[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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[1068] | 26 | |
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[182] | 27 | which arise e.g. by applying the Bayes rule. |
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| 28 | It represents density in the form: |
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| 29 | \f[ |
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| 30 | f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)} |
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| 31 | \f] |
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| 32 | where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$. |
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| 33 | |
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| 34 | In particular this type of arise by conditioning of a mixture model. |
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| 35 | |
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[211] | 36 | At present the only supported operation is evallogcond(). |
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[182] | 37 | */ |
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[693] | 38 | class mratio: public pdf { |
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[192] | 39 | protected: |
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[1064] | 40 | //! Nominator in the form of pdf |
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| 41 | const epdf* nom; |
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[504] | 42 | |
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[1064] | 43 | //!Denominator in the form of epdf |
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| 44 | shared_ptr<epdf> den; |
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[504] | 45 | |
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[1064] | 46 | //!flag for destructor |
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| 47 | bool destroynom; |
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| 48 | //!datalink between conditional and nom |
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| 49 | datalink_m2e dl; |
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[192] | 50 | public: |
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[1064] | 51 | //!Default constructor. By default, the given epdf is not copied! |
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| 52 | //! It is assumed that this function will be used only temporarily. |
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| 53 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : pdf ( ), dl ( ) { |
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| 54 | // adjust rv and rvc |
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[675] | 55 | |
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[1064] | 56 | set_rv ( rv ); |
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| 57 | dim = rv._dsize(); |
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[675] | 58 | |
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[1064] | 59 | rvc = nom0->_rv().subt ( rv ); |
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| 60 | dimc = rvc._dsize(); |
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[737] | 61 | |
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[1064] | 62 | //prepare data structures |
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| 63 | if ( copy ) { |
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| 64 | bdm_error ( "todo" ); |
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| 65 | // destroynom = true; |
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| 66 | } else { |
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| 67 | nom = nom0; |
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| 68 | destroynom = false; |
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| 69 | } |
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| 70 | bdm_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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[477] | 71 | |
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[1064] | 72 | // build denominator |
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| 73 | den = nom->marginal ( rvc ); |
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| 74 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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| 75 | }; |
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[675] | 76 | |
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[1064] | 77 | double evallogcond ( const vec &val, const vec &cond ) { |
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| 78 | double tmp; |
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| 79 | vec nom_val ( dimension() + dimc ); |
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| 80 | dl.pushup_cond ( nom_val, val, cond ); |
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| 81 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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| 82 | return tmp; |
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| 83 | } |
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[766] | 84 | |
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[1064] | 85 | //! Returns a sample from the density conditioned on \c cond, \f$x \sim epdf(rv|cond)\f$. \param cond is numeric value of \c rv |
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| 86 | virtual vec samplecond ( const vec &cond ) NOT_IMPLEMENTED(0); |
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[766] | 87 | |
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[1064] | 88 | //! Object takes ownership of nom and will destroy it |
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| 89 | void ownnom() { |
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| 90 | destroynom = true; |
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| 91 | } |
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| 92 | //! Default destructor |
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| 93 | ~mratio() { |
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| 94 | if ( destroynom ) { |
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| 95 | delete nom; |
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| 96 | } |
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| 97 | } |
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[550] | 98 | |
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[766] | 99 | |
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[550] | 100 | private: |
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[1064] | 101 | // not implemented |
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| 102 | mratio ( const mratio & ); |
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| 103 | mratio &operator= ( const mratio & ); |
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[182] | 104 | }; |
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| 105 | |
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[886] | 106 | class emix; //forward |
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| 107 | |
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[1066] | 108 | //! \brief Base class (interface) for mixtures |
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[886] | 109 | class emix_base : public epdf { |
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[1064] | 110 | protected: |
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| 111 | //! reference to vector of weights |
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| 112 | vec &w; |
