| 1 | |
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| 2 | #include "merger.h" |
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| 3 | #include "../estim/arx.h" |
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| 4 | |
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| 5 | namespace bdm { |
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| 6 | |
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| 7 | merger_base::merger_base ( const Array<mpdf*> &S, bool own ) { |
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| 8 | DBG = false; |
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| 9 | dbg_file = NULL; |
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| 10 | set_sources ( S, own ); |
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| 11 | } |
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| 12 | |
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| 13 | vec merger_base::merge_points ( mat &lW ) { |
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| 14 | int nu = lW.rows(); |
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| 15 | vec result; |
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| 16 | ivec indW; |
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| 17 | bool infexist; |
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| 18 | switch ( METHOD ) { |
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| 19 | case ARITHMETIC: |
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| 20 | result = log ( sum ( exp ( lW ) ) ); //ugly! |
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| 21 | break; |
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| 22 | case GEOMETRIC: |
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| 23 | result = sum ( lW ) / nu; |
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| 24 | break; |
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| 25 | case LOGNORMAL: |
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| 26 | vec sumlW = sum ( lW ) ; |
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| 27 | indW = find ( ( sumlW < inf ) & ( sumlW > -inf ) ); |
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| 28 | infexist = ( indW.size() < lW.cols() ); |
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| 29 | vec mu; |
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| 30 | vec lam; |
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| 31 | if ( infexist ) { |
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| 32 | mu = sumlW ( indW ) / nu; //mean of logs |
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| 33 | // |
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| 34 | mat validlW = lW.get_cols ( indW ); |
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| 35 | lam = sum ( pow ( validlW - outer_product ( ones ( validlW.rows() ), mu ), 2 ) ); |
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| 36 | } else { |
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| 37 | mu = sum ( lW ) / nu; //mean of logs |
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| 38 | lam = sum ( pow ( lW - outer_product ( ones ( lW.rows() ), mu ), 2 ) ); |
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| 39 | } |
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| 40 | // |
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| 41 | double coef = 0.0; |
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| 42 | vec sq2bl = sqrt ( 2 * beta * lam ); //this term is everywhere |
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| 43 | switch ( nu ) { |
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| 44 | case 2: |
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| 45 | coef = ( 1 - 0.5 * sqrt ( ( 4.0 * beta - 3.0 ) / beta ) ); |
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| 46 | result = coef * sq2bl + mu ; |
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| 47 | break; |
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| 48 | // case 4: == can be done similar to case 2 - is it worth it??? |
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| 49 | default: // see accompanying document merge_lognorm_derivation.lyx |
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| 50 | coef = sqrt ( 1 - ( nu + 1 ) / ( 2 * beta * nu ) ); |
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| 51 | result = log ( besselk ( ( nu - 3 ) / 2, sq2bl * coef ) ) - log ( besselk ( ( nu - 3 ) / 2, sq2bl ) ) + mu; |
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| 52 | break; |
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| 53 | } |
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| 54 | break; |
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| 55 | } |
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| 56 | if ( infexist ) { |
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| 57 | vec tmp = -inf * ones ( lW.cols() ); |
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| 58 | set_subvector ( tmp, indW, result ); |
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| 59 | return tmp; |
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| 60 | } else { |
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| 61 | return result; |
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| 62 | } |
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| 63 | } |
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| 64 | |
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| 65 | void merger_mix::merge ( ) { |
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| 66 | Array<vec> &Smp = eSmp._samples(); //aux |
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| 67 | vec &w = eSmp._w(); //aux |
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| 68 | |
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| 69 | mat Smp_ex = ones ( dim + 1, Npoints ); // Extended samples for the ARX model - the last row is ones |
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| 70 | for ( int i = 0; i < Npoints; i++ ) { |
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| 71 | set_col_part ( Smp_ex, i, Smp ( i ) ); |
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| 72 | } |
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| 73 | |
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| 74 | if ( DBG ) *dbg_file << Name ( "Smp_0" ) << Smp_ex; |
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| 75 | |
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| 76 | // Stuff for merging |
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| 77 | vec lw_src ( Npoints ); // weights of the ith source |
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| 78 | vec lw_mix ( Npoints ); // weights of the approximating mixture |
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| 79 | vec lw ( Npoints ); // tmp |
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| 80 | mat lW = zeros ( Nsources, Npoints ); // array of weights of all sources |
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| 81 | vec vec0 ( 0 ); |
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| 82 | |
