src/bp.cpp

   1 /*  Copyright (C) 2006-2009  Joris Mooij  [joris dot mooij at tuebingen dot mpg dot de]
   2     Radboud University Nijmegen, The Netherlands /
   3     Max Planck Institute for Biological Cybernetics, Germany
   4     Giuseppe Passino
   5
   6     This file is part of libDAI.
   7
   8     libDAI is free software; you can redistribute it and/or modify
   9     it under the terms of the GNU General Public License as published by
  10     the Free Software Foundation; either version 2 of the License, or
  11     (at your option) any later version.
  12
  13     libDAI is distributed in the hope that it will be useful,
  14     but WITHOUT ANY WARRANTY; without even the implied warranty of
  15     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16     GNU General Public License for more details.
  17
  18     You should have received a copy of the GNU General Public License
  19     along with libDAI; if not, write to the Free Software
  20     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  21 */
  22
  23
  24 #include <iostream>
  25 #include <sstream>
  26 #include <map>
  27 #include <set>
  28 #include <algorithm>
  29 #include <stack>
  30 #include <dai/bp.h>
  31 #include <dai/util.h>
  32 #include <dai/properties.h>
  33
  34
  35 namespace dai {
  36
  37
  38 using namespace std;
  39
  40
  41 const char *BP::Name = "BP";
  42
  43
  44 #define DAI_BP_FAST 1
  45
  46
  47 void BP::setProperties( const PropertySet &opts ) {
  48     assert( opts.hasKey("tol") );
  49     assert( opts.hasKey("maxiter") );
  50     assert( opts.hasKey("logdomain") );
  51     assert( opts.hasKey("updates") );
  52
  53     props.tol = opts.getStringAs<double>("tol");
  54     props.maxiter = opts.getStringAs<size_t>("maxiter");
  55     props.logdomain = opts.getStringAs<bool>("logdomain");
  56     props.updates = opts.getStringAs<Properties::UpdateType>("updates");
  57
  58     if( opts.hasKey("verbose") )
  59         props.verbose = opts.getStringAs<size_t>("verbose");
  60     else
  61         props.verbose = 0;
  62     if( opts.hasKey("damping") )
  63         props.damping = opts.getStringAs<double>("damping");
  64     else
  65         props.damping = 0.0;
  66     if( opts.hasKey("inference") )
  67         props.inference = opts.getStringAs<Properties::InfType>("inference");
  68     else
  69         props.inference = Properties::InfType::SUMPROD;
  70 }
  71
  72
  73 PropertySet BP::getProperties() const {
  74     PropertySet opts;
  75     opts.Set( "tol", props.tol );
  76     opts.Set( "maxiter", props.maxiter );
  77     opts.Set( "verbose", props.verbose );
  78     opts.Set( "logdomain", props.logdomain );
  79     opts.Set( "updates", props.updates );
  80     opts.Set( "damping", props.damping );
  81     opts.Set( "inference", props.inference );
  82     return opts;
  83 }
  84
  85
  86 string BP::printProperties() const {
  87     stringstream s( stringstream::out );
  88     s << "[";
  89     s << "tol=" << props.tol << ",";
  90     s << "maxiter=" << props.maxiter << ",";
  91     s << "verbose=" << props.verbose << ",";
  92     s << "logdomain=" << props.logdomain << ",";
  93     s << "updates=" << props.updates << ",";
  94     s << "damping=" << props.damping << ",";
  95     s << "inference=" << props.inference << "]";
  96     return s.str();
  97 }
  98
  99
 100 void BP::construct() {
 101     // create edge properties
 102     _edges.clear();
 103     _edges.reserve( nrVars() );
