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 EMIX_H |
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14 | #define EMIX_H |
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15 | |
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16 | #define LOG2 0.69314718055995 |
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17 | |
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18 | #include "../shared_ptr.h" |
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19 | #include "exp_family.h" |
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20 | |
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21 | namespace bdm { |
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22 | |
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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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35 | At present the only supported operation is evallogcond(). |
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36 | */ |
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37 | class mratio: public pdf { |
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38 | protected: |
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39 | //! Nominator in the form of pdf |
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40 | const epdf* nom; |
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41 | |
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42 | //!Denominator in the form of epdf |
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43 | shared_ptr<epdf> den; |
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44 | |
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45 | //!flag for destructor |
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46 | bool destroynom; |
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47 | //!datalink between conditional and nom |
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48 | datalink_m2e dl; |
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49 | public: |
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50 | //!Default constructor. By default, the given epdf is not copied! |
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51 | //! It is assumed that this function will be used only temporarily. |
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52 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : pdf ( ), dl ( ) { |
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53 | // adjust rv and rvc |
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54 | |
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55 | set_rv ( rv ); |
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56 | dim = rv._dsize(); |
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57 | |
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58 | rvc = nom0->_rv().subt ( rv ); |
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59 | dimc = rvc._dsize(); |
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60 | |
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61 | //prepare data structures |
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62 | if ( copy ) { |
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63 | bdm_error ( "todo" ); |
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64 | // destroynom = true; |
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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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69 | bdm_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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70 | |
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71 | // build denominator |
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72 | den = nom->marginal ( rvc ); |
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73 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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74 | }; |
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75 | |
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76 | double evallogcond ( const vec &val, const vec &cond ) { |
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77 | double tmp; |
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78 | vec nom_val ( dimension() + dimc ); |
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79 | dl.pushup_cond ( nom_val, val, cond ); |
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80 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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81 | return tmp; |
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82 | } |
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83 | |
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84 | //! 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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85 | virtual vec samplecond ( const vec &cond ) NOT_IMPLEMENTED(0); |
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86 | |
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87 | //! Object takes ownership of nom and will destroy it |
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88 | void ownnom() { |
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89 | destroynom = true; |
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90 | } |
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91 | //! Default destructor |
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92 | ~mratio() { |
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93 | if ( destroynom ) { |
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94 | delete nom; |
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95 | } |
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96 | } |
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97 | |
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98 | |
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99 | private: |
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100 | // not implemented |
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101 | mratio ( const mratio & ); |
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102 | mratio &operator= ( const mratio & ); |
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103 | }; |
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104 | |
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105 | class emix; //forward |
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106 | |
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107 | /*! Base class (Interface) for mixtures |
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108 | */ |
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109 | class emix_base : public epdf { |
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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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156 | }; |
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157 | |
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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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168 | class emix : public emix_base { |
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169 | protected: |
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170 | //! weights of the components |
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171 | vec weights; |
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172 | |
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173 | //! Component (epdfs) |
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174 | Array<shared_ptr<epdf> > Coms; |
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175 | |
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176 | public: |
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177 | //! Default constructor |
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178 | emix ( ) : emix_base ( weights) { } |
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179 | |
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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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184 | |
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185 | |
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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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190 | //! Load from structure with elements: |
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191 | //! \code |
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192 | //! { class='emix'; |
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193 | //! pdfs = (..., ...); // list of pdfs in the mixture |
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194 | //! weights = ( 0.5, 0.5 ); // weights of pdfs in the mixture |
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195 | //! } |
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196 | //! \endcode |
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197 | //!@} |
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198 | void from_setting ( const Setting &set ); |