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| 113 | //! function returning ith component |
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| 114 | virtual const epdf * component(const int &i) const=0; |
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| 115 | |
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| 116 | virtual int no_coms() const=0; |
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| 117 | |
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| 118 | public: |
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| 119 | |
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| 120 | emix_base(vec &w0): w(w0) {} |
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| 121 | |
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| 122 | void validate (); |
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| 123 | |
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| 124 | vec sample() const; |
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| 125 | |
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| 126 | vec mean() const; |
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| 127 | |
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| 128 | vec variance() const; |
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| 129 | |
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| 130 | double evallog ( const vec &val ) const; |
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| 131 | |
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| 132 | vec evallog_mat ( const mat &Val ) const; |
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| 133 | |
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| 134 | //! Auxiliary function that returns pdflog for each component |
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| 135 | mat evallog_coms ( const mat &Val ) const; |
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| 136 | |
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| 137 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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| 138 | //! Update already existing marginal density \c target |
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| 139 | void marginal ( const RV &rv, emix &target ) const; |
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| 140 | shared_ptr<pdf> condition ( const RV &rv ) const; |
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| 141 | |
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| 142 | //Access methods |
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| 143 | //! returns a reference to the internal weights. Use with Care! |
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| 144 | vec& _w() { |
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| 145 | return w; |
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| 146 | } |
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| 147 | |
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| 148 | const vec& _w() const { |
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| 149 | return w; |
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| 150 | } |
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| 151 | //!access |
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| 152 | const epdf* _com(int i) const { |
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| 153 | return component(i); |
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| 154 | } |
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| 155 | |
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[886] | 156 | }; |
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| 157 | |
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[107] | 158 | /*! |
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| 159 | * \brief Mixture of epdfs |
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| 160 | |
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| 161 | Density function: |
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| 162 | \f[ |
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| 163 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 164 | \f] |
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| 165 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 166 | |
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| 167 | */ |
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[886] | 168 | class emix : public emix_base { |
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[162] | 169 | protected: |
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[1064] | 170 | //! weights of the components |
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| 171 | vec weights; |
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[559] | 172 | |
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[1064] | 173 | //! Component (epdfs) |
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| 174 | Array<shared_ptr<epdf> > Coms; |
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[504] | 175 | |
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[162] | 176 | public: |
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[1064] | 177 | //! Default constructor |
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| 178 | emix ( ) : emix_base ( weights) { } |
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[559] | 179 | |
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[1064] | 180 | const epdf* component(const int &i) const { |
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| 181 | return Coms(i).get(); |
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| 182 | } |
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| 183 | void validate(); |
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[107] | 184 | |
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| 185 | |
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[1064] | 186 | int no_coms() const { |
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| 187 | return Coms.length(); |
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| 188 | } |
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| 189 | |
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[1066] | 190 | /*! Create object from the following structure |
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| 191 | |
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| 192 | \code |
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| 193 | class = 'emix'; |
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| 194 | |
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| 195 | pdfs = { list of any bdm::pdf offsprings }; % pdfs in the mixture, bdm::pdf::from_setting |
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| 196 | weights = [... ]; % vector of weights of pdfs in the mixture |
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| 197 | --- inherited fields --- |
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| 198 | bdm::emix_base::from_setting |
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| 199 | \endcode |
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| 200 | |
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| 201 | */ |
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[1064] | 202 | void from_setting ( const Setting &set ); |
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[1066] | 203 | |
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[1064] | 204 | void to_setting (Setting &set) const; |
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| 205 | |
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| 206 | void set_rv ( const RV &rv ) { |