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| 83 | //initialize importance weights |
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| 84 | lw_mix = 1.0; // assuming uniform grid density -- otherwise |
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| 85 | |
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| 86 | // Initial component in the mixture model |
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| 87 | mat V0 = 1e-8 * eye ( dim + 1 ); |
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| 88 | ARX A0; |
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| 89 | A0.set_statistics ( dim, V0 ); //initial guess of Mix: |
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| 90 | |
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| 91 | Mix.init ( &A0, Smp_ex, Ncoms ); |
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| 92 | //Preserve initial mixture for repetitive estimation via flattening |
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| 93 | MixEF Mix_init ( Mix ); |
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| 94 | |
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| 95 | // ============= MAIN LOOP ================== |
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| 96 | bool converged = false; |
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| 97 | int niter = 0; |
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| 98 | char dbg_str[100]; |
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| 99 | |
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| 100 | emix* Mpred = Mix.epredictor ( ); |
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| 101 | vec Mix_pdf ( Npoints ); |
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| 102 | while ( !converged ) { |
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| 103 | //Re-estimate Mix |
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| 104 | //Re-Initialize Mixture model |
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| 105 | Mix.flatten ( &Mix_init ); |
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| 106 | Mix.bayesB ( Smp_ex, w*Npoints ); |
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| 107 | delete Mpred; |
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| 108 | Mpred = Mix.epredictor ( ); // Allocation => must be deleted at the end!! |
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| 109 | Mpred->set_rv ( rv ); //the predictor predicts rv of this merger |
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| 110 | |
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| 111 | // This will be active only later in iterations!!! |
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| 112 | if ( 1. / sum_sqr ( w ) < effss_coef*Npoints ) { |
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| 113 | // Generate new samples |
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| 114 | eSmp.set_samples ( Mpred ); |
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| 115 | for ( int i = 0; i < Npoints; i++ ) { |
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| 116 | //////////// !!!!!!!!!!!!! |
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| 117 | //if ( Smp ( i ) ( 2 ) <0 ) {Smp ( i ) ( 2 ) = 0.01; } |
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| 118 | set_col_part ( Smp_ex, i, Smp ( i ) ); |
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| 119 | //Importance of the mixture |
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| 120 | //lw_mix ( i ) =Mix.logpred (Smp_ex.get_col(i) ); |
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| 121 | lw_mix ( i ) = Mpred->evallog ( Smp ( i ) ); |
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| 122 | } |
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| 123 | if ( DBG ) { |
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| 124 | cout << "Resampling =" << 1. / sum_sqr ( w ) << endl; |
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| 125 | cout << Mix._e()->mean() << endl; |
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| 126 | cout << sum ( Smp_ex, 2 ) / Npoints << endl; |
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| 127 | cout << Smp_ex*Smp_ex.T() / Npoints << endl; |
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| 128 | } |
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| 129 | } |
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| 130 | if ( DBG ) { |
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| 131 | sprintf ( dbg_str, "Mpred_mean%d", niter ); |
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| 132 | *dbg_file << Name ( dbg_str ) << Mpred->mean(); |
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| 133 | sprintf ( dbg_str, "Mpred_var%d", niter ); |
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| 134 | *dbg_file << Name ( dbg_str ) << Mpred->variance(); |
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| 135 | |
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| 136 | |
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| 137 | sprintf ( dbg_str, "Mpdf%d", niter ); |
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| 138 | for ( int i = 0; i < Npoints; i++ ) { |
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| 139 | Mix_pdf ( i ) = Mix.logpred ( Smp_ex.get_col ( i ) ); |
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| 140 | } |
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| 141 | *dbg_file << Name ( dbg_str ) << Mix_pdf; |
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| 142 | |
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| 143 | sprintf ( dbg_str, "Smp%d", niter ); |
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| 144 | *dbg_file << Name ( dbg_str ) << Smp_ex; |
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| 145 | |
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| 146 | } |
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| 147 | //Importace weighting |
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| 148 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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| 149 | lw_src = 0.0; |
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| 150 | //======== Same RVs =========== |
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| 151 | //Split according to dependency in rvs |
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| 152 | if ( mpdfs ( i )->dimension() == dim ) { |
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| 153 | // no need for conditioning or marginalization |
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| 154 | lw_src = mpdfs ( i )->evallogcond_m ( Smp , vec(0)); |
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| 155 | } else { |
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| 156 | // compute likelihood of marginal on the conditional variable |
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| 157 | if ( mpdfs ( i )->dimensionc() > 0 ) { |
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| 158 | // Make marginal on rvc_i |
