root/library/bdm/estim/mixtures.h @ 1085

Revision 1085, 7.5 kB (checked in by smidl, 14 years ago)

doc

  • Property svn:eol-style set to native
RevLine 
[176]1/*!
2  \file
3  \brief Bayesian Filtering for mixtures of exponential family (EF) members
4  \author Vaclav Smidl.
5
6  -----------------------------------
7  BDM++ - C++ library for Bayesian Decision Making under Uncertainty
8
9  Using IT++ for numerical operations
10  -----------------------------------
11*/
12
[394]13#ifndef MIXTURES_H
14#define MIXTURES_H
[176]15
[262]16
[384]17#include "../math/functions.h"
18#include "../stat/exp_family.h"
[394]19#include "../stat/emix.h"
[997]20#include "arx.h"
[176]21
[286]22namespace bdm {
[176]23
[536]24//! enum switch for internal approximation used in MixEF
[189]25enum MixEF_METHOD { EM = 0, QB = 1};
26
[176]27/*!
28* \brief Mixture of Exponential Family Densities
29
30An approximate estimation method for models with latent discrete variable, such as
31mixture models of the following kind:
32\f[
[1077]33f(y_t|\psi_t,     heta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t,     heta_i)
[176]34\f]
[1077]35where  \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$    heta_i\f$ are assumed to be mutually independent. \f$    heta\f$ is an aggregation af all component parameters and weights, i.e. \f$    heta = [    heta_1,\ldots,    heta_n,w]\f$.
[176]36
37The characteristic feature of this model is that if the exact values of the latent variable were known, estimation of the parameters can be handled by a single model. For example, for the case of mixture models, posterior density for each component parameters would be a BayesianModel from Exponential Family.
38
[180]39This class uses EM-style type algorithms for estimation of its parameters. Under this simplification, the posterior density is a product of exponential family members, hence under EM-style approximate estimation this class itself belongs to the exponential family.
[176]40
[1014]41Two methods are provided:
42 - QB where the probability of being from one component is computed using predictors,
43 - EM where the data is assigned to component with the highest likelihood (winner takes all)
44
45These methods are stored in attribute options:
46 - method: ["EM","QB"] estimation method as mentioned above, QB is default
47 - max_niter: maximum of iterations in bayes_batch()
48
[176]49*/
[197]50class MixEF: public BMEF {
[176]51protected:
[1077]52    //! Models for Components of \f$    heta_i\f$
[1064]53    Array<BMEF*> Coms;
54    //! Statistics for weights
55    multiBM weights;
56    //aux
57    friend class eprod_mix;
[1066]58
59    //! \brief Posterior on component parameters
[1064]60    class eprod_mix: public eprod_base {
61    protected:
62        const MixEF &mix; // pointer to parent.n
63    public:
64        eprod_mix(const MixEF &m):mix(m) {}
65        const epdf* factor(int i) const {
66            return (i==(mix.Coms.length()-1)) ? &mix.weights.posterior() : &mix.Coms(i)->posterior();
67        }
68        const int no_factors()const {
69            return mix.Coms.length()+1;
70        }
71    } est;
72    ////!indices of component rvc in common rvc
[286]73
[1077]74    class Options: public root {
[1064]75    public:
76        //! Flag for a method that is used in the inference
77        MixEF_METHOD method;
[286]78
[1064]79        //! maximum number of iterations
80        int max_niter;
81
[1077]82        Options():method(QB),max_niter(10) {};
[1064]83
[1077]84         /*! Create object from the following structure
85
[1064]86        \code
[1077]87        --- optional fields ---       
88        method = '...';            % 'EM' or 'QB', methods of computing bayes
89        max_iter = [];             % maximum number of iterations in bayes_batch
90        --- inherited fields ---
91        bdm::root::from_setting
[1064]92        \endcode
[1077]93        If the optional fields are not given, they will be filled as follows:
94        \code
95        max_niter = 10;           
96        method = 'QB';
97        \endcode
[1064]98        */
99        void from_setting(const Setting &set) {
100            string meth;
101            UI::get(meth,set,"method",UI::optional);
102            if (meth=="EM") {
103                method=EM;
104            }
105            max_niter =10;