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199 | void to_setting (Setting &set) const; |
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200 | |
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201 | void set_rv ( const RV &rv ) { |
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202 | epdf::set_rv ( rv ); |
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203 | for ( int i = 0; i < no_coms(); i++ ) { |
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204 | Coms( i )->set_rv ( rv ); |
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205 | } |
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206 | } |
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207 | |
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208 | Array<shared_ptr<epdf> >& _Coms ( ) { |
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209 | return Coms; |
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210 | } |
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211 | }; |
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212 | SHAREDPTR ( emix ); |
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213 | UIREGISTER ( emix ); |
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214 | |
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215 | |
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216 | /*! \brief Chain rule decomposition of epdf |
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217 | |
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218 | Probability density in the form of Chain-rule decomposition: |
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219 | \[ |
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220 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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221 | \] |
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222 | Note that |
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223 | */ |
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224 | class mprod: public pdf { |
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225 | private: |
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226 | Array<shared_ptr<pdf> > pdfs; |
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227 | |
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228 | //! Data link for each pdfs |
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229 | Array<shared_ptr<datalink_m2m> > dls; |
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230 | |
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231 | public: |
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232 | //! \brief Default constructor |
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233 | mprod() { } |
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234 | |
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235 | /*!\brief Constructor from list of mFacs |
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236 | */ |
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237 | mprod ( const Array<shared_ptr<pdf> > &mFacs ) { |
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238 | set_elements ( mFacs ); |
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239 | } |
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240 | //! Set internal \c pdfs from given values |
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241 | void set_elements ( const Array<shared_ptr<pdf> > &mFacs ); |
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242 | |
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243 | double evallogcond ( const vec &val, const vec &cond ); |
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244 | |
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245 | vec evallogcond_mat ( const mat &Dt, const vec &cond ); |
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246 | |
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247 | vec evallogcond_mat ( const Array<vec> &Dt, const vec &cond ); |
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248 | |
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249 | //TODO smarter... |
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250 | vec samplecond ( const vec &cond ) { |
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251 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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252 | vec smp = std::numeric_limits<double>::infinity() * ones ( dimension() ); |
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253 | vec smpi; |
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254 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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255 | for ( int i = ( pdfs.length() - 1 ); i >= 0; i-- ) { |
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256 | // generate contribution of this pdf |
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257 | smpi = pdfs ( i )->samplecond ( dls ( i )->get_cond ( smp , cond ) ); |
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258 | // copy contribution of this pdf into smp |
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259 | dls ( i )->pushup ( smp, smpi ); |
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260 | } |
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261 | return smp; |
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262 | } |
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263 | |
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264 | //! Load from structure with elements: |
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265 | //! \code |
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266 | //! { class='mprod'; |
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267 | //! pdfs = (..., ...); // list of pdfs in the order of chain rule |
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268 | //! } |
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269 | //! \endcode |
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270 | //!@} |
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271 | void from_setting ( const Setting &set ) ; |
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272 | void to_setting (Setting &set) const; |
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273 | |
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274 | |
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275 | }; |
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276 | UIREGISTER ( mprod ); |
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277 | SHAREDPTR ( mprod ); |
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278 | |
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279 | |
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280 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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281 | class eprod_base: public epdf { |
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282 | protected: |
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283 | //! Array of indices |
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284 | Array<datalink*> dls; |
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285 | //! interface for a factor |
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286 | public: |
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287 | virtual const epdf* factor(int i) const NOT_IMPLEMENTED(NULL); |
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288 | //!number of factors |
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289 | virtual const int no_factors() const NOT_IMPLEMENTED(0); |
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290 | //! Default constructor |
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291 | eprod_base () : dls (0) {}; |
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292 | //! Set internal |
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293 | vec mean() const; |
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294 | |
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295 | vec variance() const; |
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296 | |
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297 | vec sample() const; |
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298 | |
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299 | double evallog ( const vec &val ) const; |
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300 | |
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301 | //!Destructor |
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302 | ~eprod_base() { |
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303 | for ( int i = 0; i < dls.length(); i++ ) { |
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304 | delete dls ( i ); |
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305 | } |
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306 | } |
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307 | void validate() { |
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308 | epdf::validate(); |
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309 | dls.set_length ( no_factors() ); |
