[107] | 1 | /*! |
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| 2 | \file |
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| 3 | \brief Probability distributions for Mixtures of pdfs |
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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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[394] | 13 | #ifndef EMIX_H |
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| 14 | #define EMIX_H |
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[107] | 15 | |
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[477] | 16 | #define LOG2 0.69314718055995 |
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[333] | 17 | |
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[461] | 18 | #include "../shared_ptr.h" |
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[384] | 19 | #include "exp_family.h" |
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[107] | 20 | |
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[286] | 21 | namespace bdm { |
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[107] | 22 | |
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[182] | 23 | //this comes first because it is used inside emix! |
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| 24 | |
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| 25 | /*! \brief Class representing ratio of two densities |
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| 26 | which arise e.g. by applying the Bayes rule. |
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| 27 | It represents density in the form: |
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| 28 | \f[ |
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| 29 | f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)} |
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| 30 | \f] |
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| 31 | where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$. |
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| 32 | |
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| 33 | In particular this type of arise by conditioning of a mixture model. |
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| 34 | |
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[211] | 35 | At present the only supported operation is evallogcond(). |
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[182] | 36 | */ |
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| 37 | class mratio: public mpdf { |
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[192] | 38 | protected: |
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[182] | 39 | //! Nominator in the form of mpdf |
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[192] | 40 | const epdf* nom; |
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[182] | 41 | //!Denominator in the form of epdf |
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[192] | 42 | epdf* den; |
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| 43 | //!flag for destructor |
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| 44 | bool destroynom; |
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[193] | 45 | //!datalink between conditional and nom |
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| 46 | datalink_m2e dl; |
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[192] | 47 | public: |
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| 48 | //!Default constructor. By default, the given epdf is not copied! |
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[182] | 49 | //! It is assumed that this function will be used only temporarily. |
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[477] | 50 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : mpdf ( ), dl ( ) { |
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[286] | 51 | // adjust rv and rvc |
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| 52 | rvc = nom0->_rv().subt ( rv ); |
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| 53 | dimc = rvc._dsize(); |
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[477] | 54 | set_ep ( shared_ptr<epdf> ( new epdf ) ); |
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| 55 | e()->set_parameters ( rv._dsize() ); |
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| 56 | e()->set_rv ( rv ); |
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| 57 | |
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[286] | 58 | //prepare data structures |
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[477] | 59 | if ( copy ) { |
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| 60 | it_error ( "todo" ); |
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| 61 | destroynom = true; |
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| 62 | } else { |
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| 63 | nom = nom0; |
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| 64 | destroynom = false; |
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| 65 | } |
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| 66 | it_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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| 67 | |
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[286] | 68 | // build denominator |
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[192] | 69 | den = nom->marginal ( rvc ); |
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[477] | 70 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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[192] | 71 | }; |
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[211] | 72 | double evallogcond ( const vec &val, const vec &cond ) { |
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[214] | 73 | double tmp; |
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[461] | 74 | vec nom_val ( e()->dimension() + dimc ); |
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[477] | 75 | dl.pushup_cond ( nom_val, val, cond ); |
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[214] | 76 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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[477] | 77 | it_assert_debug ( std::isfinite ( tmp ), "Infinite value" ); |
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[214] | 78 | return tmp; |
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[192] | 79 | } |
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[182] | 80 | //! Object takes ownership of nom and will destroy it |
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[477] | 81 | void ownnom() { |
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| 82 | destroynom = true; |
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| 83 | } |
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[182] | 84 | //! Default destructor |
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[477] | 85 | ~mratio() { |
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| 86 | delete den; |
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| 87 | if ( destroynom ) { |
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| 88 | delete nom; |
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| 89 | } |
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| 90 | } |
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[182] | 91 | }; |
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| 92 | |
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[107] | 93 | /*! |
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| 94 | * \brief Mixture of epdfs |
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| 95 | |
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| 96 | Density function: |
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| 97 | \f[ |
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| 98 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 99 | \f] |
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| 100 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 101 | |
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| 102 | */ |
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[145] | 103 | class emix : public epdf { |
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[162] | 104 | protected: |
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| 105 | //! weights of the components |
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| 106 | vec w; |
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| 107 | //! Component (epdfs) |
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| 108 | Array<epdf*> Coms; |
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[178] | 109 | //!Flag if owning Coms |
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| 110 | bool destroyComs; |
