src/jtree.cpp

   1 /*  Copyright (C) 2006-2008  Joris Mooij  [j dot mooij at science dot ru dot nl]
   2     Radboud University Nijmegen, The Netherlands
   3
   4     This file is part of libDAI.
   5
   6     libDAI is free software; you can redistribute it and/or modify
   7     it under the terms of the GNU General Public License as published by
   8     the Free Software Foundation; either version 2 of the License, or
   9     (at your option) any later version.
  10
  11     libDAI is distributed in the hope that it will be useful,
  12     but WITHOUT ANY WARRANTY; without even the implied warranty of
  13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14     GNU General Public License for more details.
  15
  16     You should have received a copy of the GNU General Public License
  17     along with libDAI; if not, write to the Free Software
  18     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  19 */
  20
  21
  22 #include <iostream>
  23 #include <dai/jtree.h>
  24
  25
  26 namespace dai {
  27
  28
  29 using namespace std;
  30
  31
  32 const char *JTree::Name = "JTREE";
  33
  34
  35 void JTree::setProperties( const PropertySet &opts ) {
  36     assert( opts.hasKey("verbose") );
  37     assert( opts.hasKey("updates") );
  38
  39     props.verbose = opts.getStringAs<size_t>("verbose");
  40     props.updates = opts.getStringAs<Properties::UpdateType>("updates");
  41 }
  42
  43
  44 PropertySet JTree::getProperties() const {
  45     PropertySet opts;
  46     opts.Set( "verbose", props.verbose );
  47     opts.Set( "updates", props.updates );
  48     return opts;
  49 }
  50
  51
  52 string JTree::printProperties() const {
  53     stringstream s( stringstream::out );
  54     s << "[";
  55     s << "verbose=" << props.verbose << ",";
  56     s << "updates=" << props.updates << "]";
  57     return s.str();
  58 }
  59
  60
  61 JTree::JTree( const FactorGraph &fg, const PropertySet &opts, bool automatic ) : DAIAlgRG(fg), _RTree(), _Qa(), _Qb(), _mes(), _logZ(), props() {
  62     setProperties( opts );
  63
  64     if( !isConnected() )
  65        DAI_THROW(FACTORGRAPH_NOT_CONNECTED);
  66
  67     if( automatic ) {
  68         // Create ClusterGraph which contains factors as clusters
  69         vector<VarSet> cl;
  70         cl.reserve( fg.nrFactors() );
  71         for( size_t I = 0; I < nrFactors(); I++ )
  72             cl.push_back( factor(I).vars() );
  73         ClusterGraph _cg( cl );
  74
  75         if( props.verbose >= 3 )
  76             cout << "Initial clusters: " << _cg << endl;
  77
  78         // Retain only maximal clusters
  79         _cg.eraseNonMaximal();
  80         if( props.verbose >= 3 )
  81             cout << "Maximal clusters: " << _cg << endl;
  82
  83         vector<VarSet> ElimVec = _cg.VarElim_MinFill().eraseNonMaximal().toVector();
  84         if( props.verbose >= 3 )
  85             cout << "VarElim_MinFill result: " << ElimVec << endl;
  86
  87         GenerateJT( ElimVec );
  88     }
  89 }
  90
  91
  92 void JTree::GenerateJT( const std::vector<VarSet> &Cliques ) {
  93     // Construct a weighted graph (each edge is weighted with the cardinality
  94     // of the intersection of the nodes, where the nodes are the elements of
  95     // Cliques).
  96     WeightedGraph<int> JuncGraph;
  97     for( size_t i = 0; i < Cliques.size(); i++ )
  98         for( size_t j = i+1; j < Cliques.size(); j++ ) {
  99             size_t w = (Cliques[i] & Cliques[j]).size();
 100             if( w )
 101                 JuncGraph[UEdge(i,j)] = w;
 102         }
 103
 104     // Construct maximal spanning tree using Prim's algorithm
 105     _RTree = MaxSpanningTreePrims( JuncGraph );
 106
 107     // Construct corresponding region graph
 108
 109     // Create outer regions
 110     ORs.reserve( Cliques.size() );
 111     for( size_t i = 0; i < Cliques.size(); i++ )
 112         ORs.push_back( FRegion( Factor(Cliques[i], 1.0), 1.0 ) );
 113
 114     // For each factor, find an outer region that subsumes that factor.