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| 159 | shared_ptr<epdf> tmp_marg = Mpred->marginal ( mpdfs ( i )->_rvc() ); |
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| 160 | //compute vector of lw_src |
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| 161 | for ( int k = 0; k < Npoints; k++ ) { |
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| 162 | // Here val of tmp_marg = cond of mpdfs(i) ==> calling dls->get_cond |
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| 163 | lw_src ( k ) += tmp_marg->evallog ( dls ( i )->get_cond ( Smp ( k ) ) ); |
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| 164 | } |
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| 165 | |
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| 166 | // sprintf ( str,"marg%d",niter ); |
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| 167 | // *dbg << Name ( str ) << lw_src; |
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| 168 | |
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| 169 | } |
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| 170 | // Compute likelihood of the missing variable |
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| 171 | if ( dim > ( mpdfs ( i )->dimension() + mpdfs ( i )->dimensionc() ) ) { |
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| 172 | /////////////// |
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| 173 | // There are variales unknown to mpdfs(i) : rvzs |
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| 174 | shared_ptr<mpdf> tmp_cond = Mpred->condition ( rvzs ( i ) ); |
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| 175 | // Compute likelihood |
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| 176 | vec lw_dbg = lw_src; |
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| 177 | for ( int k = 0; k < Npoints; k++ ) { |
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| 178 | lw_src ( k ) += log ( |
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| 179 | tmp_cond->evallogcond ( |
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| 180 | zdls ( i )->pushdown ( Smp ( k ) ), |
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| 181 | zdls ( i )->get_cond ( Smp ( k ) ) ) ); |
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| 182 | if ( !std::isfinite ( lw_src ( k ) ) ) { |
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| 183 | lw_src ( k ) = -1e16; |
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| 184 | cout << "!"; |
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| 185 | } |
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| 186 | } |
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| 187 | } |
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| 188 | // Compute likelihood of the partial source |
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| 189 | for ( int k = 0; k < Npoints; k++ ) { |
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| 190 | lw_src ( k ) += mpdfs ( i )->evallogcond ( dls ( i )->pushdown ( Smp ( k ) ), |
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| 191 | dls ( i )->get_cond ( Smp ( k ) )); |
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| 192 | } |
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| 193 | |
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| 194 | } |
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| 195 | // it_assert_debug(std::isfinite(sum(lw_src)),"bad"); |
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| 196 | lW.set_row ( i, lw_src ); // do not divide by mix |
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| 197 | } |
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| 198 | lw = merger_base::merge_points ( lW ); //merge |
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| 199 | |
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| 200 | //Importance weighting |
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| 201 | lw -= lw_mix; // hoping that it is not numerically sensitive... |
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| 202 | w = exp ( lw - max ( lw ) ); |
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| 203 | |
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| 204 | //renormalize |
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| 205 | double sumw = sum ( w ); |
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| 206 | if ( std::isfinite ( sumw ) ) { |
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| 207 | w = w / sumw; |
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| 208 | } else { |
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| 209 | it_file itf ( "merg_err.it" ); |
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| 210 | itf << Name ( "w" ) << w; |
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| 211 | } |
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| 212 | |
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| 213 | if ( DBG ) { |
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| 214 | sprintf ( dbg_str, "lW%d", niter ); |
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| 215 | *dbg_file << Name ( dbg_str ) << lW; |
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| 216 | sprintf ( dbg_str, "w%d", niter ); |
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| 217 | *dbg_file << Name ( dbg_str ) << w; |
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| 218 | sprintf ( dbg_str, "lw_m%d", niter ); |
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| 219 | *dbg_file << Name ( dbg_str ) << lw_mix; |
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| 220 | } |
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| 221 | // ==== stopping rule === |
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| 222 | niter++; |
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| 223 | converged = ( niter > stop_niter ); |
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| 224 | } |
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| 225 | delete Mpred; |
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| 226 | // cout << endl; |
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| 227 | |
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| 228 | } |
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| 229 | |
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| 230 | // DEFAULTS FOR MERGER_BASE |
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| 231 | const MERGER_METHOD merger_base::DFLT_METHOD = LOGNORMAL; |
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| 232 | const double merger_base::DFLT_beta = 1.2; |
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| 233 | // DEFAULTS FOR MERGER_MIX |
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| 234 | const int merger_mix::DFLT_Ncoms = 10; |
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| 235 | const double merger_mix::DFLT_effss_coef = 0.5; |
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| 236 | |
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| 237 | } |
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