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[162] | 111 | public: |
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| 112 | //!Default constructor |
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[286] | 113 | emix ( ) : epdf ( ) {}; |
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[182] | 114 | //! Set weights \c w and components \c Coms |
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[224] | 115 | //!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. |
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[477] | 116 | void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy = false ); |
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[107] | 117 | |
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[162] | 118 | vec sample() const; |
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| 119 | vec mean() const { |
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[477] | 120 | int i; |
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| 121 | vec mu = zeros ( dim ); |
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| 122 | for ( i = 0; i < w.length(); i++ ) { |
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| 123 | mu += w ( i ) * Coms ( i )->mean(); |
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| 124 | } |
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[162] | 125 | return mu; |
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| 126 | } |
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[229] | 127 | vec variance() const { |
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| 128 | //non-central moment |
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[286] | 129 | vec mom2 = zeros ( dim ); |
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[477] | 130 | for ( int i = 0; i < w.length(); i++ ) { |
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| 131 | mom2 += w ( i ) * ( Coms ( i )->variance() + pow ( Coms ( i )->mean(), 2 ) ); |
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| 132 | } |
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[229] | 133 | //central moment |
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[477] | 134 | return mom2 - pow ( mean(), 2 ); |
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[229] | 135 | } |
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[211] | 136 | double evallog ( const vec &val ) const { |
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[162] | 137 | int i; |
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| 138 | double sum = 0.0; |
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[477] | 139 | for ( i = 0; i < w.length(); i++ ) { |
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| 140 | sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) ); |
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| 141 | } |
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| 142 | if ( sum == 0.0 ) { |
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| 143 | sum = std::numeric_limits<double>::epsilon(); |
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| 144 | } |
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| 145 | double tmp = log ( sum ); |
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| 146 | it_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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[214] | 147 | return tmp; |
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[162] | 148 | }; |
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[211] | 149 | vec evallog_m ( const mat &Val ) const { |
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[477] | 150 | vec x = zeros ( Val.cols() ); |
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[192] | 151 | for ( int i = 0; i < w.length(); i++ ) { |
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[477] | 152 | x += w ( i ) * exp ( Coms ( i )->evallog_m ( Val ) ); |
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[182] | 153 | } |
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[192] | 154 | return log ( x ); |
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[182] | 155 | }; |
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[214] | 156 | //! Auxiliary function that returns pdflog for each component |
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[211] | 157 | mat evallog_M ( const mat &Val ) const { |
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[192] | 158 | mat X ( w.length(), Val.cols() ); |
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| 159 | for ( int i = 0; i < w.length(); i++ ) { |
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[211] | 160 | X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ) ); |
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[189] | 161 | } |
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| 162 | return X; |
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| 163 | }; |
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[107] | 164 | |
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[182] | 165 | emix* marginal ( const RV &rv ) const; |
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| 166 | mratio* condition ( const RV &rv ) const; //why not mratio!! |
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| 167 | |
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[107] | 168 | //Access methods |
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[162] | 169 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 170 | vec& _w() { |
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| 171 | return w; |
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| 172 | } |
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| 173 | virtual ~emix() { |
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| 174 | if ( destroyComs ) { |
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| 175 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 176 | delete Coms ( i ); |
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| 177 | } |
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| 178 | } |
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| 179 | } |
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[178] | 180 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 181 | void ownComs() { |
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| 182 | destroyComs = true; |
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| 183 | } |
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[204] | 184 | |
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[193] | 185 | //!access function |
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[477] | 186 | epdf* _Coms ( int i ) { |
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| 187 | return Coms ( i ); |
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[286] | 188 | } |
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[477] | 189 | void set_rv ( const RV &rv ) { |
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| 190 | epdf::set_rv ( rv ); |
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| 191 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 192 | Coms ( i )->set_rv ( rv ); |
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| 193 | } |
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| 194 | } |
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[107] | 195 | }; |
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| 196 | |
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[333] | 197 | |
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| 198 | /*! |
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| 199 | * \brief Mixture of egiws |
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| 200 | |
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| 201 | */ |
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| 202 | class egiwmix : public egiw { |
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| 203 | protected: |
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| 204 | //! weights of the components |
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| 205 | vec w; |
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| 206 | //! Component (epdfs) |
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| 207 | Array<egiw*> Coms; |
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| 208 | //!Flag if owning Coms |
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| 209 | bool destroyComs; |
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| 210 | public: |
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| 211 | //!Default constructor |
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| 212 | egiwmix ( ) : egiw ( ) {}; |