 104     _edge2lut.clear();
 105     if( props.updates == Properties::UpdateType::SEQMAX )
 106         _edge2lut.reserve( nrVars() );
 107     for( size_t i = 0; i < nrVars(); ++i ) {
 108         _edges.push_back( vector<EdgeProp>() );
 109         _edges[i].reserve( nbV(i).size() );
 110         if( props.updates == Properties::UpdateType::SEQMAX ) {
 111             _edge2lut.push_back( vector<LutType::iterator>() );
 112             _edge2lut[i].reserve( nbV(i).size() );
 113         }
 114         foreach( const Neighbor &I, nbV(i) ) {
 115             EdgeProp newEP;
 116             newEP.message = Prob( var(i).states() );
 117             newEP.newMessage = Prob( var(i).states() );
 118
 119             if( DAI_BP_FAST ) {
 120                 newEP.index.reserve( factor(I).states() );
 121                 for( IndexFor k( var(i), factor(I).vars() ); k >= 0; ++k )
 122                     newEP.index.push_back( k );
 123             }
 124
 125             newEP.residual = 0.0;
 126             _edges[i].push_back( newEP );
 127             if( props.updates == Properties::UpdateType::SEQMAX )
 128                 _edge2lut[i].push_back( _lut.insert( make_pair( newEP.residual, make_pair( i, _edges[i].size() - 1 ))) );
 129         }
 130     }
 131 }
 132
 133
 134 void BP::init() {
 135     double c = props.logdomain ? 0.0 : 1.0;
 136     for( size_t i = 0; i < nrVars(); ++i ) {
 137         foreach( const Neighbor &I, nbV(i) ) {
 138             message( i, I.iter ).fill( c );
 139             newMessage( i, I.iter ).fill( c );
 140             if( props.updates == Properties::UpdateType::SEQMAX )
 141                 updateResidual( i, I.iter, 0.0 );
 142         }
 143     }
 144 }
 145
 146
 147 void BP::findMaxResidual( size_t &i, size_t &_I ) {
 148     assert( !_lut.empty() );
 149     LutType::const_iterator largestEl = _lut.end();
 150     --largestEl;
 151     i  = largestEl->second.first;
 152     _I = largestEl->second.second;
 153 }
 154
 155
 156 void BP::calcNewMessage( size_t i, size_t _I ) {
 157     // calculate updated message I->i
 158     size_t I = nbV(i,_I);
 159
 160     Factor Fprod( factor(I) );
 161     Prob &prod = Fprod.p();
 162     if( props.logdomain )
 163         prod.takeLog();
 164
 165     // Calculate product of incoming messages and factor I
 166     foreach( const Neighbor &j, nbF(I) )
 167         if( j != i ) { // for all j in I \ i
 168             // prod_j will be the product of messages coming into j
 169             Prob prod_j( var(j).states(), props.logdomain ? 0.0 : 1.0 );
 170             foreach( const Neighbor &J, nbV(j) )
 171                 if( J != I ) { // for all J in nb(j) \ I
 172                     if( props.logdomain )
 173                         prod_j += message( j, J.iter );
 174                     else
 175                         prod_j *= message( j, J.iter );
 176                 }
 177
 178             // multiply prod with prod_j
 179             if( !DAI_BP_FAST ) {
 180                 /* UNOPTIMIZED (SIMPLE TO READ, BUT SLOW) VERSION */
 181                 if( props.logdomain )
 182                     Fprod += Factor( var(j), prod_j );
 183                 else
 184                     Fprod *= Factor( var(j), prod_j );
 185             } else {
 186                 /* OPTIMIZED VERSION */
 187                 size_t _I = j.dual;
 188                 // ind is the precalculated IndexFor(j,I) i.e. to x_I == k corresponds x_j == ind[k]