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310 | |
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311 | bool independent = true; |
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312 | dim = 0; |
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313 | for ( int i = 0; i < no_factors(); i++ ) { |
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314 | independent = rv.add ( factor ( i )->_rv() ); |
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315 | dim += factor ( i )->dimension(); |
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316 | bdm_assert_debug ( independent, "eprod:: given components are not independent." ); |
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317 | }; |
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318 | |
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319 | // |
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320 | int cumdim = 0; |
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321 | int dimi = 0; |
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322 | int i; |
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323 | for ( i = 0; i < no_factors(); i++ ) { |
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324 | dls ( i ) = new datalink; |
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325 | if ( isnamed() ) { // rvs are complete |
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326 | dls ( i )->set_connection ( factor ( i )->_rv() , rv ); |
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327 | } else { //rvs are not reliable |
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328 | dimi = factor ( i )->dimension(); |
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329 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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330 | cumdim += dimi; |
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331 | } |
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332 | } |
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333 | |
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334 | } |
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335 | }; |
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336 | |
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337 | class eprod: public eprod_base { |
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338 | protected: |
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339 | Array<shared_ptr<epdf> > factors; |
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340 | public: |
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341 | const epdf* factor(int i) const { |
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342 | return factors(i).get(); |
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343 | } |
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344 | const int no_factors() const { |
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345 | return factors.length(); |
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346 | } |
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347 | void set_parameters ( const Array<shared_ptr<epdf> > &epdfs0) { |
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348 | factors = epdfs0; |
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349 | } |
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350 | void from_setting(const Setting &set) { |
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351 | UI::get(factors,set,"pdfs",UI::compulsory); |
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352 | } |
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353 | }; |
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354 | UIREGISTER(eprod); |
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355 | |
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356 | //! similar to eprod but used only internally -- factors are external pointers |
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357 | class eprod_internal: public eprod_base { |
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358 | protected: |
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359 | Array<epdf* > factors; |
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360 | const epdf* factor(int i) const { |
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361 | return factors(i); |
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362 | } |
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363 | const int no_factors() const { |
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364 | return factors.length(); |
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365 | } |
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366 | public: |
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367 | void set_parameters ( const Array<epdf *> &epdfs0) { |
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368 | factors = epdfs0; |
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369 | } |
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370 | }; |
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371 | |
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372 | /*! \brief Mixture of pdfs with constant weights, all pdfs are of equal RV and RVC |
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373 | |
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374 | */ |
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375 | class mmix : public pdf { |
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376 | protected: |
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377 | //! Component (pdfs) |
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378 | Array<shared_ptr<pdf> > Coms; |
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379 | //!weights of the components |
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380 | vec w; |
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381 | public: |
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382 | //!Default constructor |
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383 | mmix() : Coms ( 0 ) { }; |
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384 | |
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385 | double evallogcond ( const vec &dt, const vec &cond ) { |
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386 | double ll = 0.0; |
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387 | for ( int i = 0; i < Coms.length(); i++ ) { |
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388 | ll += Coms ( i )->evallogcond ( dt, cond ); |
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389 | } |
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390 | return ll; |
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391 | } |
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392 | |
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393 | vec samplecond ( const vec &cond ); |
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394 | |
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395 | //! Load from structure with elements: |
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396 | //! \code |
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397 | //! { class='mmix'; |
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398 | //! pdfs = (..., ...); // list of pdfs in the mixture |
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399 | //! weights = ( 0.5, 0.5 ); // weights of pdfs in the mixture |
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400 | //! } |
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401 | //! \endcode |
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402 | //!@} |
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403 | void from_setting ( const Setting &set ); |
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404 | void to_setting (Setting &set) const; |
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405 | virtual void validate(); |
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406 | }; |
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407 | SHAREDPTR ( mmix ); |
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408 | UIREGISTER ( mmix ); |
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409 | |
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410 | |
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411 | //! Base class for all BM running as parallel update of internal BMs |
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412 | |
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413 | class ProdBMBase : public BM { |
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414 | protected : |
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415 | Array<vec_from_vec> bm_yt; |
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416 | Array<vec_from_2vec> bm_cond; |
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417 | class eprod_bm : public eprod_base { |
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418 | ProdBMBase & pb; |
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419 | public : |