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| 213 | |
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| 214 | //! Set weights \c w and components \c Coms |
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| 215 | //!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. |
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[477] | 216 | void set_parameters ( const vec &w, const Array<egiw*> &Coms, bool copy = false ); |
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[333] | 217 | |
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| 218 | //!return expected value |
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| 219 | vec mean() const; |
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| 220 | |
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| 221 | //!return a sample from the density |
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| 222 | vec sample() const; |
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| 223 | |
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| 224 | //!return the expected variance |
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[477] | 225 | vec variance() const; |
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[333] | 226 | |
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| 227 | // TODO!!! Defined to follow ANSI and/or for future development |
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| 228 | void mean_mat ( mat &M, mat&R ) const {}; |
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[477] | 229 | double evallog_nn ( const vec &val ) const { |
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| 230 | return 0; |
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| 231 | }; |
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| 232 | double lognc () const { |
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| 233 | return 0; |
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| 234 | }; |
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[333] | 235 | emix* marginal ( const RV &rv ) const; |
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| 236 | |
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| 237 | //Access methods |
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| 238 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 239 | vec& _w() { |
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| 240 | return w; |
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| 241 | } |
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| 242 | virtual ~egiwmix() { |
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| 243 | if ( destroyComs ) { |
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| 244 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 245 | delete Coms ( i ); |
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| 246 | } |
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| 247 | } |
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| 248 | } |
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[333] | 249 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 250 | void ownComs() { |
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| 251 | destroyComs = true; |
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| 252 | } |
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[333] | 253 | |
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| 254 | //!access function |
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[477] | 255 | egiw* _Coms ( int i ) { |
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| 256 | return Coms ( i ); |
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| 257 | } |
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[333] | 258 | |
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[477] | 259 | void set_rv ( const RV &rv ) { |
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| 260 | egiw::set_rv ( rv ); |
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| 261 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 262 | Coms ( i )->set_rv ( rv ); |
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| 263 | } |
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[333] | 264 | } |
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| 265 | |
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| 266 | //! Approximation of a GiW mix by a single GiW pdf |
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| 267 | egiw* approx(); |
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| 268 | }; |
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| 269 | |
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[115] | 270 | /*! \brief Chain rule decomposition of epdf |
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| 271 | |
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[145] | 272 | Probability density in the form of Chain-rule decomposition: |
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| 273 | \[ |
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| 274 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 275 | \] |
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| 276 | Note that |
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[115] | 277 | */ |
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[175] | 278 | class mprod: public compositepdf, public mpdf { |
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[162] | 279 | protected: |
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[271] | 280 | //! pointers to epdfs - shortcut to mpdfs().posterior() |
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[162] | 281 | Array<epdf*> epdfs; |
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[192] | 282 | //! Data link for each mpdfs |
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| 283 | Array<datalink_m2m*> dls; |
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[461] | 284 | |
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[270] | 285 | //! dummy ep |
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[461] | 286 | shared_ptr<epdf> dummy; |
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| 287 | |
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[162] | 288 | public: |
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[168] | 289 | /*!\brief Constructor from list of mFacs, |
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[165] | 290 | */ |
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[477] | 291 | mprod() : dummy ( new epdf() ) { } |
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| 292 | mprod ( Array<mpdf*> mFacs ) : |
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| 293 | dummy ( new epdf() ) { |
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| 294 | set_elements ( mFacs ); |
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[461] | 295 | } |
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| 296 | |
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[477] | 297 | void set_elements ( Array<mpdf*> mFacs , bool own = false ) { |
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| 298 | |
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| 299 | compositepdf::set_elements ( mFacs, own ); |
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| 300 | dls.set_size ( mFacs.length() ); |
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| 301 | epdfs.set_size ( mFacs.length() ); |
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| 302 | |
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| 303 | set_ep ( dummy ); |
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| 304 | RV rv = getrv ( true ); |
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[395] | 305 | set_rv ( rv ); |
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[477] | 306 | dummy->set_parameters ( rv._dsize() ); |
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| 307 | setrvc ( e()->_rv(), rvc ); |
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[192] | 308 | // rv and rvc established = > we can link them with mpdfs |
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[477] | 309 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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[286] | 310 | dls ( i ) = new datalink_m2m; |
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[477] | 311 | dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), _rv(), _rvc() ); |
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[181] | 312 | } |
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| 313 | |
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[477] | 314 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 315 | epdfs ( i ) = mpdfs ( i )->e(); |
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[181] | 316 | } |