106            UI::get(max_niter,set,"max_niter",UI::optional);
107        };
[1077]108
[1064]109        void to_setting(Setting &set)const {
110            string meth=(method==EM ? "EM" : "QB");
111            UI::save(meth,set,"method");
112            UI::save(max_niter,set,"max_niter");
113        };
114    };
115
[1077]116    Options options;
[176]117public:
[1064]118    //! Full constructor
119    MixEF ( const Array<BMEF*> &Coms0, const vec &alpha0 ) :
120        BMEF ( ), Coms ( Coms0.length() ),
121        weights (), est(*this), options() {
122        for ( int i = 0; i < Coms0.length(); i++ ) {
123            Coms ( i ) = ( BMEF* ) Coms0 ( i )->_copy();
124        }
125        weights.set_parameters(alpha0);
126        weights.validate();
127    }
[565]128
[1064]129    //! Constructor of empty mixture
130    MixEF () :
131        BMEF ( ), Coms ( 0 ),
132        weights (), est(*this), options() {
133    }
134    //! Copy constructor
135    MixEF ( const MixEF &M2 ) : BMEF ( ),  Coms ( M2.Coms.length() ),
136        weights ( M2.weights ), est(*this), options(M2.options) {
137        for ( int i = 0; i < M2.Coms.length(); i++ ) {
138            Coms ( i ) = (BMEF*) M2.Coms ( i )->_copy();
139        }
140    }
[565]141
[1064]142    //! Initializing the mixture by a random pick of centroids from data
143    //! \param Com0 Initial component - necessary to determine its type.
144    //! \param Data Data on which the initialization will be done
145    //! \param c Initial number of components, default=5
146    //! 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.
147    void init ( BMEF* Com0, const mat &Data, const int c = 5 );
148    //Destructor
149    //! Recursive EM-like algorithm (QB-variant), see Karny et. al, 2006
150    void bayes ( const vec &yt, const vec &cond );
151    //! batch weighted Bayes rule
152    double bayes_batch_weighted ( const mat &yt, const mat &cond, const vec &wData );
153    double bayes_batch ( const mat &yt, const mat &cond) {
154        return bayes_batch_weighted(yt,cond,ones(yt.cols()));
155    };
156    double logpred ( const vec &yt, const vec &cond ) const;
157    //! return correctly typed posterior (covariant return)
158    const eprod_mix& posterior() const {
159        return est;
160    }
[746]161
[1064]162    emix* epredictor(const vec &cond=vec()) const;
163    //! Flatten the density as if it was not estimated from the data
164    void flatten ( const BMEF* M2, double weight );
165    //! Access function
166    BMEF* _Coms ( int i ) {
167        return Coms ( i );
168    }
[286]169
[1064]170    //!Set which method is to be used
171    void set_method ( MixEF_METHOD M ) {
172        options.method = M;
173    }
[737]174
[1064]175    void to_setting ( Setting &set ) const {
176        BMEF::to_setting( set );
177        UI::save ( Coms, set, "Coms" );
178        UI::save ( &weights, set, "weights" );
179        UI::save (options, set, "options");
180    }
[1077]181
182    /*! Create object from the following structure
183
[1064]184    \code
[1077]185    class = 'MixEF';
186    Coms = { list of bdm::BMEF };                    % list of components containing any offsprings of Bayesian models BMEF, bdm::BMEF::from_setting
187    weights = [...];                                 % vector containing weights of components
188    --- optional fields ---
189    options = configuration of bdm::MixEF::Options;  % see MixEF::Options, bdm::MixEF::Options::from_setting
190    --- inherited fields ---
191    bdm::BMEF::from_setting
[1064]192    \endcode
193    */
194    void from_setting (const  Setting &set ) {
195        BMEF::from_setting( set );
196        UI::get ( Coms, set, "Coms" );
197        UI::get ( weights, set, "weights" );
198        UI::get (options, set, "options",UI::optional);
199    }
[176]200};
[746]201UIREGISTER ( MixEF );
[176]202
[1085]203//! \brief Product of ARX models forming an ARX model with potentially reduced structure
[997]204class ARXprod: public ProdBMBase {
[1064]205    Array<shared_ptr<ARX> > arxs;
206public:
207    ARX* bm(int i) {
208        return arxs(i).get();
209    }
210    int no_bms() {
211        return arxs.length();
212    }
[997]213};
214UIREGISTER(ARXprod);
215
[254]216}
[384]217#endif // MIXTURES_H
Note: See TracBrowser for help on using the browser.