[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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[693] | 37 | class mratio: public pdf { |
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[192] | 38 | protected: |
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[693] | 39 | //! Nominator in the form of pdf |
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[192] | 40 | const epdf* nom; |
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[504] | 41 | |
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[182] | 42 | //!Denominator in the form of epdf |
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[504] | 43 | shared_ptr<epdf> den; |
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| 44 | |
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[192] | 45 | //!flag for destructor |
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| 46 | bool destroynom; |
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[193] | 47 | //!datalink between conditional and nom |
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| 48 | datalink_m2e dl; |
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[192] | 49 | public: |
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| 50 | //!Default constructor. By default, the given epdf is not copied! |
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[182] | 51 | //! It is assumed that this function will be used only temporarily. |
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[693] | 52 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : pdf ( ), dl ( ) { |
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[286] | 53 | // adjust rv and rvc |
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[675] | 54 | |
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[737] | 55 | set_rv ( rv ); // TODO co kdyby tohle samo uz nastavovalo dimension?!?! |
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[675] | 56 | dim = rv._dsize(); |
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| 57 | |
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[286] | 58 | rvc = nom0->_rv().subt ( rv ); |
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| 59 | dimc = rvc._dsize(); |
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[737] | 60 | |
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[286] | 61 | //prepare data structures |
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[477] | 62 | if ( copy ) { |
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[565] | 63 | bdm_error ( "todo" ); |
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| 64 | // destroynom = true; |
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[477] | 65 | } else { |
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| 66 | nom = nom0; |
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| 67 | destroynom = false; |
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| 68 | } |
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[565] | 69 | bdm_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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[477] | 70 | |
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[286] | 71 | // build denominator |
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[192] | 72 | den = nom->marginal ( rvc ); |
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[477] | 73 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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[192] | 74 | }; |
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[675] | 75 | |
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[211] | 76 | double evallogcond ( const vec &val, const vec &cond ) { |
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[214] | 77 | double tmp; |
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[487] | 78 | vec nom_val ( dimension() + dimc ); |
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[477] | 79 | dl.pushup_cond ( nom_val, val, cond ); |
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[214] | 80 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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| 81 | return tmp; |
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[192] | 82 | } |
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[182] | 83 | //! Object takes ownership of nom and will destroy it |
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[477] | 84 | void ownnom() { |
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| 85 | destroynom = true; |
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| 86 | } |
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[182] | 87 | //! Default destructor |
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[477] | 88 | ~mratio() { |
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| 89 | if ( destroynom ) { |
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| 90 | delete nom; |
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| 91 | } |
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| 92 | } |
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[550] | 93 | |
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| 94 | private: |
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| 95 | // not implemented |
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| 96 | mratio ( const mratio & ); |
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[737] | 97 | mratio &operator= ( const mratio & ); |
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[182] | 98 | }; |
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| 99 | |
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[107] | 100 | /*! |
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| 101 | * \brief Mixture of epdfs |
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| 102 | |
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| 103 | Density function: |
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| 104 | \f[ |
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| 105 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 106 | \f] |
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| 107 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 108 | |
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| 109 | */ |
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[145] | 110 | class emix : public epdf { |
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[162] | 111 | protected: |
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| 112 | //! weights of the components |
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| 113 | vec w; |
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[559] | 114 | |
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[162] | 115 | //! Component (epdfs) |
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[504] | 116 | Array<shared_ptr<epdf> > Coms; |
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| 117 | |
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[162] | 118 | public: |
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[559] | 119 | //! Default constructor |
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| 120 | emix ( ) : epdf ( ) { } |
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| 121 | |
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[737] | 122 | /*! |
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| 123 | \brief Set weights \c w and components \c Coms |
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[559] | 124 | |