 115     // Then, multiply the outer region with that factor.
 116     for( size_t I = 0; I < nrFactors(); I++ ) {
 117         size_t alpha;
 118         for( alpha = 0; alpha < nrORs(); alpha++ )
 119             if( OR(alpha).vars() >> factor(I).vars() ) {
 120                 fac2OR.push_back( alpha );
 121                 break;
 122             }
 123         assert( alpha != nrORs() );
 124     }
 125     RecomputeORs();
 126
 127     // Create inner regions and edges
 128     IRs.reserve( _RTree.size() );
 129     vector<Edge> edges;
 130     edges.reserve( 2 * _RTree.size() );
 131     for( size_t i = 0; i < _RTree.size(); i++ ) {
 132         edges.push_back( Edge( _RTree[i].n1, nrIRs() ) );
 133         edges.push_back( Edge( _RTree[i].n2, nrIRs() ) );
 134         // inner clusters have counting number -1
 135         IRs.push_back( Region( Cliques[_RTree[i].n1] & Cliques[_RTree[i].n2], -1.0 ) );
 136     }
 137
 138     // create bipartite graph
 139     G.construct( nrORs(), nrIRs(), edges.begin(), edges.end() );
 140
 141     // Create messages and beliefs
 142     _Qa.clear();
 143     _Qa.reserve( nrORs() );
 144     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 145         _Qa.push_back( OR(alpha) );
 146
 147     _Qb.clear();
 148     _Qb.reserve( nrIRs() );
 149     for( size_t beta = 0; beta < nrIRs(); beta++ )
 150         _Qb.push_back( Factor( IR(beta), 1.0 ) );
 151
 152     _mes.clear();
 153     _mes.reserve( nrORs() );
 154     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 155         _mes.push_back( vector<Factor>() );
 156         _mes[alpha].reserve( nbOR(alpha).size() );
 157         foreach( const Neighbor &beta, nbOR(alpha) )
 158             _mes[alpha].push_back( Factor( IR(beta), 1.0 ) );
 159     }
 160
 161     // Check counting numbers
 162     Check_Counting_Numbers();
 163
 164     if( props.verbose >= 3 ) {
 165         cout << "Resulting regiongraph: " << *this << endl;
 166     }
 167 }
 168
 169
 170 string JTree::identify() const {
 171     return string(Name) + printProperties();
 172 }
 173
 174
 175 Factor JTree::belief( const VarSet &ns ) const {
 176     vector<Factor>::const_iterator beta;
 177     for( beta = _Qb.begin(); beta != _Qb.end(); beta++ )
 178         if( beta->vars() >> ns )
 179             break;
 180     if( beta != _Qb.end() )
 181         return( beta->marginal(ns) );
 182     else {
 183         vector<Factor>::const_iterator alpha;
 184         for( alpha = _Qa.begin(); alpha != _Qa.end(); alpha++ )
 185             if( alpha->vars() >> ns )
 186                 break;
 187         assert( alpha != _Qa.end() );
 188         return( alpha->marginal(ns) );
 189     }
 190 }
 191
 192
 193 vector<Factor> JTree::beliefs() const {
 194     vector<Factor> result;
 195     for( size_t beta = 0; beta < nrIRs(); beta++ )
 196         result.push_back( _Qb[beta] );
 197     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 198         result.push_back( _Qa[alpha] );
 199     return result;
 200 }
 201
 202
 203 Factor JTree::belief( const Var &n ) const {
 204     return belief( (VarSet)n );
 205 }
 206
 207
 208 // Needs no init
 209 void JTree::runHUGIN() {
 210     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 211         _Qa[alpha] = OR(alpha);