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| 207 | epdf::set_rv ( rv ); |
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| 208 | for ( int i = 0; i < no_coms(); i++ ) { |
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| 209 | Coms( i )->set_rv ( rv ); |
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| 210 | } |
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| 211 | } |
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| 212 | |
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| 213 | Array<shared_ptr<epdf> >& _Coms ( ) { |
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| 214 | return Coms; |
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| 215 | } |
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[333] | 216 | }; |
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[886] | 217 | SHAREDPTR ( emix ); |
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| 218 | UIREGISTER ( emix ); |
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[333] | 219 | |
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[886] | 220 | |
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[115] | 221 | /*! \brief Chain rule decomposition of epdf |
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| 222 | |
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[145] | 223 | Probability density in the form of Chain-rule decomposition: |
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| 224 | \[ |
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| 225 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 226 | \] |
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| 227 | Note that |
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[115] | 228 | */ |
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[693] | 229 | class mprod: public pdf { |
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[507] | 230 | private: |
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[1064] | 231 | Array<shared_ptr<pdf> > pdfs; |
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[507] | 232 | |
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[1064] | 233 | //! Data link for each pdfs |
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| 234 | Array<shared_ptr<datalink_m2m> > dls; |
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[461] | 235 | |
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[162] | 236 | public: |
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[1064] | 237 | //! \brief Default constructor |
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| 238 | mprod() { } |
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[507] | 239 | |
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[1064] | 240 | /*!\brief Constructor from list of mFacs |
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| 241 | */ |
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| 242 | mprod ( const Array<shared_ptr<pdf> > &mFacs ) { |
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| 243 | set_elements ( mFacs ); |
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| 244 | } |
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| 245 | //! Set internal \c pdfs from given values |
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| 246 | void set_elements ( const Array<shared_ptr<pdf> > &mFacs ); |
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[477] | 247 | |
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[1064] | 248 | double evallogcond ( const vec &val, const vec &cond ); |
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[395] | 249 | |
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[1064] | 250 | vec evallogcond_mat ( const mat &Dt, const vec &cond ); |
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[395] | 251 | |
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[1064] | 252 | vec evallogcond_mat ( const Array<vec> &Dt, const vec &cond ); |
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[739] | 253 | |
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[1064] | 254 | //TODO smarter... |
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| 255 | vec samplecond ( const vec &cond ) { |
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| 256 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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| 257 | vec smp = std::numeric_limits<double>::infinity() * ones ( dimension() ); |
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| 258 | vec smpi; |
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| 259 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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| 260 | for ( int i = ( pdfs.length() - 1 ); i >= 0; i-- ) { |
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| 261 | // generate contribution of this pdf |
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| 262 | smpi = pdfs ( i )->samplecond ( dls ( i )->get_cond ( smp , cond ) ); |
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| 263 | // copy contribution of this pdf into smp |
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| 264 | dls ( i )->pushup ( smp, smpi ); |
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| 265 | } |
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| 266 | return smp; |
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| 267 | } |
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[162] | 268 | |
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[1068] | 269 | //! Create object from the following structure |
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| 270 | //! \code |
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| 271 | //! class='mprod'; |
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| 272 | //! pdfs = { list of bdm::pdf }; % list of bdm::pdf offsprings stored in the order of chain rule, bdm::pdf::from_setting |
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| 273 | //! --- inherited fields --- |
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| 274 | //! bdm::pdf::from_setting |
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[1064] | 275 | //! \endcode |
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| 276 | //!@} |
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| 277 | void from_setting ( const Setting &set ) ; |
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[1068] | 278 | void to_setting (Setting &set) const; |
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[107] | 279 | }; |
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[477] | 280 | UIREGISTER ( mprod ); |
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[529] | 281 | SHAREDPTR ( mprod ); |
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[107] | 282 | |
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[886] | 283 | |
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[1066] | 284 | //! \brief Base class (interface) for bdm::eprod |
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[886] | 285 | class eprod_base: public epdf { |
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[168] | 286 | protected: |
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[1064] | 287 | //! Array of indices |
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| 288 | Array<datalink*> dls; |
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| 289 | //! interface for a factor |
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[979] | 290 | public: |
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[1064] | 291 | virtual const epdf* factor(int i) const NOT_IMPLEMENTED(NULL); |