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[737] | 125 | Shared pointers in Coms are kept inside this instance and |
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| 126 | shouldn't be modified after being passed to this method. |
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| 127 | */ |
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[504] | 128 | void set_parameters ( const vec &w, const Array<shared_ptr<epdf> > &Coms ); |
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[750] | 129 | |
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| 130 | virtual void validate (); |
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[107] | 131 | |
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[162] | 132 | vec sample() const; |
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[715] | 133 | |
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[739] | 134 | vec mean() const; |
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[715] | 135 | |
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[739] | 136 | vec variance() const; |
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| 137 | |
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| 138 | double evallog ( const vec &val ) const; |
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| 139 | |
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| 140 | vec evallog_mat ( const mat &Val ) const; |
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| 141 | |
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[214] | 142 | //! Auxiliary function that returns pdflog for each component |
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[739] | 143 | mat evallog_coms ( const mat &Val ) const; |
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[107] | 144 | |
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[504] | 145 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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[536] | 146 | //! Update already existing marginal density \c target |
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[504] | 147 | void marginal ( const RV &rv, emix &target ) const; |
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[693] | 148 | shared_ptr<pdf> condition ( const RV &rv ) const; |
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[182] | 149 | |
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[713] | 150 | //Access methods |
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[162] | 151 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 152 | vec& _w() { |
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| 153 | return w; |
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| 154 | } |
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[204] | 155 | |
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[193] | 156 | //!access function |
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[504] | 157 | shared_ptr<epdf> _Coms ( int i ) { |
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[477] | 158 | return Coms ( i ); |
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[286] | 159 | } |
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[504] | 160 | |
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[477] | 161 | void set_rv ( const RV &rv ) { |
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| 162 | epdf::set_rv ( rv ); |
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| 163 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 164 | Coms ( i )->set_rv ( rv ); |
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| 165 | } |
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| 166 | } |
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[713] | 167 | |
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| 168 | //! Load from structure with elements: |
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| 169 | //! \code |
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| 170 | //! { class='emix'; |
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| 171 | //! pdfs = (..., ...); // list of pdfs in the mixture |
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| 172 | //! weights = ( 0.5, 0.5 ); // weights of pdfs in the mixture |
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| 173 | //! } |
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| 174 | //! \endcode |
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| 175 | //!@} |
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| 176 | void from_setting ( const Setting &set ) { |
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[737] | 177 | |
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| 178 | vec w0; |
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[716] | 179 | Array<shared_ptr<epdf> > Coms0; |
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[737] | 180 | |
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[716] | 181 | UI::get ( Coms0, set, "pdfs", UI::compulsory ); |
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[713] | 182 | |
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[737] | 183 | if ( !UI::get ( w0, set, "weights", UI::optional ) ) { |
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[713] | 184 | int len = Coms.length(); |
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[737] | 185 | w0.set_length ( len ); |
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[716] | 186 | w0 = 1.0 / len; |
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[713] | 187 | } |
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[716] | 188 | |
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| 189 | // TODO asi lze nacitat primocare do w a coms, jen co bude hotovy validate() |
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[737] | 190 | set_parameters ( w0, Coms0 ); |
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[750] | 191 | validate(); |
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[713] | 192 | } |
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[107] | 193 | }; |
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[737] | 194 | SHAREDPTR ( emix ); |
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[713] | 195 | UIREGISTER ( emix ); |
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[107] | 196 | |
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[333] | 197 | /*! |
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| 198 | * \brief Mixture of egiws |
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| 199 | |
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| 200 | */ |
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| 201 | class egiwmix : public egiw { |
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| 202 | protected: |
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| 203 | //! weights of the components |
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| 204 | vec w; |
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| 205 | //! Component (epdfs) |
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| 206 | Array<egiw*> Coms; |
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| 207 | //!Flag if owning Coms |
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| 208 | bool destroyComs; |
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| 209 | public: |
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| 210 | //!Default constructor |
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| 211 | egiwmix ( ) : egiw ( ) {}; |
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| 212 | |
