1 | #include "arx.h" |
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2 | namespace bdm { |
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3 | |
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4 | void ARX::bayes_weighted ( const vec &yt, const vec &cond, const double w ) { |
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5 | bdm_assert_debug ( yt.length() == dimy, "BM::bayes yt is of size "+num2str(yt.length())+" expected dimension is "+num2str(dimy) ); |
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6 | bdm_assert_debug ( cond.length() == rgrlen , "BM::bayes cond is of size "+num2str(cond.length())+" expected dimension is "+num2str(rgrlen) ); |
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7 | |
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8 | BMEF::bayes_weighted(yt,cond,w); //potential discount scheduling |
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9 | |
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10 | double lnc; |
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11 | //cache |
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12 | ldmat &V = est._V(); |
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13 | double &nu = est._nu(); |
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14 | |
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15 | dyad.set_subvector ( 0, yt ); |
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16 | if (cond.length()>0) |
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17 | dyad.set_subvector ( dimy, cond ); |
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18 | // possible "1" is there from the beginning |
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19 | |
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20 | if ( frg < 1.0 ) { |
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21 | est.pow ( frg ); // multiply V and nu |
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22 | |
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23 | |
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24 | //stabilize |
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25 | ldmat V0 = alter_est._V(); //$ copy |
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26 | double &nu0 = alter_est._nu(); |
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27 | |
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28 | V0 *= ( 1 - frg ); |
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29 | V += V0; //stabilization |
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30 | nu += ( 1 - frg ) * nu0; |
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31 | |
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32 | // recompute loglikelihood of new "prior" |
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33 | if ( evalll ) { |
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34 | last_lognc = est.lognc(); |
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35 | } |
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36 | } |
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37 | V.opupdt ( dyad, w ); |
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38 | nu += w; |
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39 | |
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40 | // log(sqrt(2*pi)) = 0.91893853320467 |
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41 | if ( evalll ) { |
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42 | lnc = est.lognc(); |
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43 | ll = lnc - last_lognc - 0.91893853320467; |
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44 | last_lognc = lnc; |
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45 | } |
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46 | } |
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47 | |
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48 | double ARX::logpred ( const vec &yt, const vec &cond ) const { |
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49 | egiw pred ( est ); |
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50 | ldmat &V = pred._V(); |
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51 | double &nu = pred._nu(); |
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52 | |
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53 | double lll; |
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54 | vec dyad_p = dyad; |
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55 | dyad_p.set_subvector ( 0, yt ); |
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56 | dyad_p.set_subvector(dimy,cond); |
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57 | |
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58 | if ( frg < 1.0 ) { |
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59 | pred.pow ( frg ); |
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60 | lll = pred.lognc(); |
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61 | } else//should be save: last_lognc is changed only by bayes; |
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62 | if ( evalll ) { |
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63 | lll = last_lognc; |
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64 | } else { |
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65 | lll = pred.lognc(); |
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66 | } |
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67 | |
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68 | V.opupdt ( dyad_p, 1.0 ); |
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69 | nu += 1.0; |
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70 | // log(sqrt(2*pi)) = 0.91893853320467 |
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71 | return pred.lognc() - lll - 0.91893853320467; |
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72 | } |
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73 | |
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74 | void ARX::flatten ( const BMEF* B , double weight =1.0) { |
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75 | const ARX* A = dynamic_cast<const ARX*> ( B ); |
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76 | // nu should be equal to B.nu |
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77 | est.pow ( A->posterior()._nu() / posterior()._nu() *weight); |
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78 | if ( evalll ) { |
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79 | last_lognc = est.lognc(); |
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80 | } |
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81 | } |
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82 | |
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83 | ARX* ARX::_copy ( ) const { |
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84 | ARX* Tmp = new ARX ( *this ); |
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85 | return Tmp; |
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86 | } |
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87 | |
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88 | void ARX::set_statistics ( const BMEF* B0 ) { |
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89 | const ARX* A0 = dynamic_cast<const ARX*> ( B0 ); |
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90 | |