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[175] | 317 | }; |
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[124] | 318 | |
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[211] | 319 | double evallogcond ( const vec &val, const vec &cond ) { |
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[162] | 320 | int i; |
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[270] | 321 | double res = 0.0; |
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[477] | 322 | for ( i = mpdfs.length() - 1; i >= 0; i-- ) { |
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[193] | 323 | /* if ( mpdfs(i)->_rvc().count() >0) { |
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| 324 | mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) ); |
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| 325 | } |
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| 326 | // add logarithms |
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[270] | 327 | res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/ |
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| 328 | res += mpdfs ( i )->evallogcond ( |
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| 329 | dls ( i )->pushdown ( val ), |
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[204] | 330 | dls ( i )->get_cond ( val, cond ) |
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| 331 | ); |
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[145] | 332 | } |
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[193] | 333 | return res; |
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[162] | 334 | } |
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[477] | 335 | vec evallogcond_m ( const mat &Dt, const vec &cond ) { |
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| 336 | vec tmp ( Dt.cols() ); |
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| 337 | for ( int i = 0; i < Dt.cols(); i++ ) { |
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| 338 | tmp ( i ) = evallogcond ( Dt.get_col ( i ), cond ); |
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[395] | 339 | } |
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| 340 | return tmp; |
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| 341 | }; |
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[477] | 342 | vec evallogcond_m ( const Array<vec> &Dt, const vec &cond ) { |
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| 343 | vec tmp ( Dt.length() ); |
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| 344 | for ( int i = 0; i < Dt.length(); i++ ) { |
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| 345 | tmp ( i ) = evallogcond ( Dt ( i ), cond ); |
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[395] | 346 | } |
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[477] | 347 | return tmp; |
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[395] | 348 | }; |
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| 349 | |
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| 350 | |
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[270] | 351 | //TODO smarter... |
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| 352 | vec samplecond ( const vec &cond ) { |
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[477] | 353 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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| 354 | vec smp = std::numeric_limits<double>::infinity() * ones ( e()->dimension() ); |
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[165] | 355 | vec smpi; |
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[192] | 356 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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[477] | 357 | for ( int i = ( mpdfs.length() - 1 ); i >= 0; i-- ) { |
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[270] | 358 | if ( mpdfs ( i )->dimensionc() ) { |
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[477] | 359 | mpdfs ( i )->condition ( dls ( i )->get_cond ( smp , cond ) ); // smp is val here!! |
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[145] | 360 | } |
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[165] | 361 | smpi = epdfs ( i )->sample(); |
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[162] | 362 | // copy contribution of this pdf into smp |
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[270] | 363 | dls ( i )->pushup ( smp, smpi ); |
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[165] | 364 | // add ith likelihood contribution |
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[145] | 365 | } |
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[162] | 366 | return smp; |
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| 367 | } |
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[270] | 368 | mat samplecond ( const vec &cond, int N ) { |
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[477] | 369 | mat Smp ( dimension(), N ); |
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| 370 | for ( int i = 0; i < N; i++ ) { |
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| 371 | Smp.set_col ( i, samplecond ( cond ) ); |
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| 372 | } |
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[162] | 373 | return Smp; |
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| 374 | } |
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| 375 | |
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| 376 | ~mprod() {}; |
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[395] | 377 | //! Load from structure with elements: |
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| 378 | //! \code |
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| 379 | //! { class='mprod'; |
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| 380 | //! mpdfs = (..., ...); // list of mpdfs in the order of chain rule |
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| 381 | //! } |
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| 382 | //! \endcode |
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| 383 | //!@} |
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[477] | 384 | void from_setting ( const Setting &set ) { |
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[395] | 385 | Array<mpdf*> Atmp; //temporary Array |
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[477] | 386 | UI::get ( Atmp, set, "mpdfs", UI::compulsory ); |
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| 387 | set_elements ( Atmp, true ); |
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[395] | 388 | } |
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[477] | 389 | |
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[107] | 390 | }; |
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[477] | 391 | UIREGISTER ( mprod ); |
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[107] | 392 | |
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[168] | 393 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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| 394 | class eprod: public epdf { |
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| 395 | protected: |
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| 396 | //! Components (epdfs) |
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[170] | 397 | Array<const epdf*> epdfs; |
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[168] | 398 | //! Array of indeces |
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[270] | 399 | Array<datalink*> dls; |
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[168] | 400 | public: |
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[477] | 401 | eprod () : epdfs ( 0 ), dls ( 0 ) {}; |
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| 402 | void set_parameters ( const Array<const epdf*> &epdfs0, bool named = true ) { |
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| 403 | epdfs = epdfs0;//.set_length ( epdfs0.length() ); |
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[286] | 404 | dls.set_length ( epdfs.length() ); |
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| 405 | |
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[477] | 406 | bool independent = true; |
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[286] | 407 | if ( named ) { |
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[477] | 408 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 409 | independent = rv.add ( epdfs ( i )->_rv() ); |
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| 410 | it_assert_debug ( independent == true, "eprod:: given components are not independent." ); |
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[286] | 411 | } |