 189                 const ind_t &ind = index(j, _I);
 190                 for( size_t r = 0; r < prod.size(); ++r )
 191                     if( props.logdomain )
 192                         prod[r] += prod_j[ind[r]];
 193                     else
 194                         prod[r] *= prod_j[ind[r]];
 195             }
 196         }
 197
 198     if( props.logdomain ) {
 199         prod -= prod.max();
 200         prod.takeExp();
 201     }
 202
 203     // Marginalize onto i
 204     Prob marg;
 205     if( !DAI_BP_FAST ) {
 206         /* UNOPTIMIZED (SIMPLE TO READ, BUT SLOW) VERSION */
 207         if( props.inference == Properties::InfType::SUMPROD )
 208             marg = Fprod.marginal( var(i) ).p();
 209         else
 210             marg = Fprod.maxMarginal( var(i) ).p();
 211     } else {
 212         /* OPTIMIZED VERSION */
 213         marg = Prob( var(i).states(), 0.0 );
 214         // ind is the precalculated IndexFor(i,I) i.e. to x_I == k corresponds x_i == ind[k]
 215         const ind_t ind = index(i,_I);
 216         if( props.inference == Properties::InfType::SUMPROD )
 217             for( size_t r = 0; r < prod.size(); ++r )
 218                 marg[ind[r]] += prod[r];
 219         else
 220             for( size_t r = 0; r < prod.size(); ++r )
 221                 if( prod[r] > marg[ind[r]] )
 222                     marg[ind[r]] = prod[r];
 223         marg.normalize();
 224     }
 225
 226     // Store result
 227     if( props.logdomain )
 228         newMessage(i,_I) = marg.log();
 229     else
 230         newMessage(i,_I) = marg;
 231
 232     // Update the residual if necessary
 233     if( props.updates == Properties::UpdateType::SEQMAX )
 234         updateResidual( i, _I , dist( newMessage( i, _I ), message( i, _I ), Prob::DISTLINF ) );
 235 }
 236
 237
 238 // BP::run does not check for NANs for performance reasons
 239 // Somehow NaNs do not often occur in BP...
 240 double BP::run() {
 241     if( props.verbose >= 1 )
 242         cerr << "Starting " << identify() << "...";
 243     if( props.verbose >= 3)
 244         cerr << endl;
 245
 246     double tic = toc();
 247     Diffs diffs(nrVars(), 1.0);
 248
 249     vector<Edge> update_seq;
 250
 251     vector<Factor> old_beliefs;
 252     old_beliefs.reserve( nrVars() );
 253     for( size_t i = 0; i < nrVars(); ++i )
 254         old_beliefs.push_back( beliefV(i) );
 255
 256     size_t nredges = nrEdges();
 257
 258     if( props.updates == Properties::UpdateType::SEQMAX ) {
 259         // do the first pass
 260         for( size_t i = 0; i < nrVars(); ++i )
 261             foreach( const Neighbor &I, nbV(i) ) {
 262                 calcNewMessage( i, I.iter );
 263             }
 264     } else {
 265         update_seq.reserve( nredges );
 266         /// \todo Investigate whether performance increases by switching the order of following two loops:
 267         for( size_t i = 0; i < nrVars(); ++i )
 268             foreach( const Neighbor &I, nbV(i) )
 269                 update_seq.push_back( Edge( i, I.iter ) );
 270     }
 271
 272     // do several passes over the network until maximum number of iterations has
 273     // been reached or until the maximum belief difference is smaller than tolerance
 274     for( _iters=0; _iters < props.maxiter && diffs.maxDiff() > props.tol; ++_iters ) {
 275         if( props.updates == Properties::UpdateType::SEQMAX ) {
 276             // Residuals-BP by Koller et al.