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| 213 | //! Set weights \c w and components \c Coms |
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| 214 | //!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] | 215 | void set_parameters ( const vec &w, const Array<egiw*> &Coms, bool copy = false ); |
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[333] | 216 | |
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| 217 | //!return expected value |
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| 218 | vec mean() const; |
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| 219 | |
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| 220 | //!return a sample from the density |
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| 221 | vec sample() const; |
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| 222 | |
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| 223 | //!return the expected variance |
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[477] | 224 | vec variance() const; |
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[333] | 225 | |
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| 226 | // TODO!!! Defined to follow ANSI and/or for future development |
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| 227 | void mean_mat ( mat &M, mat&R ) const {}; |
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[477] | 228 | double evallog_nn ( const vec &val ) const { |
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| 229 | return 0; |
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| 230 | }; |
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| 231 | double lognc () const { |
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| 232 | return 0; |
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[504] | 233 | } |
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[333] | 234 | |
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[504] | 235 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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[660] | 236 | //! marginal density update |
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[504] | 237 | void marginal ( const RV &rv, emix &target ) const; |
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| 238 | |
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[333] | 239 | //Access methods |
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| 240 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 241 | vec& _w() { |
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| 242 | return w; |
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| 243 | } |
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| 244 | virtual ~egiwmix() { |
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| 245 | if ( destroyComs ) { |
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| 246 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 247 | delete Coms ( i ); |
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| 248 | } |
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| 249 | } |
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| 250 | } |
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[333] | 251 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 252 | void ownComs() { |
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| 253 | destroyComs = true; |
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| 254 | } |
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[333] | 255 | |
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| 256 | //!access function |
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[477] | 257 | egiw* _Coms ( int i ) { |
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| 258 | return Coms ( i ); |
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| 259 | } |
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[333] | 260 | |
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[477] | 261 | void set_rv ( const RV &rv ) { |
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| 262 | egiw::set_rv ( rv ); |
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| 263 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 264 | Coms ( i )->set_rv ( rv ); |
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| 265 | } |
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[333] | 266 | } |
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| 267 | |
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| 268 | //! Approximation of a GiW mix by a single GiW pdf |
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| 269 | egiw* approx(); |
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| 270 | }; |
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| 271 | |
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[115] | 272 | /*! \brief Chain rule decomposition of epdf |
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| 273 | |
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[145] | 274 | Probability density in the form of Chain-rule decomposition: |
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| 275 | \[ |
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| 276 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 277 | \] |
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| 278 | Note that |
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[115] | 279 | */ |
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[693] | 280 | class mprod: public pdf { |
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[507] | 281 | private: |
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[693] | 282 | Array<shared_ptr<pdf> > pdfs; |
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[507] | 283 | |
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[693] | 284 | //! Data link for each pdfs |
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[546] | 285 | Array<shared_ptr<datalink_m2m> > dls; |
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[461] | 286 | |
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[546] | 287 | protected: |
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[487] | 288 | //! dummy epdf used only as storage for RV and dim |
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| 289 | epdf iepdf; |
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[461] | 290 | |
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[162] | 291 | public: |
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[507] | 292 | //! \brief Default constructor |
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| 293 | mprod() { } |
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| 294 | |
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| 295 | /*!\brief Constructor from list of mFacs |
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[165] | 296 | */ |
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[693] | 297 | mprod ( const Array<shared_ptr<pdf> > &mFacs ) { |
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[477] | 298 | set_elements ( mFacs ); |
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[461] | 299 | } |
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[693] | 300 | //! Set internal \c pdfs from given values |
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[737] | 301 | void set_elements ( const Array<shared_ptr<pdf> > &mFacs ); |
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[477] | 302 | |
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[739] | 303 | double evallogcond ( const vec &val, const vec &cond ); |