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91 | bdm_assert_debug ( dimension() == A0->dimension(), "Statistics of different dimensions" ); |
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92 | set_statistics ( A0->dimensiony(), A0->posterior()._V(), A0->posterior()._nu() ); |
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93 | } |
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94 | |
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95 | enorm<ldmat>* ARX::epredictor ( const vec &cond ) const { |
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96 | bdm_assert_debug ( cond.length() == rgrlen , "ARX::epredictor cond is of size "+num2str(cond.length())+" expected dimension is "+num2str(rgrlen) ); |
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97 | |
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98 | mat mu ( dimy, posterior()._V().rows() - dimy ); |
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99 | mat R ( dimy, dimy ); |
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100 | |
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101 | vec ext_rgr; |
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102 | if (have_constant) { |
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103 | ext_rgr = concat(cond,vec_1(1.0)); |
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104 | } else { |
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105 | ext_rgr = cond; |
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106 | } |
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107 | |
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108 | enorm<ldmat>* tmp; |
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109 | tmp = new enorm<ldmat> ( ); |
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110 | //TODO: too hackish |
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111 | if ( yrv._dsize() > 0 ) { |
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112 | } |
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113 | |
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114 | est.mean_mat ( mu, R ); //mu = |
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115 | //correction for student-t -- TODO check if correct!! |
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116 | //R*=nu/(nu-2); |
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117 | if (mu.cols()>0) {// nonempty egiw |
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118 | mat p_mu = mu.T() * ext_rgr; //the result is one column |
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119 | tmp->set_parameters ( p_mu.get_col ( 0 ), ldmat ( R ) ); |
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120 | } else { |
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121 | tmp->set_parameters ( zeros( R.rows() ), ldmat ( R ) ); |
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122 | } |
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123 | if (dimy==yrv._dsize()) |
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124 | tmp->set_rv(yrv); |
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125 | return tmp; |
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126 | } |
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127 | |
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128 | mlstudent* ARX::predictor_student ( ) const { |
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129 | const ldmat &V = posterior()._V(); |
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130 | |
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131 | mat mu ( dimy, V.rows() - dimy ); |
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132 | mat R ( dimy, dimy ); |
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133 | mlstudent* tmp; |
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134 | tmp = new mlstudent ( ); |
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135 | |
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136 | est.mean_mat ( mu, R ); // |
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137 | mu = mu.T(); |
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138 | |
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139 | int end = V._L().rows() - 1; |
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140 | ldmat Lam ( V._L() ( dimy, end, dimy, end ), V._D() ( dimy, end ) ); //exp val of R |
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141 | |
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142 | |
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143 | if ( have_constant ) { // no constant term |
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144 | //Assume the constant term is the last one: |
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145 | if ( mu.cols() > 1 ) { |
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146 | tmp->set_parameters ( mu.get_cols ( 0, mu.cols() - 2 ), mu.get_col ( mu.cols() - 1 ), ldmat ( R ), Lam ); |
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147 | } else { |
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148 | tmp->set_parameters ( mat ( dimy, dimc ), mu.get_col ( mu.cols() - 1 ), ldmat ( R ), Lam ); |
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149 | } |
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150 | } else { |
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151 | // no constant term |
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152 | tmp->set_parameters ( mu, zeros ( dimy ), ldmat ( R ), Lam ); |
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153 | } |
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154 | return tmp; |
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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 Return the best structure |
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160 | @param Eg a copy of GiW density that is being examined |
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161 | @param Eg0 a copy of prior GiW density before estimation |
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162 | @param Egll likelihood of the current Eg |
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163 | @param indices current indices |
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164 | \return best likelihood in the structure below the given one |
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165 | */ |
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166 | double egiw_bestbelow ( egiw Eg, egiw Eg0, double Egll, ivec &indices ) { //parameter Eg is a copy! |
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167 | ldmat Vo = Eg._V(); //copy |
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168 | ldmat Vo0 = Eg._V(); //copy |
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169 | ldmat& Vp = Eg._V(); // pointer into Eg |
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170 | ldmat& Vp0 = Eg._V(); // pointer into Eg |
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171 | int end = Vp.rows() - 1; |
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172 | int i; |
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173 | mat Li; |
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174 | mat Li0; |
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175 | double maxll = Egll; |
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176 | double tmpll = Egll; |
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177 | double belll = Egll; |
