1 | /*! |
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2 | \file |
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3 | \brief Mergers for combination 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 MERGER_H |
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14 | #define MERGER_H |
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15 | |
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16 | |
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17 | #include "../estim/mixtures.h" |
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18 | |
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19 | namespace bdm { |
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20 | using std::string; |
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21 | |
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22 | //!Merging methods |
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23 | enum MERGER_METHOD {ARITHMETIC = 1, GEOMETRIC = 2, LOGNORMAL = 3}; |
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24 | |
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25 | /*! |
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26 | @brief Base class for general combination of pdfs on discrete support |
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27 | |
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28 | Mixtures of Gaussian densities are used internally. Switching to other densities should be trivial. |
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29 | |
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30 | The merged pdfs are expected to be of the form: |
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31 | \f[ f(x_i|y_i), i=1..n \f] |
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32 | where the resulting merger is a density on \f$ \cup [x_i,y_i] \f$ . |
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33 | Note that all variables will be joined. |
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34 | |
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35 | As a result of this feature, each source must be extended to common support |
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36 | \f[ f(z_i|y_i,x_i) f(x_i|y_i) f(y_i) i=1..n \f] |
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37 | where \f$ z_i \f$ accumulate variables that were not in the original source. |
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38 | These extensions are calculated on-the-fly. |
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39 | |
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40 | However, these operations can not be performed in general. Hence, this class merges only sources on common support, \f$ y_i={}, z_i={}, \forall i \f$. |
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41 | For merging of more general cases, use offsprings merger_mix and merger_grid. |
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42 | */ |
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43 | |
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44 | class merger_base : public epdf { |
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45 | protected: |
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46 | //! Elements of composition |
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47 | Array<shared_ptr<mpdf> > mpdfs; |
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48 | |
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49 | //! Data link for each mpdf in mpdfs |
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50 | Array<datalink_m2e*> dls; |
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51 | |
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52 | //! Array of rvs that are not modelled by mpdfs at all, \f$ z_i \f$ |
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53 | Array<RV> rvzs; |
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54 | |
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55 | //! Data Links for extension \f$ f(z_i|x_i,y_i) \f$ |
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56 | Array<datalink_m2e*> zdls; |
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57 | |
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58 | //! number of support points |
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59 | int Npoints; |
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60 | |
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61 | //! number of sources |
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62 | int Nsources; |
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63 | |
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64 | //! switch of the methoh used for merging |
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65 | MERGER_METHOD METHOD; |
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66 | //! Default for METHOD |
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67 | static const MERGER_METHOD DFLT_METHOD; |
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68 | |
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69 | //!Prior on the log-normal merging model |
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70 | double beta; |
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71 | //! default for beta |
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72 | static const double DFLT_beta; |
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73 | |
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74 | //! Projection to empirical density (could also be piece-wise linear) |
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75 | eEmp eSmp; |
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76 | |
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77 | //! debug or not debug |
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78 | bool DBG; |
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79 | |
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80 | //! debugging file |
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81 | it_file* dbg_file; |
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82 | public: |
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83 | //! \name Constructors |
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84 | //! @{ |
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85 | |
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86 | //! Default constructor |
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87 | merger_base () : Npoints(0), Nsources(0), DBG(false), dbg_file(0) { |
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88 | } |
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89 | |
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90 | //!Constructor from sources |
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91 | merger_base ( const Array<shared_ptr<mpdf> > &S ); |
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92 | |
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93 | //! Function setting the main internal structures |
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94 | void set_sources ( const Array<shared_ptr<mpdf> > &Sources ) { |
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95 | mpdfs = Sources; |
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96 | Nsources = mpdfs.length(); |
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97 | //set sizes |
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98 | dls.set_size ( Sources.length() ); |
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99 | rvzs.set_size ( Sources.length() ); |
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100 | zdls.set_size ( Sources.length() ); |
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101 | |
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102 | rv = get_composite_rv ( mpdfs, /* checkoverlap = */ false ); |
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103 | |
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104 | RV rvc; |
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105 | // Extend rv by rvc! |
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106 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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107 | RV rvx = mpdfs ( i )->_rvc().subt ( rv ); |
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108 | rvc.add ( rvx ); // add rv to common rvc |
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109 | } |
