[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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| 13 | #ifndef MX_H |
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| 14 | #define MX_H |
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| 15 | |
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| 16 | #include "libBM.h" |
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| 17 | #include "libEF.h" |
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| 18 | //#include <std> |
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| 19 | |
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[254] | 20 | namespace bdm{ |
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[107] | 21 | |
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[182] | 22 | //this comes first because it is used inside emix! |
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| 23 | |
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| 24 | /*! \brief Class representing ratio of two densities |
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| 25 | which arise e.g. by applying the Bayes rule. |
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| 26 | It represents density in the form: |
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| 27 | \f[ |
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| 28 | f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)} |
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| 29 | \f] |
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| 30 | where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$. |
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| 31 | |
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| 32 | In particular this type of arise by conditioning of a mixture model. |
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| 33 | |
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[211] | 34 | At present the only supported operation is evallogcond(). |
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[182] | 35 | */ |
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| 36 | class mratio: public mpdf { |
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[192] | 37 | protected: |
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[182] | 38 | //! Nominator in the form of mpdf |
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[192] | 39 | const epdf* nom; |
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[182] | 40 | //!Denominator in the form of epdf |
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[192] | 41 | epdf* den; |
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| 42 | //!flag for destructor |
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| 43 | bool destroynom; |
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[193] | 44 | //!datalink between conditional and nom |
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| 45 | datalink_m2e dl; |
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[192] | 46 | public: |
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| 47 | //!Default constructor. By default, the given epdf is not copied! |
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[182] | 48 | //! It is assumed that this function will be used only temporarily. |
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[270] | 49 | mratio ( const epdf* nom0, const RV &rv, bool copy=false ) :mpdf ( ), dl ( rv,rvc,nom0->_rv() ) { |
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| 50 | ep->set_rv(_rv()); |
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| 51 | set_rvc(nom0->_rv().subt ( rv ) ); |
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[192] | 52 | if ( copy ) { |
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[182] | 53 | // nom = nom0->_copy_(); |
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[204] | 54 | it_error ( "todo" ); |
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[192] | 55 | destroynom=true; |
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[182] | 56 | } |
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[192] | 57 | else { |
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| 58 | nom = nom0; |
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| 59 | destroynom = false; |
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| 60 | } |
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| 61 | it_assert_debug ( rvc.length() >0,"Makes no sense to use this object!" ); |
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| 62 | den = nom->marginal ( rvc ); |
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| 63 | }; |
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[211] | 64 | double evallogcond ( const vec &val, const vec &cond ) { |
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[214] | 65 | double tmp; |
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[270] | 66 | vec nom_val ( ep->dimension() + dimc ); |
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| 67 | dl.pushup_cond ( nom_val,val,cond ); |
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[214] | 68 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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| 69 | it_assert_debug(std::isfinite(tmp),"Infinite value"); |
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| 70 | return tmp; |
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[192] | 71 | } |
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[182] | 72 | //! Object takes ownership of nom and will destroy it |
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[192] | 73 | void ownnom() {destroynom=true;} |
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[182] | 74 | //! Default destructor |
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[192] | 75 | ~mratio() {delete den; if ( destroynom ) {delete nom;}} |
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[182] | 76 | }; |
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| 77 | |
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[107] | 78 | /*! |
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| 79 | * \brief Mixture of epdfs |
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| 80 | |
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| 81 | Density function: |
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| 82 | \f[ |
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| 83 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 84 | \f] |
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| 85 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 86 | |
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| 87 | */ |
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[145] | 88 | class emix : public epdf { |
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[162] | 89 | protected: |
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| 90 | //! weights of the components |
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| 91 | vec w; |