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178 | |
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179 | ivec tmpindices; |
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180 | ivec maxindices = indices; |
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181 | |
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182 | |
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183 | cout << "bb:(" << indices << ") ll=" << Egll << endl; |
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184 | |
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185 | //try to remove only one rv |
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186 | for ( i = 0; i < end; i++ ) { |
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187 | //copy original |
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188 | Li = Vo._L(); |
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189 | Li0 = Vo0._L(); |
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190 | //remove stuff |
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191 | Li.del_col ( i + 1 ); |
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192 | Li0.del_col ( i + 1 ); |
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193 | Vp.ldform ( Li, Vo._D() ); |
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194 | Vp0.ldform ( Li0, Vo0._D() ); |
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195 | tmpll = Eg.lognc() - Eg0.lognc(); // likelihood is difference of norm. coefs. |
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196 | |
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197 | cout << "i=(" << i << ") ll=" << tmpll << endl; |
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198 | |
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199 | // |
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200 | if ( tmpll > Egll ) { //increase of the likelihood |
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201 | tmpindices = indices; |
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202 | tmpindices.del ( i ); |
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203 | //search for a better match in this substructure |
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204 | belll = egiw_bestbelow ( Eg, Eg0, tmpll, tmpindices ); |
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205 | if ( belll > maxll ) { //better match found |
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206 | maxll = belll; |
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207 | maxindices = tmpindices; |
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208 | } |
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209 | } |
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210 | } |
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211 | indices = maxindices; |
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212 | return maxll; |
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213 | } |
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214 | |
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215 | ivec ARX::structure_est ( const egiw &est0 ) { |
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216 | ivec ind = linspace ( 1, est.dimension() - 1 ); |
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217 | egiw_bestbelow ( est, est0, est.lognc() - est0.lognc(), ind ); |
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218 | return ind; |
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219 | } |
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220 | |
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221 | |
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222 | |
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223 | ivec ARX::structure_est_LT ( const egiw &est0 ) { |
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224 | //some stuff with beliefs etc. |
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225 | ivec belief = vec_1 ( 2 ); // default belief |
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226 | int nbest = 1; // nbest: how many regressors are returned |
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227 | int nrep = 5; // nrep: number of random repetions of structure estimation |
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228 | double lambda = 0.9; |
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229 | int k = 2; |
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230 | |
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231 | Array<str_aux> o2; |
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232 | |
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233 | ivec ind = bdm::straux1(est._V(),est._nu(), est0._V(), est0._nu(), belief, nbest, nrep, lambda, k, o2); |
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234 | |
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235 | return ind; |
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236 | } |
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237 | |
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238 | void ARX::from_setting ( const Setting &set ) { |
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239 | BMEF::from_setting(set); |
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240 | |
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241 | UI::get (rgr, set, "rgr", UI::compulsory ); |
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242 | |
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243 | dimy = yrv._dsize(); |
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244 | bdm_assert(dimy>0,"ARX::yrv should not be empty"); |
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245 | rgrlen = rgr._dsize(); |
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246 | |
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247 | int constant; |
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248 | if ( !UI::get ( constant, set, "constant", UI::optional ) ) { |
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249 | have_constant = true; |
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250 | } else { |
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251 | have_constant = constant > 0; |
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252 | } |
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253 | dimc = rgrlen; |
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254 | rvc = rgr; |
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255 | |
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256 | //init |
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257 | shared_ptr<egiw> pri = UI::build<egiw> ( set, "prior", UI::optional ); |
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258 | if (pri) { |
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259 | set_prior(pri.get()); |
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260 | } else { |
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261 | shared_ptr<egiw> post = UI::build<egiw> ( set, "posterior", UI::optional ); |
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262 | set_prior(post.get()); |
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263 | } |
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264 | |
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265 | |