 277             for( size_t t = 0; t < nredges; ++t ) {
 278                 // update the message with the largest residual
 279                 size_t i, _I;
 280                 findMaxResidual( i, _I );
 281                 updateMessage( i, _I );
 282
 283                 // I->i has been updated, which means that residuals for all
 284                 // J->j with J in nb[i]\I and j in nb[J]\i have to be updated
 285                 foreach( const Neighbor &J, nbV(i) ) {
 286                     if( J.iter != _I ) {
 287                         foreach( const Neighbor &j, nbF(J) ) {
 288                             size_t _J = j.dual;
 289                             if( j != i )
 290                                 calcNewMessage( j, _J );
 291                         }
 292                     }
 293                 }
 294             }
 295         } else if( props.updates == Properties::UpdateType::PARALL ) {
 296             // Parallel updates
 297             for( size_t i = 0; i < nrVars(); ++i )
 298                 foreach( const Neighbor &I, nbV(i) )
 299                     calcNewMessage( i, I.iter );
 300
 301             for( size_t i = 0; i < nrVars(); ++i )
 302                 foreach( const Neighbor &I, nbV(i) )
 303                     updateMessage( i, I.iter );
 304         } else {
 305             // Sequential updates
 306             if( props.updates == Properties::UpdateType::SEQRND )
 307                 random_shuffle( update_seq.begin(), update_seq.end() );
 308
 309             foreach( const Edge &e, update_seq ) {
 310                 calcNewMessage( e.first, e.second );
 311                 updateMessage( e.first, e.second );
 312             }
 313         }
 314
 315         // calculate new beliefs and compare with old ones
 316         for( size_t i = 0; i < nrVars(); ++i ) {
 317             Factor nb( beliefV(i) );
 318             diffs.push( dist( nb, old_beliefs[i], Prob::DISTLINF ) );
 319             old_beliefs[i] = nb;
 320         }
 321
 322         if( props.verbose >= 3 )
 323             cerr << Name << "::run:  maxdiff " << diffs.maxDiff() << " after " << _iters+1 << " passes" << endl;
 324     }
 325
 326     if( diffs.maxDiff() > _maxdiff )
 327         _maxdiff = diffs.maxDiff();
 328
 329     if( props.verbose >= 1 ) {
 330         if( diffs.maxDiff() > props.tol ) {
 331             if( props.verbose == 1 )
 332                 cerr << endl;
 333                 cerr << Name << "::run:  WARNING: not converged within " << props.maxiter << " passes (" << toc() - tic << " seconds)...final maxdiff:" << diffs.maxDiff() << endl;
 334         } else {
 335             if( props.verbose >= 3 )
 336                 cerr << Name << "::run:  ";
 337                 cerr << "converged in " << _iters << " passes (" << toc() - tic << " seconds)." << endl;
 338         }
 339     }
 340
 341     return diffs.maxDiff();
 342 }
 343
 344
 345 void BP::calcBeliefV( size_t i, Prob &p ) const {
 346     p = Prob( var(i).states(), props.logdomain ? 0.0 : 1.0 );
 347     foreach( const Neighbor &I, nbV(i) )
 348         if( props.logdomain )
 349             p += newMessage( i, I.iter );
 350         else
 351             p *= newMessage( i, I.iter );
 352 }
 353
 354
 355 void BP::calcBeliefF( size_t I, Prob &p ) const {
 356     Factor Fprod( factor( I ) );
 357     Prob &prod = Fprod.p();
 358
 359     if( props.logdomain )
 360         prod.takeLog();
 361
 362     foreach( const Neighbor &j, nbF(I) ) {
 363         // prod_j will be the product of messages coming into j
 364         Prob prod_j( var(j).states(), props.logdomain ? 0.0 : 1.0 );
 365         foreach( const Neighbor &J, nbV(j) )
 366             if( J != I ) { // for all J in nb(j) \ I
 367                 if( props.logdomain )
 368                     prod_j += newMessage( j, J.iter );
 369                 else
 370                     prod_j *= newMessage( j, J.iter );
 371             }