 212
 213     for( size_t beta = 0; beta < nrIRs(); beta++ )
 214         _Qb[beta].fill( 1.0 );
 215
 216     // CollectEvidence
 217     _logZ = 0.0;
 218     for( size_t i = _RTree.size(); (i--) != 0; ) {
 219 //      Make outer region _RTree[i].n1 consistent with outer region _RTree[i].n2
 220 //      IR(i) = seperator OR(_RTree[i].n1) && OR(_RTree[i].n2)
 221         Factor new_Qb = _Qa[_RTree[i].n2].partSum( IR( i ) );
 222         _logZ += log(new_Qb.normalize());
 223         _Qa[_RTree[i].n1] *= new_Qb.divided_by( _Qb[i] );
 224         _Qb[i] = new_Qb;
 225     }
 226     if( _RTree.empty() )
 227         _logZ += log(_Qa[0].normalize() );
 228     else
 229         _logZ += log(_Qa[_RTree[0].n1].normalize());
 230
 231     // DistributeEvidence
 232     for( size_t i = 0; i < _RTree.size(); i++ ) {
 233 //      Make outer region _RTree[i].n2 consistent with outer region _RTree[i].n1
 234 //      IR(i) = seperator OR(_RTree[i].n1) && OR(_RTree[i].n2)
 235         Factor new_Qb = _Qa[_RTree[i].n1].marginal( IR( i ) );
 236         _Qa[_RTree[i].n2] *= new_Qb.divided_by( _Qb[i] );
 237         _Qb[i] = new_Qb;
 238     }
 239
 240     // Normalize
 241     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 242         _Qa[alpha].normalize();
 243 }
 244
 245
 246 // Really needs no init! Initial messages can be anything.
 247 void JTree::runShaferShenoy() {
 248     // First pass
 249     _logZ = 0.0;
 250     for( size_t e = nrIRs(); (e--) != 0; ) {
 251         // send a message from _RTree[e].n2 to _RTree[e].n1
 252         // or, actually, from the seperator IR(e) to _RTree[e].n1
 253
 254         size_t i = nbIR(e)[1].node; // = _RTree[e].n2
 255         size_t j = nbIR(e)[0].node; // = _RTree[e].n1
 256         size_t _e = nbIR(e)[0].dual;
 257
 258         Factor piet = OR(i);
 259         foreach( const Neighbor &k, nbOR(i) )
 260             if( k != e )
 261                 piet *= message( i, k.iter );
 262         message( j, _e ) = piet.partSum( IR(e) );
 263         _logZ += log( message(j,_e).normalize() );
 264     }
 265
 266     // Second pass
 267     for( size_t e = 0; e < nrIRs(); e++ ) {
 268         size_t i = nbIR(e)[0].node; // = _RTree[e].n1
 269         size_t j = nbIR(e)[1].node; // = _RTree[e].n2
 270         size_t _e = nbIR(e)[1].dual;
 271
 272         Factor piet = OR(i);
 273         foreach( const Neighbor &k, nbOR(i) )
 274             if( k != e )
 275                 piet *= message( i, k.iter );
 276         message( j, _e ) = piet.marginal( IR(e) );
 277     }
 278
 279     // Calculate beliefs
 280     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 281         Factor piet = OR(alpha);
 282         foreach( const Neighbor &k, nbOR(alpha) )
 283             piet *= message( alpha, k.iter );
 284         if( nrIRs() == 0 ) {
 285             _logZ += log( piet.normalize() );
 286             _Qa[alpha] = piet;
 287         } else if( alpha == nbIR(0)[0].node /*_RTree[0].n1*/ ) {
 288             _logZ += log( piet.normalize() );
 289             _Qa[alpha] = piet;
 290         } else
 291             _Qa[alpha] = piet.normalized();
 292     }
 293
 294     // Only for logZ (and for belief)...