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266 | shared_ptr<egiw> alt = UI::build<egiw> ( set, "alternative", UI::optional ); |
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267 | if ( alt ) { |
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268 | bdm_assert ( alt->_dimx() == dimy, "alternative is not compatible" ); |
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269 | bdm_assert ( alt->_V().rows() == dimy + rgrlen + int(have_constant==true), "alternative is not compatible" ); |
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270 | alter_est.set_parameters ( alt->_dimx(), alt->_V(), alt->_nu() ); |
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271 | alter_est.validate(); |
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272 | } |
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273 | // frg handled by BMEF |
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274 | |
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275 | } |
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276 | |
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277 | void ARX::set_prior(const epdf *pri) { |
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278 | const egiw * eg=dynamic_cast<const egiw*>(pri); |
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279 | if ( eg ) { |
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280 | bdm_assert ( eg->_dimx() == dimy, "prior is not compatible" ); |
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281 | bdm_assert ( eg->_V().rows() == dimy + rgrlen + int(have_constant==true), "prior is not compatible" ); |
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282 | est.set_parameters ( eg->_dimx(), eg->_V(), eg->_nu() ); |
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283 | est.validate(); |
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284 | } else { |
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285 | est.set_parameters ( dimy, zeros ( dimy + rgrlen +int(have_constant==true)) ); |
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286 | set_prior_default ( est ); |
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287 | } |
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288 | //check alternative |
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289 | if (alter_est.dimension()!=dimension()) { |
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290 | alter_est = est; |
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291 | } |
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292 | } |
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293 | |
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294 | void ARXpartialforg::bayes ( const vec &val, const vec &cond ) { |
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295 | #define LOG2 0.69314718055995 |
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296 | vec frg = cond.right(cond.length() - rgrlen); |
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297 | vec cond_rgr = cond.left(rgrlen); // regression vector |
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298 | |
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299 | int dimV = est._V().cols(); |
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300 | int nparams = dimV - 1; // number of parameters |
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301 | int nalternatives = 1 << nparams; // number of alternatives |
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302 | |
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303 | // Permutation matrix |
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304 | mat perm_matrix = ones(nalternatives, nparams); |
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305 | int i, j, period, idx_from, idx_to, start, end; |
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306 | for(i = 0; i < nparams; i++) { |
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307 | idx_from = 1 << i; |
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308 | period = ( idx_from << 1 ); |
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309 | idx_to = period - 1; |
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310 | j = 0; |
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311 | start = idx_from; |
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312 | end = idx_to; |
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313 | while ( start < nalternatives ) { |
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314 | perm_matrix.set_submatrix(start, end, i, i, 0); |
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315 | j++; |
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316 | start = idx_from + period * j; |
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317 | end = idx_to + period * j; |
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318 | } |
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319 | } |
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320 | |
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321 | // Array of egiws for approximation |
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322 | Array<egiw*> egiw_array(nalternatives + 1); |
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323 | // No. of conditioning rows in LD |
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324 | int nalternatives_cond, position; |
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325 | |
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326 | for(int i = 0; i < nalternatives; i++) { |
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327 | // vector defining alternatives |
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328 | vec vec_alt = perm_matrix.get_row(i); |
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329 | |
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330 | // full alternative or filtered |
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331 | if( sum(vec_alt) == vec_alt.length() ) { |
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332 | egiw_array(i) = &alter_est; |
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333 | continue; |
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334 | } else if( sum(vec_alt) == 0 ) { |
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335 | egiw_array(i) = &est; |
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336 | continue; |
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337 | } |
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338 | |
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339 | nalternatives_cond = (int) sum(vec_alt) + 1; |
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340 | ivec vec_perm(0); // permutation vector |
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341 | |
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342 | for(int j = 0; j < nparams; j++) { |
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343 | position = dimV - j - 2; |
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344 | if ( vec_alt(position) == 0 ) { |
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345 | vec_perm.ins(j, position + 1); |
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346 | } |
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347 | else { |
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348 | vec_perm.ins(0, position + 1); |
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349 | } |