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420 | eprod_bm(ProdBMBase &pb0): pb(pb0) {} |
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421 | const epdf* factor(int i ) const { |
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422 | return &(pb.bm(i)->posterior()); |
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423 | } |
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424 | const int no_factors() const { |
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425 | return pb.no_bms(); |
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426 | } |
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427 | } est; |
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428 | public: |
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429 | ProdBMBase():est(*this) {} |
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430 | virtual BM* bm(int i) NOT_IMPLEMENTED(NULL); |
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431 | virtual int no_bms() const { |
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432 | return 0; |
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433 | } |
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434 | const epdf& posterior() const { |
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435 | return est; |
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436 | } |
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437 | void set_prior(const epdf *pri) { |
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438 | const eprod_base* ep=dynamic_cast<const eprod_base*>(pri); |
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439 | if (ep) { |
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440 | bdm_assert(ep->no_factors()!=no_bms() , "Given prior has "+ num2str(ep->no_factors()) + " while this ProdBM has "+ |
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441 | num2str(no_bms()) + "BMs"); |
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442 | for (int i=0; i<no_bms(); i++) { |
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443 | bm(i)->set_prior(ep->factor(i)); |
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444 | } |
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445 | } |
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446 | } |
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447 | |
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448 | void validate() { |
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449 | est.validate(); |
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450 | BM::validate(); |
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451 | // set links |
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452 | bm_yt.set_length(no_bms()); |
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453 | bm_cond.set_length(no_bms()); |
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454 | |
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455 | // |
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456 | |
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457 | for (int i=0; i<no_bms(); i++) { |
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458 | yrv.add(bm(i)->_yrv()); |
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459 | rvc.add(bm(i)->_rvc()); |
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460 | } |
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461 | rvc=rvc.subt(yrv); |
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462 | |
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463 | dimy = yrv._dsize(); |
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464 | dimc = rvc._dsize(); |
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465 | |
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466 | for (int i=0; i<no_bms(); i++) { |
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467 | bm_yt(i).connect(bm(i)->_yrv(), yrv); |
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468 | bm_cond(i).connect(bm(i)->_rvc(), yrv, rvc); |
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469 | } |
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470 | } |
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471 | void bayes(const vec &dt, const vec &cond) { |
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472 | ll=0; |
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473 | for(int i=0; i<no_bms(); i++) { |
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474 | bm_yt(i).update(dt); |
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475 | bm_cond(i).update(dt,cond); |
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476 | bm(i)->bayes(bm_yt(i), bm_cond(i)); |
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477 | } |
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478 | } |
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479 | |
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480 | }; |
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481 | |
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482 | class ProdBM: public ProdBMBase { |
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483 | protected: |
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484 | Array<shared_ptr<BM> > BMs; |
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485 | public: |
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486 | virtual BM* bm(int i) { |
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487 | return BMs(i).get(); |
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488 | } |
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489 | virtual int no_bms() const { |
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490 | return BMs.length(); |
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491 | } |
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492 | void from_setting(const Setting &set) { |
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493 | BM::from_setting(set); |
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494 | UI::get(BMs,set,"BMs"); |
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495 | } |
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496 | void to_setting(Setting &set) const { |
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497 | BM::to_setting(set); |
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498 | UI::save(BMs,set,"BMs"); |
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499 | } |
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500 | |
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501 | }; |
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502 | UIREGISTER(ProdBM); |
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503 | |
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504 | //! \brief class for on-line model selection |
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505 | class ModelComparator: public ProdBM { |
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506 | protected: |
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507 | multiBM weights; |
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508 | public: |
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509 | void bayes(const vec &yt, const vec &cond) { |
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510 | vec w_nn(no_bms()); |
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511 | for (int i=0; i<no_bms(); i++) { |
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512 | bm(i)->bayes(yt,cond); |
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513 | w_nn(i) += bm(i)->_ll(); |
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514 | } |
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515 | vec w=exp(w_nn-max(w_nn)); |
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516 | weights.bayes(w/sum(w)); |
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517 | } |
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518 | void validate() { |
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519 | ProdBM::validate(); |
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520 | weights.validate(); |
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521 | } |
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522 | void from_setting(const Setting& set) { |
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523 | ProdBM::from_setting(set); |
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524 | UI::get(weights.frg, set, "frg",UI::optional); |
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525 | } |
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526 | void to_setting(Setting& set) const { |
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527 | ProdBM::to_setting(set); |
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528 | UI::save(weights.frg, set, "frg"); |
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529 | } |
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530 | }; |
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531 | |
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532 | } |
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533 | #endif //MX_H |
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