1 | /*! |
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2 | \file |
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3 | \brief Bayesian Filtering for mixtures of exponential family (EF) members |
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4 | \author Vaclav Smidl. |
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5 | |
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6 | ----------------------------------- |
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7 | BDM++ - C++ library for Bayesian Decision Making under Uncertainty |
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8 | |
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9 | Using IT++ for numerical operations |
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10 | ----------------------------------- |
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11 | */ |
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12 | |
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13 | #ifndef MIXTURES_H |
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14 | #define MIXTURES_H |
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15 | |
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16 | |
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17 | #include "../math/functions.h" |
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18 | #include "../stat/exp_family.h" |
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19 | #include "../stat/emix.h" |
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20 | |
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21 | namespace bdm { |
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22 | |
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23 | //! enum switch for internal approximation used in MixEF |
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24 | enum MixEF_METHOD { EM = 0, QB = 1}; |
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25 | |
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26 | /*! |
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27 | * \brief Mixture of Exponential Family Densities |
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28 | |
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29 | An approximate estimation method for models with latent discrete variable, such as |
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30 | mixture models of the following kind: |
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31 | \f[ |
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32 | f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i) |
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33 | \f] |
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34 | 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$\Theta = [\theta_1,\ldots,\theta_n,w]\f$. |
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35 | |
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36 | 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. |
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37 | |
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38 | 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. |
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39 | |
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40 | TODO: Extend BM to use rvc. |
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41 | */ |
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42 | class MixEF: public BMEF { |
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43 | protected: |
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44 | //!Number of components |
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45 | int n; |
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46 | //! Models for Components of \f$\theta_i\f$ |
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47 | Array<BMEF*> Coms; |
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48 | //! Statistics for weights |
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49 | multiBM weights; |
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50 | //!Posterior on component parameters |
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51 | eprod* est; |
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52 | ////!Indeces of component rvc in common rvc |
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53 | |
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54 | //! Flag for a method that is used in the inference |
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55 | MixEF_METHOD method; |
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56 | |
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57 | //! Auxiliary function for use in constructors |
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58 | void build_est() { |
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59 | est = new eprod; |
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60 | if ( n > 0 ) { |
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61 | Array<const epdf*> epdfs ( n + 1 ); |
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62 | for ( int i = 0; i < Coms.length(); i++ ) { |
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63 | // it_assert_debug(!x,"MixEF::MixEF : Incompatible components"); |
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64 | epdfs ( i ) = & ( Coms ( i )->posterior() ); |
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65 | } |
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66 | // last in the product is the weight |
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67 | epdfs ( n ) = & ( weights.posterior() ); |
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68 | est->set_parameters ( epdfs, false ); |
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69 | } |
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70 | } |
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71 | |
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72 | public: |
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73 | //! Full constructor |
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74 | MixEF ( const Array<BMEF*> &Coms0, const vec &alpha0 ) : |
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75 | BMEF ( ), n ( Coms0.length() ), Coms ( n ), |
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76 | weights (), method ( QB ) { |
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77 | // it_assert_debug ( n>0,"MixEF::MixEF : Empty Component list" ); |
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78 | |
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79 | for ( int i = 0; i < n; i++ ) { |
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80 | Coms ( i ) = ( BMEF* ) Coms0 ( i )->_copy_(); |
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81 | } |
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82 | build_est(); |
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83 | }; |
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84 | //! Constructor of empty mixture |
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85 | MixEF () : |
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86 | BMEF ( ), n ( 0 ), Coms ( 0 ), |
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87 | weights (), method ( QB ) { |
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88 | build_est(); |
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89 | } |
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90 | //! Copy constructor |
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91 | MixEF ( const MixEF &M2 ) : BMEF ( ), n ( M2.n ), Coms ( n ), |
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92 | weights ( M2.weights ), method ( M2.method ) { |
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93 | // it_assert_debug ( n>0,"MixEF::MixEF : Empty Component list" ); |
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94 | |
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95 | for ( int i = 0; i < n; i++ ) { |
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96 | Coms ( i ) = M2.Coms ( i )->_copy_(); |
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97 | } |
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98 | build_est(); |
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99 | } |
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100 | //! Initializing the mixture by a random pick of centroids from data |
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101 | //! \param Com0 Initial component - necessary to determine its type. |
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102 | //! \param Data Data on which the initialization will be done |
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103 | //! \param c Initial number of components, default=5 |
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104 | void init ( BMEF* Com0, const mat &Data, int c = 5 ); |
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105 | //Destructor |
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106 | ~MixEF() { |
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107 | delete est; |
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108 | for ( int i = 0; i < n; i++ ) { |
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109 | delete Coms ( i ); |
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110 | } |
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111 | } |
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112 | //! Recursive EM-like algorithm (QB-variant), see Karny et. al, 2006 |
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113 | void bayes ( const vec &dt ); |
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114 | //! EM algorithm |
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115 | void bayes ( const mat &dt ); |
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116 | void bayesB ( const mat &dt, const vec &wData ); |
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117 | double logpred ( const vec &dt ) const; |
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118 | const epdf& posterior() const { |
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119 | return *est; |
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120 | } |
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121 | emix* epredictor() const; |
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122 | //! Flatten the density as if it was not estimated from the data |
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123 | void flatten ( const BMEF* M2 ); |
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124 | //! Access function |
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125 | BMEF* _Coms ( int i ) { |
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126 | return Coms ( i ); |
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127 | } |
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128 | |
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129 | //!Set which method is to be used |
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130 | void set_method ( MixEF_METHOD M ) { |
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131 | method = M; |
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132 | } |
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133 | }; |
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134 | |
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135 | } |
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136 | #endif // MIXTURES_H |
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137 | |
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