 295     for( size_t beta = 0; beta < nrIRs(); beta++ )
 296         _Qb[beta] = _Qa[nbIR(beta)[0].node].marginal( IR(beta) );
 297 }
 298
 299
 300 double JTree::run() {
 301     if( props.updates == Properties::UpdateType::HUGIN )
 302         runHUGIN();
 303     else if( props.updates == Properties::UpdateType::SHSH )
 304         runShaferShenoy();
 305     return 0.0;
 306 }
 307
 308
 309 Real JTree::logZ() const {
 310     Real sum = 0.0;
 311     for( size_t beta = 0; beta < nrIRs(); beta++ )
 312         sum += IR(beta).c() * _Qb[beta].entropy();
 313     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 314         sum += OR(alpha).c() * _Qa[alpha].entropy();
 315         sum += (OR(alpha).log0() * _Qa[alpha]).totalSum();
 316     }
 317     return sum;
 318 }
 319
 320
 321
 322 size_t JTree::findEfficientTree( const VarSet& ns, DEdgeVec &Tree, size_t PreviousRoot ) const {
 323     // find new root clique (the one with maximal statespace overlap with ns)
 324     size_t maxval = 0, maxalpha = 0;
 325     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 326         size_t val = (ns & OR(alpha).vars()).states();
 327         if( val > maxval ) {
 328             maxval = val;
 329             maxalpha = alpha;
 330         }
 331     }
 332
 333 //  for( size_t e = 0; e < _RTree.size(); e++ )
 334 //      cout << OR(_RTree[e].n1).vars() << "->" << OR(_RTree[e].n2).vars() << ",  ";
 335 //  cout << endl;
 336     // grow new tree
 337     Graph oldTree;
 338     for( DEdgeVec::const_iterator e = _RTree.begin(); e != _RTree.end(); e++ )
 339         oldTree.insert( UEdge(e->n1, e->n2) );
 340     DEdgeVec newTree = GrowRootedTree( oldTree, maxalpha );
 341 //  cout << ns << ": ";
 342 //  for( size_t e = 0; e < newTree.size(); e++ )
 343 //      cout << OR(newTree[e].n1).vars() << "->" << OR(newTree[e].n2).vars() << ",  ";
 344 //  cout << endl;
 345
 346     // identify subtree that contains variables of ns which are not in the new root
 347     VarSet nsrem = ns / OR(maxalpha).vars();
 348 //  cout << "nsrem:" << nsrem << endl;
 349     set<DEdge> subTree;
 350     // for each variable in ns that is not in the root clique
 351     for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ ) {
 352         // find first occurence of *n in the tree, which is closest to the root
 353         size_t e = 0;
 354         for( ; e != newTree.size(); e++ ) {
 355             if( OR(newTree[e].n2).vars().contains( *n ) )
 356                 break;
 357         }
 358         assert( e != newTree.size() );
 359
 360         // track-back path to root and add edges to subTree
 361         subTree.insert( newTree[e] );
 362         size_t pos = newTree[e].n1;
 363         for( ; e > 0; e-- )
 364             if( newTree[e-1].n2 == pos ) {
 365                 subTree.insert( newTree[e-1] );
 366                 pos = newTree[e-1].n1;
 367             }
 368     }
 369     if( PreviousRoot != (size_t)-1 && PreviousRoot != maxalpha) {
 370         // find first occurence of PreviousRoot in the tree, which is closest to the new root
 371         size_t e = 0;
 372         for( ; e != newTree.size(); e++ ) {
 373             if( newTree[e].n2 == PreviousRoot )
 374                 break;
 375         }
 376         assert( e != newTree.size() );
 377
 378         // track-back path to root and add edges to subTree
 379         subTree.insert( newTree[e] );
 380         size_t pos = newTree[e].n1;
 381         for( ; e > 0; e-- )
 382             if( newTree[e-1].n2 == pos ) {
 383                 subTree.insert( newTree[e-1] );
 384                 pos = newTree[e-1].n1;
 385             }
 386     }
 387 //  cout << "subTree: " << endl;
 388 //  for( set<DEdge>::const_iterator sTi = subTree.begin(); sTi != subTree.end(); sTi++ )
 389 //      cout << OR(sTi->n1).vars() << "->" << OR(sTi->n2).vars() << ",  ";
 390 //  cout << endl;
 391
 392     // Resulting Tree is a reordered copy of newTree
 393     // First add edges in subTree to Tree
 394     Tree.clear();
 395     for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 396         if( subTree.count( *e ) ) {
 397             Tree.push_back( *e );
 398 //          cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 399         }
 400 //  cout << endl;