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| 292 | //!number of factors |
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| 293 | virtual const int no_factors() const NOT_IMPLEMENTED(0); |
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| 294 | //! Default constructor |
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| 295 | eprod_base () : dls (0) {}; |
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| 296 | //! Set internal |
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| 297 | vec mean() const; |
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[886] | 298 | |
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[1064] | 299 | vec variance() const; |
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[886] | 300 | |
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[1064] | 301 | vec sample() const; |
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[886] | 302 | |
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[1064] | 303 | double evallog ( const vec &val ) const; |
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[886] | 304 | |
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[1064] | 305 | //!Destructor |
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| 306 | ~eprod_base() { |
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| 307 | for ( int i = 0; i < dls.length(); i++ ) { |
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| 308 | delete dls ( i ); |
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| 309 | } |
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| 310 | } |
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| 311 | void validate() { |
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| 312 | epdf::validate(); |
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| 313 | dls.set_length ( no_factors() ); |
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| 314 | |
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| 315 | bool independent = true; |
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| 316 | dim = 0; |
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| 317 | for ( int i = 0; i < no_factors(); i++ ) { |
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| 318 | independent = rv.add ( factor ( i )->_rv() ); |
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| 319 | dim += factor ( i )->dimension(); |
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| 320 | bdm_assert_debug ( independent, "eprod:: given components are not independent." ); |
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| 321 | }; |
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| 322 | |
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| 323 | // |
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| 324 | int cumdim = 0; |
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| 325 | int dimi = 0; |
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| 326 | int i; |
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| 327 | for ( i = 0; i < no_factors(); i++ ) { |
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| 328 | dls ( i ) = new datalink; |
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| 329 | if ( isnamed() ) { // rvs are complete |
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| 330 | dls ( i )->set_connection ( factor ( i )->_rv() , rv ); |
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| 331 | } else { //rvs are not reliable |
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| 332 | dimi = factor ( i )->dimension(); |
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| 333 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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| 334 | cumdim += dimi; |
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| 335 | } |
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| 336 | } |
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| 337 | |
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| 338 | } |
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[886] | 339 | }; |
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[168] | 340 | |
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[1066] | 341 | //! \brief Product of independent epdfs. For dependent pdfs, use bdm::mprod. |
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[1064] | 342 | class eprod: public eprod_base { |
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| 343 | protected: |
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| 344 | Array<shared_ptr<epdf> > factors; |
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| 345 | public: |
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| 346 | const epdf* factor(int i) const { |
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| 347 | return factors(i).get(); |
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| 348 | } |
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| 349 | const int no_factors() const { |
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| 350 | return factors.length(); |
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| 351 | } |
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| 352 | void set_parameters ( const Array<shared_ptr<epdf> > &epdfs0) { |
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| 353 | factors = epdfs0; |
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| 354 | } |
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[1066] | 355 | |
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| 356 | /*! Create object from the following structure |
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| 357 | |
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| 358 | \code |
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| 359 | class = 'eprod'; |
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| 360 | pdfs = { list of any bdm::epdf offsprings }; % pdfs in the product, bdm::epdf::from_setting |
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| 361 | --- inherited fields --- |
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| 362 | bdm::eprod_base::from_setting |
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| 363 | \endcode |
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| 364 | |
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| 365 | */ |
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[1064] | 366 | void from_setting(const Setting &set) { |
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| 367 | UI::get(factors,set,"pdfs",UI::compulsory); |
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| 368 | } |
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[886] | 369 | }; |
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[944] | 370 | UIREGISTER(eprod); |
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[204] | 371 | |
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[1068] | 372 | //! \brief Internal class similar to eprod - factors are external pointers. To be used internally! |
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[1064] | 373 | class eprod_internal: public eprod_base { |
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| 374 | protected: |
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| 375 | Array<epdf* > factors; |
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| 376 | const epdf* factor(int i) const { |
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| 377 | return factors(i); |
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| 378 | } |
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| 379 | const int no_factors() const { |