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| 92 | //! Component (epdfs) |
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| 93 | Array<epdf*> Coms; |
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[178] | 94 | //!Flag if owning Coms |
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| 95 | bool destroyComs; |
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[162] | 96 | public: |
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| 97 | //!Default constructor |
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[270] | 98 | emix ( ) : epdf ( ) {}; |
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[182] | 99 | //! Set weights \c w and components \c Coms |
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[224] | 100 | //!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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[270] | 101 | void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy=false ); |
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[107] | 102 | |
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[162] | 103 | vec sample() const; |
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| 104 | vec mean() const { |
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[270] | 105 | int i; vec mu = zeros ( dim); |
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[162] | 106 | for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); } |
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| 107 | return mu; |
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| 108 | } |
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[229] | 109 | vec variance() const { |
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| 110 | //non-central moment |
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[270] | 111 | vec mom2 = zeros(dim); |
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[229] | 112 | for ( int i = 0;i < w.length();i++ ) {mom2 += w ( i ) * pow(Coms ( i )->mean(),2); } |
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| 113 | //central moment |
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| 114 | return mom2-pow(mean(),2); |
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| 115 | } |
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[211] | 116 | double evallog ( const vec &val ) const { |
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[162] | 117 | int i; |
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| 118 | double sum = 0.0; |
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[211] | 119 | for ( i = 0;i < w.length();i++ ) {sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) );} |
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[214] | 120 | if (sum==0.0){sum=std::numeric_limits<double>::epsilon();} |
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| 121 | double tmp=log ( sum ); |
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| 122 | it_assert_debug(std::isfinite(tmp),"Infinite"); |
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| 123 | return tmp; |
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[162] | 124 | }; |
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[211] | 125 | vec evallog_m ( const mat &Val ) const { |
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[193] | 126 | vec x=zeros ( Val.cols() ); |
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[192] | 127 | for ( int i = 0; i < w.length(); i++ ) { |
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[211] | 128 | x+= w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ); |
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[182] | 129 | } |
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[192] | 130 | return log ( x ); |
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[182] | 131 | }; |
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[214] | 132 | //! Auxiliary function that returns pdflog for each component |
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[211] | 133 | mat evallog_M ( const mat &Val ) const { |
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[192] | 134 | mat X ( w.length(), Val.cols() ); |
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| 135 | for ( int i = 0; i < w.length(); i++ ) { |
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[211] | 136 | X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ) ); |
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[189] | 137 | } |
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| 138 | return X; |
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| 139 | }; |
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[107] | 140 | |
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[182] | 141 | emix* marginal ( const RV &rv ) const; |
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| 142 | mratio* condition ( const RV &rv ) const; //why not mratio!! |
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| 143 | |
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[107] | 144 | //Access methods |
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[162] | 145 | //! returns a pointer to the internal mean value. Use with Care! |
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| 146 | vec& _w() {return w;} |
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[181] | 147 | virtual ~emix() {if ( destroyComs ) {for ( int i=0;i<Coms.length();i++ ) {delete Coms ( i );}}} |
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[178] | 148 | //! Auxiliary function for taking ownership of the Coms() |
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[181] | 149 | void ownComs() {destroyComs=true;} |
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[204] | 150 | |
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[193] | 151 | //!access function |
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[204] | 152 | epdf* _Coms ( int i ) {return Coms ( i );} |
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[107] | 153 | }; |
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| 154 | |
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[115] | 155 | /*! \brief Chain rule decomposition of epdf |
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| 156 | |
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[145] | 157 | Probability density in the form of Chain-rule decomposition: |
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| 158 | \[ |
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| 159 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 160 | \] |
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| 161 | Note that |
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[115] | 162 | */ |
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[175] | 163 | class mprod: public compositepdf, public mpdf { |
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[162] | 164 | protected: |
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[181] | 165 | //! pointers to epdfs - shortcut to mpdfs()._epdf() |