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[395] | 304 | |
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[739] | 305 | vec evallogcond_mat ( const mat &Dt, const vec &cond ); |
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[395] | 306 | |
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[739] | 307 | vec evallogcond_mat ( const Array<vec> &Dt, const vec &cond ); |
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| 308 | |
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[270] | 309 | //TODO smarter... |
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| 310 | vec samplecond ( const vec &cond ) { |
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[477] | 311 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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[487] | 312 | vec smp = std::numeric_limits<double>::infinity() * ones ( dimension() ); |
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[165] | 313 | vec smpi; |
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[192] | 314 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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[693] | 315 | for ( int i = ( pdfs.length() - 1 ); i >= 0; i-- ) { |
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| 316 | // generate contribution of this pdf |
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[737] | 317 | smpi = pdfs ( i )->samplecond ( dls ( i )->get_cond ( smp , cond ) ); |
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[162] | 318 | // copy contribution of this pdf into smp |
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[270] | 319 | dls ( i )->pushup ( smp, smpi ); |
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[145] | 320 | } |
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[162] | 321 | return smp; |
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| 322 | } |
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| 323 | |
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[395] | 324 | //! Load from structure with elements: |
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| 325 | //! \code |
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| 326 | //! { class='mprod'; |
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[693] | 327 | //! pdfs = (..., ...); // list of pdfs in the order of chain rule |
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[395] | 328 | //! } |
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| 329 | //! \endcode |
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| 330 | //!@} |
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[477] | 331 | void from_setting ( const Setting &set ) { |
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[693] | 332 | Array<shared_ptr<pdf> > atmp; //temporary Array |
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| 333 | UI::get ( atmp, set, "pdfs", UI::compulsory ); |
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[527] | 334 | set_elements ( atmp ); |
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[395] | 335 | } |
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[107] | 336 | }; |
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[477] | 337 | UIREGISTER ( mprod ); |
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[529] | 338 | SHAREDPTR ( mprod ); |
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[107] | 339 | |
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[168] | 340 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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| 341 | class eprod: public epdf { |
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| 342 | protected: |
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| 343 | //! Components (epdfs) |
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[170] | 344 | Array<const epdf*> epdfs; |
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[168] | 345 | //! Array of indeces |
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[270] | 346 | Array<datalink*> dls; |
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[168] | 347 | public: |
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[536] | 348 | //! Default constructor |
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[477] | 349 | eprod () : epdfs ( 0 ), dls ( 0 ) {}; |
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[737] | 350 | //! Set internal |
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[477] | 351 | void set_parameters ( const Array<const epdf*> &epdfs0, bool named = true ) { |
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| 352 | epdfs = epdfs0;//.set_length ( epdfs0.length() ); |
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[286] | 353 | dls.set_length ( epdfs.length() ); |
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| 354 | |
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[477] | 355 | bool independent = true; |
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[286] | 356 | if ( named ) { |
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[477] | 357 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 358 | independent = rv.add ( epdfs ( i )->_rv() ); |
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[565] | 359 | bdm_assert_debug ( independent, "eprod:: given components are not independent." ); |
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[286] | 360 | } |
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[477] | 361 | dim = rv._dsize(); |
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| 362 | } else { |
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| 363 | dim = 0; |
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| 364 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 365 | dim += epdfs ( i )->dimension(); |
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[286] | 366 | } |
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[204] | 367 | } |
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[286] | 368 | // |
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[477] | 369 | int cumdim = 0; |
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| 370 | int dimi = 0; |
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[286] | 371 | int i; |
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[477] | 372 | for ( i = 0; i < epdfs.length(); i++ ) { |
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[286] | 373 | dls ( i ) = new datalink; |
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[477] | 374 | if ( named ) { |
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| 375 | dls ( i )->set_connection ( epdfs ( i )->_rv() , rv ); |
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| 376 | } else { |
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[286] | 377 | dimi = epdfs ( i )->dimension(); |
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[477] | 378 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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| 379 | cumdim += dimi; |
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[286] | 380 | } |
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| 381 | } |
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[168] | 382 | } |
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| 383 | |
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[739] | 384 | vec mean() const; |
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| 385 | |
