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