 372
 373         // multiply prod with prod_j
 374         if( !DAI_BP_FAST ) {
 375             /* UNOPTIMIZED (SIMPLE TO READ, BUT SLOW) VERSION */
 376             if( props.logdomain )
 377                 Fprod += Factor( var(j), prod_j );
 378             else
 379                 Fprod *= Factor( var(j), prod_j );
 380         } else {
 381             /* OPTIMIZED VERSION */
 382             size_t _I = j.dual;
 383             // ind is the precalculated IndexFor(j,I) i.e. to x_I == k corresponds x_j == ind[k]
 384             const ind_t & ind = index(j, _I);
 385
 386             for( size_t r = 0; r < prod.size(); ++r ) {
 387                 if( props.logdomain )
 388                     prod[r] += prod_j[ind[r]];
 389                 else
 390                     prod[r] *= prod_j[ind[r]];
 391             }
 392         }
 393     }
 394
 395     p = prod;
 396 }
 397
 398
 399 Factor BP::beliefV( size_t i ) const {
 400     Prob p;
 401     calcBeliefV( i, p );
 402
 403     if( props.logdomain ) {
 404         p -= p.max();
 405         p.takeExp();
 406     }
 407     p.normalize();
 408
 409     return( Factor( var(i), p ) );
 410 }
 411
 412
 413 Factor BP::beliefF( size_t I ) const {
 414     Prob p;
 415     calcBeliefF( I, p );
 416
 417     if( props.logdomain ) {
 418         p -= p.max();
 419         p.takeExp();
 420     }
 421     p.normalize();
 422
 423     return( Factor( factor(I).vars(), p ) );
 424 }
 425
 426
 427 Factor BP::belief( const Var &n ) const {
 428     return( beliefV( findVar( n ) ) );
 429 }
 430
 431
 432 vector<Factor> BP::beliefs() const {
 433     vector<Factor> result;
 434     for( size_t i = 0; i < nrVars(); ++i )
 435         result.push_back( beliefV(i) );
 436     for( size_t I = 0; I < nrFactors(); ++I )
 437         result.push_back( beliefF(I) );
 438     return result;
 439 }
 440
 441
 442 Factor BP::belief( const VarSet &ns ) const {
 443     if( ns.size() == 1 )
 444         return belief( *(ns.begin()) );
 445     else {
 446         size_t I;
 447         for( I = 0; I < nrFactors(); I++ )
 448             if( factor(I).vars() >> ns )
 449                 break;
 450         assert( I != nrFactors() );
 451         return beliefF(I).marginal(ns);
 452     }
 453 }
 454
 455
 456 Real BP::logZ() const {
 457     Real sum = 0.0;
 458     for(size_t i = 0; i < nrVars(); ++i )
 459         sum += (1.0 - nbV(i).size()) * beliefV(i).entropy();
 460     for( size_t I = 0; I < nrFactors(); ++I )
 461         sum -= dist( beliefF(I), factor(I), Prob::DISTKL );
 462     return sum;
 463 }
 464
 465
 466 string BP::identify() const {
 467     return string(Name) + printProperties();
 468 }
 469
 470
 471 void BP::init( const VarSet &ns ) {
 472     for( VarSet::const_iterator n = ns.begin(); n != ns.end(); ++n ) {
 473         size_t ni = findVar( *n );
 474         foreach( const Neighbor &I, nbV( ni ) ) {
 475             double val = props.logdomain ? 0.0 : 1.0;
 476             message( ni, I.iter ).fill( val );
 477             newMessage( ni, I.iter ).fill( val );
 478             if( props.updates == Properties::UpdateType::SEQMAX )
 479                 updateResidual( ni, I.iter, 0.0 );
 480         }
 481     }
 482 }
 483
 484
 485 void BP::updateMessage( size_t i, size_t _I ) {
 486     if( recordSentMessages )
 487         _sentMessages.push_back(make_pair(i,_I));
 488     if( props.damping == 0.0 ) {
 489         message(i,_I) = newMessage(i,_I);
 490         if( props.updates == Properties::UpdateType::SEQMAX )
 491             updateResidual( i, _I, 0.0 );
 492     } else {
 493         message(i,_I) = (message(i,_I) ^ props.damping) * (newMessage(i,_I) ^ (1.0 - props.damping));
 494         if( props.updates == Properties::UpdateType::SEQMAX )
 495             updateResidual( i, _I, dist( newMessage(i,_I), message(i,_I), Prob::DISTLINF ) );
 496     }
 497 }
 498
 499
 500 void BP::updateResidual( size_t i, size_t _I, double r ) {