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| 386 | vec variance() const; |
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| 387 | |
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| 388 | vec sample() const; |
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| 389 | |
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| 390 | double evallog ( const vec &val ) const; |
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| 391 | |
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[170] | 392 | //!access function |
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[477] | 393 | const epdf* operator () ( int i ) const { |
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[565] | 394 | bdm_assert_debug ( i < epdfs.length(), "wrong index" ); |
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[477] | 395 | return epdfs ( i ); |
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| 396 | } |
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[204] | 397 | |
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[193] | 398 | //!Destructor |
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[477] | 399 | ~eprod() { |
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| 400 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 401 | delete dls ( i ); |
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| 402 | } |
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| 403 | } |
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[168] | 404 | }; |
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| 405 | |
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| 406 | |
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[693] | 407 | /*! \brief Mixture of pdfs with constant weights, all pdfs are of equal RV and RVC |
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[124] | 408 | |
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| 409 | */ |
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[693] | 410 | class mmix : public pdf { |
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[488] | 411 | protected: |
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[693] | 412 | //! Component (pdfs) |
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| 413 | Array<shared_ptr<pdf> > Coms; |
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[488] | 414 | //!weights of the components |
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| 415 | vec w; |
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| 416 | public: |
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| 417 | //!Default constructor |
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[737] | 418 | mmix() : Coms ( 0 ) { } |
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[461] | 419 | |
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[488] | 420 | //! Set weights \c w and components \c R |
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[693] | 421 | void set_parameters ( const vec &w0, const Array<shared_ptr<pdf> > &Coms0 ) { |
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[536] | 422 | //!\todo check if all components are OK |
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[488] | 423 | Coms = Coms0; |
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[737] | 424 | w = w0; |
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[503] | 425 | |
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[737] | 426 | if ( Coms0.length() > 0 ) { |
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| 427 | set_rv ( Coms ( 0 )->_rv() ); |
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[675] | 428 | dim = rv._dsize(); |
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[737] | 429 | set_rvc ( Coms ( 0 )->_rvc() ); |
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[513] | 430 | dimc = rvc._dsize(); |
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| 431 | } |
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[488] | 432 | } |
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[737] | 433 | double evallogcond ( const vec &dt, const vec &cond ) { |
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| 434 | double ll = 0.0; |
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| 435 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 436 | ll += Coms ( i )->evallogcond ( dt, cond ); |
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[488] | 437 | } |
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| 438 | return ll; |
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| 439 | } |
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| 440 | |
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[737] | 441 | vec samplecond ( const vec &cond ); |
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[488] | 442 | |
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[711] | 443 | //! Load from structure with elements: |
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| 444 | //! \code |
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| 445 | //! { class='mmix'; |
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| 446 | //! pdfs = (..., ...); // list of pdfs in the mixture |
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| 447 | //! weights = ( 0.5, 0.5 ); // weights of pdfs in the mixture |
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| 448 | //! } |
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| 449 | //! \endcode |
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| 450 | //!@} |
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| 451 | void from_setting ( const Setting &set ) { |
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[737] | 452 | UI::get ( Coms, set, "pdfs", UI::compulsory ); |
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[711] | 453 | |
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[716] | 454 | // TODO ma byt zde, ci ve validate()? |
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[737] | 455 | if ( Coms.length() > 0 ) { |
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| 456 | set_rv ( Coms ( 0 )->_rv() ); |
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[716] | 457 | dim = rv._dsize(); |
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[737] | 458 | set_rvc ( Coms ( 0 )->_rvc() ); |
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[716] | 459 | dimc = rvc._dsize(); |
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| 460 | } |
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| 461 | |
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[737] | 462 | if ( !UI::get ( w, set, "weights", UI::optional ) ) { |
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[711] | 463 | int len = Coms.length(); |
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[737] | 464 | w.set_length ( len ); |
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[715] | 465 | w = 1.0 / len; |
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[711] | 466 | } |
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| 467 | } |
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[488] | 468 | }; |
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[737] | 469 | SHAREDPTR ( mmix ); |
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[711] | 470 | UIREGISTER ( mmix ); |
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[488] | 471 | |
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[254] | 472 | } |
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[107] | 473 | #endif //MX_H |
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