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| 380 | return factors.length(); |
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| 381 | } |
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| 382 | public: |
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| 383 | void set_parameters ( const Array<epdf *> &epdfs0) { |
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| 384 | factors = epdfs0; |
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| 385 | } |
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[168] | 386 | }; |
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| 387 | |
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[693] | 388 | /*! \brief Mixture of pdfs with constant weights, all pdfs are of equal RV and RVC |
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[124] | 389 | |
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| 390 | */ |
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[693] | 391 | class mmix : public pdf { |
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[488] | 392 | protected: |
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[1064] | 393 | //! Component (pdfs) |
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| 394 | Array<shared_ptr<pdf> > Coms; |
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| 395 | //!weights of the components |
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| 396 | vec w; |
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[488] | 397 | public: |
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[1064] | 398 | //!Default constructor |
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| 399 | mmix() : Coms ( 0 ) { }; |
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[461] | 400 | |
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[1064] | 401 | double evallogcond ( const vec &dt, const vec &cond ) { |
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| 402 | double ll = 0.0; |
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| 403 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 404 | ll += Coms ( i )->evallogcond ( dt, cond ); |
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| 405 | } |
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| 406 | return ll; |
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| 407 | } |
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[488] | 408 | |
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[1064] | 409 | vec samplecond ( const vec &cond ); |
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[488] | 410 | |
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[1064] | 411 | //! } |
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| 412 | //! \endcode |
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| 413 | //!@} |
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[1068] | 414 | |
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| 415 | /*! Create object from the following structure |
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| 416 | \code |
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| 417 | class = 'mmix'; |
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| 418 | pdfs = { list of components bdm::pdf }; % list of pdf offsprings, bdm::pdf::from_setting |
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| 419 | --- optional fields --- |
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| 420 | weights = [...]; % weights of pdfs in the mixture |
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| 421 | --- inherited fields --- |
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| 422 | bdm::pdf::from_setting |
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| 423 | \endcode |
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| 424 | \endcode |
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| 425 | If the optional fields are not given, they will be filled as follows: |
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| 426 | \code |
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| 427 | weights = 1/n * [1,1,1,...]; |
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| 428 | \endcode |
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| 429 | */ |
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[1064] | 430 | void from_setting ( const Setting &set ); |
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[1066] | 431 | void to_setting (Setting &set) const; |
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[1064] | 432 | virtual void validate(); |
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[488] | 433 | }; |
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[737] | 434 | SHAREDPTR ( mmix ); |
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[711] | 435 | UIREGISTER ( mmix ); |
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[488] | 436 | |
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[979] | 437 | |
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[1066] | 438 | //! \brief Base class for all BM running as parallel update of internal BMs |
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[979] | 439 | class ProdBMBase : public BM { |
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[1064] | 440 | protected : |
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| 441 | Array<vec_from_vec> bm_yt; |
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| 442 | Array<vec_from_2vec> bm_cond; |
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[1068] | 443 | |
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| 444 | //! \brief Internal class |
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[1064] | 445 | class eprod_bm : public eprod_base { |
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| 446 | ProdBMBase & pb; |
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| 447 | public : |
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| 448 | eprod_bm(ProdBMBase &pb0): pb(pb0) {} |
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| 449 | const epdf* factor(int i ) const { |
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| 450 | return &(pb.bm(i)->posterior()); |
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| 451 | } |
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| 452 | const int no_factors() const { |
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| 453 | return pb.no_bms(); |
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| 454 | } |
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| 455 | } est; |
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| 456 | public: |
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| 457 | ProdBMBase():est(*this) {} |
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| 458 | virtual BM* bm(int i) NOT_IMPLEMENTED(NULL); |
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| 459 | virtual int no_bms() const { |
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| 460 | return 0; |
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| 461 | } |
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| 462 | const epdf& posterior() const { |
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| 463 | return est; |
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| 464 | } |
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| 465 | void set_prior(const epdf *pri) { |
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| 466 | const eprod_base* ep=dynamic_cast<const eprod_base*>(pri); |
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| 467 | if (ep) { |
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| 468 | bdm_assert(ep->no_factors()!=no_bms() , "Given prior has "+ num2str(ep->no_factors()) + " while this ProdBM has "+ |