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[477] | 412 | dim = rv._dsize(); |
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| 413 | } else { |
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| 414 | dim = 0; |
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| 415 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 416 | dim += epdfs ( i )->dimension(); |
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[286] | 417 | } |
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[204] | 418 | } |
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[286] | 419 | // |
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[477] | 420 | int cumdim = 0; |
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| 421 | int dimi = 0; |
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[286] | 422 | int i; |
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[477] | 423 | for ( i = 0; i < epdfs.length(); i++ ) { |
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[286] | 424 | dls ( i ) = new datalink; |
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[477] | 425 | if ( named ) { |
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| 426 | dls ( i )->set_connection ( epdfs ( i )->_rv() , rv ); |
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| 427 | } else { |
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[286] | 428 | dimi = epdfs ( i )->dimension(); |
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[477] | 429 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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| 430 | cumdim += dimi; |
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[286] | 431 | } |
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| 432 | } |
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[168] | 433 | } |
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| 434 | |
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| 435 | vec mean() const { |
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[270] | 436 | vec tmp ( dim ); |
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[477] | 437 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[168] | 438 | vec pom = epdfs ( i )->mean(); |
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[270] | 439 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 440 | } |
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| 441 | return tmp; |
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| 442 | } |
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[229] | 443 | vec variance() const { |
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[270] | 444 | vec tmp ( dim ); //second moment |
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[477] | 445 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[229] | 446 | vec pom = epdfs ( i )->mean(); |
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[477] | 447 | dls ( i )->pushup ( tmp, pow ( pom, 2 ) ); |
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[229] | 448 | } |
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[477] | 449 | return tmp - pow ( mean(), 2 ); |
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[229] | 450 | } |
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[168] | 451 | vec sample() const { |
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[270] | 452 | vec tmp ( dim ); |
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[477] | 453 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[168] | 454 | vec pom = epdfs ( i )->sample(); |
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[270] | 455 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 456 | } |
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| 457 | return tmp; |
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| 458 | } |
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[211] | 459 | double evallog ( const vec &val ) const { |
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[477] | 460 | double tmp = 0; |
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| 461 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 462 | tmp += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) ); |
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[168] | 463 | } |
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[477] | 464 | it_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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[168] | 465 | return tmp; |
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| 466 | } |
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[170] | 467 | //!access function |
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[477] | 468 | const epdf* operator () ( int i ) const { |
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| 469 | it_assert_debug ( i < epdfs.length(), "wrong index" ); |
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| 470 | return epdfs ( i ); |
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| 471 | } |
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[204] | 472 | |
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[193] | 473 | //!Destructor |
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[477] | 474 | ~eprod() { |
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| 475 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 476 | delete dls ( i ); |
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| 477 | } |
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| 478 | } |
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[168] | 479 | }; |
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| 480 | |
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| 481 | |
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[145] | 482 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type |
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[124] | 483 | |
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| 484 | */ |
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[145] | 485 | class mmix : public mpdf { |
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[162] | 486 | protected: |
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| 487 | //! Component (epdfs) |
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| 488 | Array<mpdf*> Coms; |
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[461] | 489 | |
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[162] | 490 | //!Internal epdf |
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[461] | 491 | shared_ptr<emix> iepdf; |
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| 492 | |
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[162] | 493 | public: |
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| 494 | //!Default constructor |
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[477] | 495 | mmix() : iepdf ( new emix() ) { |
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| 496 | set_ep ( iepdf ); |
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[461] | 497 | } |
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| 498 | |
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[162] | 499 | //! Set weights \c w and components \c R |
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| 500 | void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) { |
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| 501 | Array<epdf*> Eps ( Coms.length() ); |
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[124] | 502 | |
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[477] | 503 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 504 | Eps ( i ) = Coms ( i )->e(); |
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[162] | 505 | } |
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[124] | 506 | |
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[477] | 507 | iepdf->set_parameters ( w, Eps ); |
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[461] | 508 | } |
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| 509 | |
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[162] | 510 | void condition ( const vec &cond ) { |
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[477] | 511 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 512 | Coms ( i )->condition ( cond ); |
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| 513 | } |
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[162] | 514 | }; |
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[124] | 515 | }; |
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[182] | 516 | |
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[254] | 517 | } |
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[107] | 518 | #endif //MX_H |
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