                        Coms ( i ) = (BMEF*) M2.Coms ( i )->_copy();
                }
        }

        //! Initializing the mixture by a random pick of centroids from data
        //! \param Com0 Initial component - necessary to determine its type.
        //! \param Data Data on which the initialization will be done
        //! \param c Initial number of components, default=5
        //! when the number of data records (columns of Data) is equal to the number of requested components, each data is used, otherwise, they are picked randomly.
        void init ( BMEF* Com0, const mat &Data, const int c = 5 );
        //Destructor
        //! Recursive EM-like algorithm (QB-variant), see Karny et. al, 2006
        void bayes ( const vec &yt, const vec &cond );
        //! batch weighted Bayes rule
        double bayes_batch_weighted ( const mat &yt, const mat &cond, const vec &wData );
        double bayes_batch ( const mat &yt, const mat &cond){
                return bayes_batch_weighted(yt,cond,ones(yt.cols()));
        };
        double logpred ( const vec &yt, const vec &cond ) const;
        //! return correctly typed posterior (covariant return)
        const eprod_mix& posterior() const {
                return est;
        }

        emix* epredictor(const vec &cond=vec()) const;
        //! Flatten the density as if it was not estimated from the data
        void flatten ( const BMEF* M2, double weight );
        //! Access function
        BMEF* _Coms ( int i ) {
                return Coms ( i );
        }

        //!Set which method is to be used
        void set_method ( MixEF_METHOD M ) {
                options.method = M;
        }

void to_setting ( Setting &set ) const {
        BMEF::to_setting( set );
        UI::save ( Coms, set, "Coms" );
        UI::save ( &weights, set, "weights" );
        UI::save (options, set, "options");
}
/*! \brief reads data from setting
*/
void from_setting (const  Setting &set ) {
        BMEF::from_setting( set );
        UI::get ( Coms, set, "Coms" );
        UI::get ( weights, set, "weights" );
        UI::get (options, set, "options",UI::optional);
}
};
UIREGISTER ( MixEF );

class ARXprod: public ProdBMBase {
        Array<shared_ptr<ARX> > arxs;
        public:
                ARX* bm(int i){return arxs(i).get();}
                int no_bms() {return arxs.length();}
};
UIREGISTER(ARXprod);

}
#endif // MIXTURES_H