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110 | |
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111 | // join rv and rvc - see descriprion |
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112 | rv.add ( rvc ); |
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113 | // get dimension |
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114 | dim = rv._dsize(); |
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115 | |
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116 | // create links between sources and common rv |
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117 | RV xytmp; |
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118 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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119 | //Establich connection between mpdfs and merger |
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120 | dls ( i ) = new datalink_m2e; |
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121 | dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), rv ); |
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122 | |
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123 | // find out what is missing in each mpdf |
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124 | xytmp = mpdfs ( i )->_rv(); |
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125 | xytmp.add ( mpdfs ( i )->_rvc() ); |
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126 | // z_i = common_rv-xy |
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127 | rvzs ( i ) = rv.subt ( xytmp ); |
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128 | //establish connection between extension (z_i|x,y)s and common rv |
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129 | zdls ( i ) = new datalink_m2e; |
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130 | zdls ( i )->set_connection ( rvzs ( i ), xytmp, rv ) ; |
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131 | }; |
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132 | } |
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133 | //! Rectangular support each vector of XYZ specifies (begining-end) interval for each dimension. Same number of points, \c dimsize, in each dimension. |
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134 | void set_support ( const Array<vec> &XYZ, const int dimsize ) { |
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135 | set_support ( XYZ, dimsize*ones_i ( XYZ.length() ) ); |
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136 | } |
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137 | //! Rectangular support each vector of XYZ specifies (begining-end) interval for each dimension. \c gridsize specifies number of points is each dimension. |
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138 | void set_support ( const Array<vec> &XYZ, const ivec &gridsize ) { |
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139 | int dim = XYZ.length(); //check with internal dim!! |
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140 | Npoints = prod ( gridsize ); |
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141 | eSmp.set_parameters ( Npoints, false ); |
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142 | Array<vec> &samples = eSmp._samples(); |
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143 | eSmp._w() = ones ( Npoints ) / Npoints; //unifrom size of bins |
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144 | //set samples |
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145 | ivec ind = zeros_i ( dim ); //indeces of dimensions in for cycle; |
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146 | vec smpi ( dim ); // ith sample |
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147 | vec steps = zeros ( dim ); // ith sample |
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148 | // first corner |
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149 | for ( int j = 0; j < dim; j++ ) { |
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150 | smpi ( j ) = XYZ ( j ) ( 0 ); /* beginning of the interval*/ |
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151 | it_assert ( gridsize ( j ) != 0.0, "Zeros in gridsize!" ); |
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152 | steps ( j ) = ( XYZ ( j ) ( 1 ) - smpi ( j ) ) / gridsize ( j ); |
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153 | } |
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154 | // fill samples |
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155 | for ( int i = 0; i < Npoints; i++ ) { |
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156 | // copy |
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157 | samples ( i ) = smpi; |
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158 | // go through all dimensions |
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159 | for ( int j = 0; j < dim; j++ ) { |
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160 | if ( ind ( j ) == gridsize ( j ) - 1 ) { //j-th index is full |
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161 | ind ( j ) = 0; //shift back |
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162 | smpi ( j ) = XYZ ( j ) ( 0 ); |
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163 | |
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164 | if ( i < Npoints - 1 ) { |
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165 | ind ( j + 1 ) ++; //increase the next dimension; |
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166 | smpi ( j + 1 ) += steps ( j + 1 ); |
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167 | break; |
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168 | } |
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169 | |
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170 | } else { |
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171 | ind ( j ) ++; |
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172 | smpi ( j ) += steps ( j ); |
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173 | break; |
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174 | } |
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175 | } |
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176 | } |
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177 | } |
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178 | //! set debug file |
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179 | void set_debug_file ( const string fname ) { |
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180 | if ( DBG ) delete dbg_file; |
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181 | dbg_file = new it_file ( fname ); |
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182 | if ( dbg_file ) DBG = true; |
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183 | } |
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184 | //! Set internal parameters used in approximation |
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185 | void set_method ( MERGER_METHOD MTH = DFLT_METHOD, double beta0 = DFLT_beta ) { |
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186 | METHOD = MTH; |
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187 | beta = beta0; |
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188 | } |
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189 | //! Set support points from a pdf by drawing N samples |
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190 | void set_support ( const epdf &overall, int N ) { |
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191 | eSmp.set_statistics ( overall, N ); |
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192 | Npoints = N; |
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193 | } |
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194 | |
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195 | //! Destructor |
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196 | virtual ~merger_base() { |
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197 | for ( int i = 0; i < Nsources; i++ ) { |
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198 | delete dls ( i ); |
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199 | delete zdls ( i ); |
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200 | } |
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201 | if ( DBG ) delete dbg_file; |
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202 | }; |