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[162] | 166 | Array<epdf*> epdfs; |
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[192] | 167 | //! Data link for each mpdfs |
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| 168 | Array<datalink_m2m*> dls; |
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[270] | 169 | //! dummy ep |
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| 170 | epdf dummy; |
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[162] | 171 | public: |
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[168] | 172 | /*!\brief Constructor from list of mFacs, |
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[165] | 173 | */ |
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[270] | 174 | mprod ( Array<mpdf*> mFacs ) : compositepdf ( mFacs ), mpdf (), epdfs ( n ), dls ( n ) { |
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| 175 | ep=&dummy; |
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| 176 | RV rv=getrv(true); |
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| 177 | set_rv(rv);dummy.set_parameters(rv._dsize()); |
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| 178 | setrvc ( ep->_rv(),rvc ); |
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[192] | 179 | // rv and rvc established = > we can link them with mpdfs |
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[181] | 180 | for ( int i = 0;i < n;i++ ) { |
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[270] | 181 | dls ( i ) = new datalink_m2m ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), _rv(), _rvc() ); |
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[181] | 182 | } |
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| 183 | |
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| 184 | for ( int i=0;i<n;i++ ) { |
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| 185 | epdfs ( i ) =& ( mpdfs ( i )->_epdf() ); |
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| 186 | } |
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[175] | 187 | }; |
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[124] | 188 | |
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[211] | 189 | double evallogcond ( const vec &val, const vec &cond ) { |
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[162] | 190 | int i; |
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[270] | 191 | double res = 0.0; |
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[182] | 192 | for ( i = n - 1;i >= 0;i-- ) { |
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[193] | 193 | /* if ( mpdfs(i)->_rvc().count() >0) { |
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| 194 | mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) ); |
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| 195 | } |
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| 196 | // add logarithms |
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[270] | 197 | res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/ |
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| 198 | res += mpdfs ( i )->evallogcond ( |
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| 199 | dls ( i )->pushdown ( val ), |
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[204] | 200 | dls ( i )->get_cond ( val, cond ) |
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| 201 | ); |
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[145] | 202 | } |
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[193] | 203 | return res; |
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[162] | 204 | } |
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[270] | 205 | //TODO smarter... |
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| 206 | vec samplecond ( const vec &cond ) { |
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[192] | 207 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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[270] | 208 | vec smp= std::numeric_limits<double>::infinity() * ones ( ep->dimension() ); |
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[165] | 209 | vec smpi; |
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[192] | 210 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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[162] | 211 | for ( int i = ( n - 1 );i >= 0;i-- ) { |
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[270] | 212 | if ( mpdfs ( i )->dimensionc() ) { |
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[192] | 213 | mpdfs ( i )->condition ( dls ( i )->get_cond ( smp ,cond ) ); // smp is val here!! |
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[145] | 214 | } |
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[165] | 215 | smpi = epdfs ( i )->sample(); |
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[162] | 216 | // copy contribution of this pdf into smp |
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[270] | 217 | dls ( i )->pushup ( smp, smpi ); |
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[165] | 218 | // add ith likelihood contribution |
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[145] | 219 | } |
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[162] | 220 | return smp; |
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| 221 | } |
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[270] | 222 | mat samplecond ( const vec &cond, int N ) { |
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| 223 | mat Smp ( dimension(),N ); |
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| 224 | for ( int i=0;i<N;i++ ) {Smp.set_col ( i,samplecond ( cond ) );} |
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[162] | 225 | return Smp; |
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| 226 | } |
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| 227 | |
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| 228 | ~mprod() {}; |
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[107] | 229 | }; |
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| 230 | |
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[168] | 231 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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| 232 | class eprod: public epdf { |
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| 233 | protected: |
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| 234 | //! Components (epdfs) |
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[170] | 235 | Array<const epdf*> epdfs; |
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[168] | 236 | //! Array of indeces |
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[270] | 237 | Array<datalink*> dls; |
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[168] | 238 | public: |
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[270] | 239 | eprod ( const Array<const epdf*> epdfs0 ) : epdf ( ),epdfs ( epdfs0 ),dls ( epdfs.length() ) { |
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[168] | 240 | bool independent=true; |