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| 469 | num2str(no_bms()) + "BMs"); |
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| 470 | for (int i=0; i<no_bms(); i++) { |
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| 471 | bm(i)->set_prior(ep->factor(i)); |
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| 472 | } |
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| 473 | } |
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| 474 | } |
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| 475 | |
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| 476 | void validate() { |
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| 477 | est.validate(); |
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| 478 | BM::validate(); |
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| 479 | // set links |
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| 480 | bm_yt.set_length(no_bms()); |
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| 481 | bm_cond.set_length(no_bms()); |
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| 482 | |
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| 483 | // |
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| 484 | |
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| 485 | for (int i=0; i<no_bms(); i++) { |
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| 486 | yrv.add(bm(i)->_yrv()); |
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| 487 | rvc.add(bm(i)->_rvc()); |
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| 488 | } |
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| 489 | rvc=rvc.subt(yrv); |
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| 490 | |
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| 491 | dimy = yrv._dsize(); |
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| 492 | dimc = rvc._dsize(); |
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| 493 | |
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| 494 | for (int i=0; i<no_bms(); i++) { |
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| 495 | bm_yt(i).connect(bm(i)->_yrv(), yrv); |
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| 496 | bm_cond(i).connect(bm(i)->_rvc(), yrv, rvc); |
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| 497 | } |
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| 498 | } |
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| 499 | void bayes(const vec &dt, const vec &cond) { |
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| 500 | ll=0; |
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| 501 | for(int i=0; i<no_bms(); i++) { |
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| 502 | bm_yt(i).update(dt); |
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| 503 | bm_cond(i).update(dt,cond); |
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| 504 | bm(i)->bayes(bm_yt(i), bm_cond(i)); |
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| 505 | } |
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| 506 | } |
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| 507 | |
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[979] | 508 | }; |
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| 509 | |
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[1064] | 510 | class ProdBM: public ProdBMBase { |
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| 511 | protected: |
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| 512 | Array<shared_ptr<BM> > BMs; |
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| 513 | public: |
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| 514 | virtual BM* bm(int i) { |
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| 515 | return BMs(i).get(); |
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| 516 | } |
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| 517 | virtual int no_bms() const { |
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| 518 | return BMs.length(); |
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| 519 | } |
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| 520 | void from_setting(const Setting &set) { |
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| 521 | BM::from_setting(set); |
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| 522 | UI::get(BMs,set,"BMs"); |
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| 523 | } |
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| 524 | void to_setting(Setting &set) const { |
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| 525 | BM::to_setting(set); |
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| 526 | UI::save(BMs,set,"BMs"); |
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| 527 | } |
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| 528 | |
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[979] | 529 | }; |
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| 530 | UIREGISTER(ProdBM); |
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| 531 | |
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[1064] | 532 | //! \brief class for on-line model selection |
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| 533 | class ModelComparator: public ProdBM { |
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| 534 | protected: |
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| 535 | multiBM weights; |
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| 536 | public: |
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| 537 | void bayes(const vec &yt, const vec &cond) { |
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| 538 | vec w_nn(no_bms()); |
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| 539 | for (int i=0; i<no_bms(); i++) { |
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| 540 | bm(i)->bayes(yt,cond); |
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| 541 | w_nn(i) += bm(i)->_ll(); |
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| 542 | } |
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| 543 | vec w=exp(w_nn-max(w_nn)); |
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| 544 | weights.bayes(w/sum(w)); |
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| 545 | } |
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| 546 | void validate() { |
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| 547 | ProdBM::validate(); |
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| 548 | weights.validate(); |
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| 549 | } |
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| 550 | void from_setting(const Setting& set) { |
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| 551 | ProdBM::from_setting(set); |
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| 552 | UI::get(weights.frg, set, "frg",UI::optional); |
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| 553 | } |
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| 554 | void to_setting(Setting& set) const { |
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| 555 | ProdBM::to_setting(set); |
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| 556 | UI::save(weights.frg, set, "frg"); |
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| 557 | } |
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[1020] | 558 | }; |
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| 559 | |
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[254] | 560 | } |
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[107] | 561 | #endif //MX_H |
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