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203 | //!@} |
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204 | |
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205 | //! \name Mathematical operations |
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206 | //!@{ |
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207 | |
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208 | //!Merge given sources in given points |
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209 | virtual void merge () { |
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210 | validate(); |
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211 | |
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212 | //check if sources overlap: |
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213 | bool OK = true; |
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214 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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215 | OK &= ( rvzs ( i )._dsize() == 0 ); // z_i is empty |
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216 | OK &= ( mpdfs ( i )->_rvc()._dsize() == 0 ); // y_i is empty |
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217 | } |
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218 | |
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219 | if ( OK ) { |
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220 | mat lW = zeros ( mpdfs.length(), eSmp._w().length() ); |
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221 | |
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222 | vec emptyvec ( 0 ); |
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223 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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224 | for ( int j = 0; j < eSmp._w().length(); j++ ) { |
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225 | lW ( i, j ) = mpdfs ( i )->evallogcond ( eSmp._samples() ( j ), emptyvec ); |
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226 | } |
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227 | } |
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228 | |
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229 | vec w_nn = merge_points ( lW ); |
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230 | vec wtmp = exp ( w_nn - max ( w_nn ) ); |
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231 | //renormalize |
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232 | eSmp._w() = wtmp / sum ( wtmp ); |
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233 | } else { |
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234 | it_error ( "Sources are not compatible - use merger_mix" ); |
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235 | } |
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236 | }; |
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237 | |
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238 | |
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239 | //! Merge log-likelihood values in points using method specified by parameter METHOD |
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240 | vec merge_points ( mat &lW ); |
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241 | |
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242 | |
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243 | //! sample from merged density |
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244 | //! weight w is a |
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245 | vec mean() const { |
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246 | const Vec<double> &w = eSmp._w(); |
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247 | const Array<vec> &S = eSmp._samples(); |
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248 | vec tmp = zeros ( dim ); |
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249 | for ( int i = 0; i < Npoints; i++ ) { |
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250 | tmp += w ( i ) * S ( i ); |
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251 | } |
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252 | return tmp; |
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253 | } |
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254 | mat covariance() const { |
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255 | const vec &w = eSmp._w(); |
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256 | const Array<vec> &S = eSmp._samples(); |
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257 | |
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258 | vec mea = mean(); |
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259 | |
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260 | // cout << sum (w) << "," << w*w << endl; |
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261 | |
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262 | mat Tmp = zeros ( dim, dim ); |
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263 | for ( int i = 0; i < Npoints; i++ ) { |
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264 | Tmp += w ( i ) * outer_product ( S ( i ), S ( i ) ); |
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265 | } |
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266 | return Tmp - outer_product ( mea, mea ); |
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267 | } |
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268 | vec variance() const { |
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269 | const vec &w = eSmp._w(); |
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270 | const Array<vec> &S = eSmp._samples(); |
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271 | |
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272 | vec tmp = zeros ( dim ); |
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273 | for ( int i = 0; i < Nsources; i++ ) { |
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274 | tmp += w ( i ) * pow ( S ( i ), 2 ); |
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275 | } |
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276 | return tmp - pow ( mean(), 2 ); |
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277 | } |
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278 | //!@} |
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279 | |
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280 | //! \name Access to attributes |
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281 | //! @{ |
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282 | |
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283 | //! Access function |
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284 | eEmp& _Smp() { |
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285 | return eSmp; |
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286 | } |
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287 | |
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288 | //! load from setting |
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289 | void from_setting ( const Setting& set ) { |
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290 | // get support |
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291 | // find which method to use |
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292 | string meth_str; |
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293 | UI::get<string> ( meth_str, set, "method", UI::compulsory ); |
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294 | if ( !strcmp ( meth_str.c_str(), "arithmetic" ) ) |
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295 | set_method ( ARITHMETIC ); |
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296 | else { |
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297 | if ( !strcmp ( meth_str.c_str(), "geometric" ) ) |
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298 | set_method ( GEOMETRIC ); |
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299 | else if ( !strcmp ( meth_str.c_str(), "lognormal" ) ) { |
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300 | set_method ( LOGNORMAL ); |
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301 | set.lookupValue ( "beta", beta ); |
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302 | } |
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303 | } |
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304 | string dbg_file; |