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| 241 | for ( int i=0;i<epdfs.length();i++ ) { |
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| 242 | independent=rv.add ( epdfs ( i )->_rv() ); |
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| 243 | it_assert_debug ( independent==true, "eprod:: given components are not independent ." ); |
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| 244 | } |
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[204] | 245 | for ( int i=0;i<epdfs.length();i++ ) { |
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[270] | 246 | dls ( i ) = new datalink ( epdfs ( i )->_rv() , rv ); |
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[204] | 247 | } |
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[168] | 248 | } |
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| 249 | |
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| 250 | vec mean() const { |
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[270] | 251 | vec tmp ( dim ); |
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[168] | 252 | for ( int i=0;i<epdfs.length();i++ ) { |
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| 253 | vec pom = epdfs ( i )->mean(); |
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[270] | 254 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 255 | } |
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| 256 | return tmp; |
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| 257 | } |
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[229] | 258 | vec variance() const { |
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[270] | 259 | vec tmp ( dim ); //second moment |
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[229] | 260 | for ( int i=0;i<epdfs.length();i++ ) { |
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| 261 | vec pom = epdfs ( i )->mean(); |
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[270] | 262 | dls ( i )->pushup ( tmp, pow(pom,2) ); |
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[229] | 263 | } |
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| 264 | return tmp-pow(mean(),2); |
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| 265 | } |
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[168] | 266 | vec sample() const { |
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[270] | 267 | vec tmp ( dim ); |
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[168] | 268 | for ( int i=0;i<epdfs.length();i++ ) { |
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| 269 | vec pom = epdfs ( i )->sample(); |
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[270] | 270 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 271 | } |
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| 272 | return tmp; |
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| 273 | } |
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[211] | 274 | double evallog ( const vec &val ) const { |
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[168] | 275 | double tmp=0; |
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| 276 | for ( int i=0;i<epdfs.length();i++ ) { |
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[270] | 277 | tmp+=epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) ); |
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[168] | 278 | } |
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[214] | 279 | it_assert_debug(std::isfinite(tmp),"Infinite"); |
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[168] | 280 | return tmp; |
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| 281 | } |
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[170] | 282 | //!access function |
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[181] | 283 | const epdf* operator () ( int i ) const {it_assert_debug ( i<epdfs.length(),"wrong index" );return epdfs ( i );} |
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[204] | 284 | |
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[193] | 285 | //!Destructor |
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[204] | 286 | ~eprod() {for ( int i=0;i<epdfs.length();i++ ) {delete dls ( i );}} |
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[168] | 287 | }; |
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| 288 | |
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| 289 | |
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[145] | 290 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type |
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[124] | 291 | |
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| 292 | */ |
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[145] | 293 | class mmix : public mpdf { |
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[162] | 294 | protected: |
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| 295 | //! Component (epdfs) |
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| 296 | Array<mpdf*> Coms; |
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| 297 | //!Internal epdf |
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| 298 | emix Epdf; |
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| 299 | public: |
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| 300 | //!Default constructor |
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[270] | 301 | mmix ( ) : mpdf ( ), Epdf () {ep = &Epdf;}; |
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[162] | 302 | //! Set weights \c w and components \c R |
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| 303 | void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) { |
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| 304 | Array<epdf*> Eps ( Coms.length() ); |
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[124] | 305 | |
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[162] | 306 | for ( int i = 0;i < Coms.length();i++ ) { |
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| 307 | Eps ( i ) = & ( Coms ( i )->_epdf() ); |
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| 308 | } |
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| 309 | Epdf.set_parameters ( w, Eps ); |
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| 310 | }; |
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[124] | 311 | |
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[162] | 312 | void condition ( const vec &cond ) { |
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| 313 | for ( int i = 0;i < Coms.length();i++ ) {Coms ( i )->condition ( cond );} |
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| 314 | }; |
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[124] | 315 | }; |
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[182] | 316 | |
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[254] | 317 | } |
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[107] | 318 | #endif //MX_H |
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