 501     EdgeProp* pEdge = &_edges[i][_I];
 502     pEdge->residual = r;
 503
 504     // rearrange look-up table (delete and reinsert new key)
 505     _lut.erase( _edge2lut[i][_I] );
 506     _edge2lut[i][_I] = _lut.insert( make_pair( r, make_pair(i, _I) ) );
 507 }
 508
 509
 510 std::vector<size_t> BP::findMaximum() const {
 511     vector<size_t> maximum( nrVars() );
 512     vector<bool> visitedVars( nrVars(), false );
 513     vector<bool> visitedFactors( nrFactors(), false );
 514     stack<size_t> scheduledFactors;
 515     for( size_t i = 0; i < nrVars(); ++i ) {
 516         if( visitedVars[i] )
 517             continue;
 518         visitedVars[i] = true;
 519
 520         // Maximise with respect to variable i
 521         Prob prod;
 522         calcBeliefV( i, prod );
 523         maximum[i] = max_element( prod.begin(), prod.end() ) - prod.begin();
 524
 525         foreach( const Neighbor &I, nbV(i) )
 526             if( !visitedFactors[I] )
 527                 scheduledFactors.push(I);
 528
 529         while( !scheduledFactors.empty() ){
 530             size_t I = scheduledFactors.top();
 531             scheduledFactors.pop();
 532             if( visitedFactors[I] )
 533                 continue;
 534             visitedFactors[I] = true;
 535
 536             // Evaluate if some neighboring variables still need to be fixed; if not, we're done
 537             bool allDetermined = true;
 538             foreach( const Neighbor &j, nbF(I) )
 539                 if( !visitedVars[j.node] ) {
 540                     allDetermined = false;
 541                     break;
 542                 }
 543             if( allDetermined )
 544                 continue;
 545
 546             // Calculate product of incoming messages on factor I
 547             Prob prod2;
 548             calcBeliefF( I, prod2 );
 549
 550             // The allowed configuration is restrained according to the variables assigned so far:
 551             // pick the argmax amongst the allowed states
 552             Real maxProb = numeric_limits<Real>::min();
 553             State maxState( factor(I).vars() );
 554             for( State s( factor(I).vars() ); s.valid(); ++s ){
 555                 // First, calculate whether this state is consistent with variables that
 556                 // have been assigned already
 557                 bool allowedState = true;
 558                 foreach( const Neighbor &j, nbF(I) )
 559                     if( visitedVars[j.node] && maximum[j.node] != s(var(j.node)) ) {
 560                         allowedState = false;
 561                         break;
 562                     }
 563                 // If it is consistent, check if its probability is larger than what we have seen so far
 564                 if( allowedState && prod2[s] > maxProb ) {
 565                     maxState = s;
 566                     maxProb = prod2[s];
 567                 }
 568             }
 569
 570             // Decode the argmax
 571             foreach( const Neighbor &j, nbF(I) ) {
 572                 if( visitedVars[j.node] ) {
 573                     // We have already visited j earlier - hopefully our state is consistent
 574                     if( maximum[j.node] != maxState(var(j.node)) && props.verbose >= 1 )
 575                         cerr << "BP::findMaximum - warning: maximum not consistent due to loops." << endl;
 576                 } else {
 577                     // We found a consistent state for variable j
 578                     visitedVars[j.node] = true;
 579                     maximum[j.node] = maxState( var(j.node) );
 580                     foreach( const Neighbor &J, nbV(j) )
 581                         if( !visitedFactors[J] )
 582                             scheduledFactors.push(J);
 583                 }
 584             }
 585         }
 586     }
 587     return maximum;
 588 }
 589
 590
 591 } // end of namespace dai