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305 | if ( UI::get ( dbg_file, set, "dbg_file" ) ) |
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306 | set_debug_file ( dbg_file ); |
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307 | //validate() - not used |
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308 | } |
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309 | |
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310 | void validate() { |
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311 | it_assert ( eSmp._w().length() > 0, "Empty support, use set_support()." ); |
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312 | it_assert ( dim == eSmp._samples() ( 0 ).length(), "Support points and rv are not compatible!" ); |
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313 | it_assert ( isnamed(), "mergers must be named" ); |
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314 | } |
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315 | //!@} |
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316 | }; |
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317 | UIREGISTER ( merger_base ); |
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318 | SHAREDPTR ( merger_base ); |
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319 | |
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320 | //! Merger using importance sampling with mixture proposal density |
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321 | class merger_mix : public merger_base { |
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322 | protected: |
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323 | //!Internal mixture of EF models |
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324 | MixEF Mix; |
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325 | //!Number of components in a mixture |
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326 | int Ncoms; |
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327 | //! coefficient of resampling [0,1] |
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328 | double effss_coef; |
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329 | //! stop after niter iterations |
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330 | int stop_niter; |
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331 | |
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332 | //! default value for Ncoms |
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333 | static const int DFLT_Ncoms; |
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334 | //! default value for efss_coef; |
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335 | static const double DFLT_effss_coef; |
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336 | |
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337 | public: |
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338 | //!\name Constructors |
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339 | //!@{ |
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340 | merger_mix ():Ncoms(0), effss_coef(0), stop_niter(0) { } |
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341 | |
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342 | merger_mix ( const Array<shared_ptr<mpdf> > &S ): |
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343 | Ncoms(0), effss_coef(0), stop_niter(0) { |
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344 | set_sources ( S ); |
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345 | } |
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346 | |
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347 | //! Set sources and prepare all internal structures |
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348 | void set_sources ( const Array<shared_ptr<mpdf> > &S ) { |
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349 | merger_base::set_sources ( S ); |
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350 | Nsources = S.length(); |
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351 | } |
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352 | |
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353 | //! Set internal parameters used in approximation |
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354 | void set_parameters ( int Ncoms0 = DFLT_Ncoms, double effss_coef0 = DFLT_effss_coef ) { |
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355 | Ncoms = Ncoms0; |
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356 | effss_coef = effss_coef0; |
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357 | } |
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358 | //!@} |
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359 | |
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360 | //! \name Mathematical operations |
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361 | //!@{ |
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362 | |
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363 | //!Merge values using mixture approximation |
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364 | void merge (); |
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365 | |
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366 | //! sample from the approximating mixture |
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367 | vec sample () const { |
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368 | return Mix.posterior().sample(); |
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369 | } |
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370 | //! loglikelihood computed on mixture models |
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371 | double evallog ( const vec &dt ) const { |
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372 | vec dtf = ones ( dt.length() + 1 ); |
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373 | dtf.set_subvector ( 0, dt ); |
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374 | return Mix.logpred ( dtf ); |
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375 | } |
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376 | //!@} |
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377 | |
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378 | //!\name Access functions |
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379 | //!@{ |
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380 | //! Access function |
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381 | MixEF& _Mix() { |
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382 | return Mix; |
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383 | } |
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384 | //! Access function |
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385 | emix* proposal() { |
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386 | emix* tmp = Mix.epredictor(); |
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387 | tmp->set_rv ( rv ); |
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388 | return tmp; |
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389 | } |
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390 | //! from_settings |
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391 | void from_setting ( const Setting& set ) { |
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392 | merger_base::from_setting ( set ); |
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393 | set.lookupValue ( "ncoms", Ncoms ); |
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394 | set.lookupValue ( "effss_coef", effss_coef ); |
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395 | set.lookupValue ( "stop_niter", stop_niter ); |
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396 | } |
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397 | |
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398 | //! @} |
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399 | |
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400 | }; |
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401 | UIREGISTER ( merger_mix ); |
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402 | SHAREDPTR ( merger_mix ); |
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403 | |
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404 | } |
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405 | |
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406 | #endif // MER_H |
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