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350 | } |
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351 | vec_perm.ins(0, 0); |
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352 | |
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353 | ldmat filt (est._V(), vec_perm); |
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354 | ldmat alt (alter_est._V(), vec_perm); |
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355 | |
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356 | mat tmpL(dimV, dimV); |
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357 | tmpL.set_rows( 0, alt._L().get_rows(0, nalternatives_cond - 1) ); |
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358 | tmpL.set_rows( nalternatives_cond, filt._L().get_rows(nalternatives_cond, nparams) ); |
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359 | |
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360 | vec tmpD(dimV); |
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361 | tmpD.set_subvector( 0, alt._D()(0, nalternatives_cond - 1) ); |
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362 | tmpD.set_subvector( nalternatives_cond, filt._D()(nalternatives_cond, nparams) ); |
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363 | |
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364 | ldmat tmpLD (tmpL, tmpD); |
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365 | |
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366 | vec_perm = sort_index(vec_perm); |
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367 | ldmat newLD (tmpLD, vec_perm); |
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368 | |
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369 | egiw_array(i) = new egiw(1, newLD, alter_est._nu()); |
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370 | } |
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371 | |
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372 | // Approximation |
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373 | double sumVecCommon; // frequently used term |
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374 | vec vecNu(nalternatives); // vector of nus of components |
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375 | vec vecD(nalternatives); // vector of LS reminders |
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376 | vec vecCommon(nalternatives); // vector of common parts |
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377 | mat matVecsTheta; // matrix whose rows are theta vects. |
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378 | |
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379 | for (i = 0; i < nalternatives; i++) { |
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380 | vecNu.shift_left( egiw_array(i)->_nu() ); |
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381 | vecD.shift_left( egiw_array(i)->_V()._D()(0) ); |
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382 | matVecsTheta.append_row( egiw_array(i)->est_theta() ); |
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383 | } |
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384 | |
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385 | vecCommon = elem_mult ( frg, elem_div(vecNu, vecD) ); |
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386 | sumVecCommon = sum(vecCommon); |
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387 | |
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388 | // approximation of est. regr. coefficients |
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389 | vec aprEstTheta(nparams); |
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390 | aprEstTheta.zeros(); |
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391 | for (i = 0; i < nalternatives; i++) { |
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392 | aprEstTheta += matVecsTheta.get_row(i) * vecCommon(i); |
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393 | } |
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394 | aprEstTheta /= sumVecCommon; |
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395 | |
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396 | // approximation of degr. of freedom |
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397 | double aprNu; |
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398 | double A = log( sumVecCommon ); // Term 'A' in equation |
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399 | for ( int i = 0; i < nalternatives; i++ ) { |
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400 | A += frg(i) * ( log( vecD(i) ) - psi( 0.5 * vecNu(i) ) ); |
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401 | } |
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402 | aprNu = ( 1 + sqrt(1 + 4 * (A - LOG2)/3 ) ) / ( 2 * (A - LOG2) ); |
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403 | |
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404 | // approximation of LS reminder D(0,0) |
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405 | double aprD = aprNu / sumVecCommon; |
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406 | |
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407 | // Aproximation of covariance of LS est. |
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408 | mat aprC = zeros(nparams, nparams); |
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409 | for ( int i = 0; i < nalternatives; i++ ) { |
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410 | aprC += egiw_array(i)->est_theta_cov().to_mat() * frg(i); |
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411 | vec tmp = ( matVecsTheta.get_row(i) - aprEstTheta ); |
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412 | aprC += vecCommon(i) * outer_product( tmp, tmp); |
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413 | } |
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414 | |
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415 | // Construct GiW pdf |
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416 | ldmat aprCinv ( inv(aprC) ); |
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417 | vec D = concat( aprD, aprCinv._D() ); |
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418 | mat L = eye(dimV); |
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419 | L.set_submatrix(1, 0, aprCinv._L() * aprEstTheta); |
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420 | L.set_submatrix(1, 1, aprCinv._L()); |
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421 | ldmat aprLD (L, D); |
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422 | est = egiw(1, aprLD, aprNu); |
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423 | |
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424 | if ( evalll ) { |
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425 | last_lognc = est.lognc(); |
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426 | } |
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427 | |
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428 | // update |
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429 | ARX::bayes ( val, cond_rgr ); |
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430 | } |
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431 | |
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432 | } |
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