 401     // Then add edges pointing away from nsrem
 402     // FIXME
 403 /*  for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 404         for( set<DEdge>::const_iterator sTi = subTree.begin(); sTi != subTree.end(); sTi++ )
 405             if( *e != *sTi ) {
 406                 if( e->n1 == sTi->n1 || e->n1 == sTi->n2 ||
 407                     e->n2 == sTi->n1 || e->n2 == sTi->n2 ) {
 408                     Tree.push_back( *e );
 409 //                  cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 410                 }
 411             }*/
 412     // FIXME
 413 /*  for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 414         if( find( Tree.begin(), Tree.end(), *e) == Tree.end() ) {
 415             bool found = false;
 416             for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ )
 417                 if( (OR(e->n1).vars() && *n) ) {
 418                     found = true;
 419                     break;
 420                 }
 421             if( found ) {
 422                 Tree.push_back( *e );
 423                 cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 424             }
 425         }
 426     cout << endl;*/
 427     size_t subTreeSize = Tree.size();
 428     // Then add remaining edges
 429     for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 430         if( find( Tree.begin(), Tree.end(), *e ) == Tree.end() )
 431             Tree.push_back( *e );
 432
 433     return subTreeSize;
 434 }
 435
 436
 437 // Cutset conditioning
 438 // assumes that run() has been called already
 439 Factor JTree::calcMarginal( const VarSet& ns ) {
 440     vector<Factor>::const_iterator beta;
 441     for( beta = _Qb.begin(); beta != _Qb.end(); beta++ )
 442         if( beta->vars() >> ns )
 443             break;
 444     if( beta != _Qb.end() )
 445         return( beta->marginal(ns) );
 446     else {
 447         vector<Factor>::const_iterator alpha;
 448         for( alpha = _Qa.begin(); alpha != _Qa.end(); alpha++ )
 449             if( alpha->vars() >> ns )
 450                 break;
 451         if( alpha != _Qa.end() )
 452             return( alpha->marginal(ns) );
 453         else {
 454             // Find subtree to do efficient inference
 455             DEdgeVec T;
 456             size_t Tsize = findEfficientTree( ns, T );
 457
 458             // Find remaining variables (which are not in the new root)
 459             VarSet nsrem = ns / OR(T.front().n1).vars();
 460             Factor Pns (ns, 0.0);
 461
 462             // Save _Qa and _Qb on the subtree
 463             map<size_t,Factor> _Qa_old;
 464             map<size_t,Factor> _Qb_old;
 465             vector<size_t> b(Tsize, 0);
 466             for( size_t i = Tsize; (i--) != 0; ) {
 467                 size_t alpha1 = T[i].n1;
 468                 size_t alpha2 = T[i].n2;
 469                 size_t beta;
 470                 for( beta = 0; beta < nrIRs(); beta++ )
 471                     if( UEdge( _RTree[beta].n1, _RTree[beta].n2 ) == UEdge( alpha1, alpha2 ) )
 472                         break;
 473                 assert( beta != nrIRs() );
 474                 b[i] = beta;
 475
 476                 if( !_Qa_old.count( alpha1 ) )
 477                     _Qa_old[alpha1] = _Qa[alpha1];
 478                 if( !_Qa_old.count( alpha2 ) )
 479                     _Qa_old[alpha2] = _Qa[alpha2];
 480                 if( !_Qb_old.count( beta ) )
 481                     _Qb_old[beta] = _Qb[beta];
 482             }
 483
 484             // For all states of nsrem
 485             for( State s(nsrem); s.valid(); s++ ) {
 486                 // CollectEvidence
 487                 double logZ = 0.0;
 488                 for( size_t i = Tsize; (i--) != 0; ) {
 489                 // Make outer region T[i].n1 consistent with outer region T[i].n2
 490                 // IR(i) = seperator OR(T[i].n1) && OR(T[i].n2)
 491
 492                     for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ )
 493                         if( _Qa[T[i].n2].vars() >> *n ) {
 494                             Factor piet( *n, 0.0 );
 495                             piet[s(*n)] = 1.0;
 496                             _Qa[T[i].n2] *= piet;
 497                         }
 498
 499                     Factor new_Qb = _Qa[T[i].n2].partSum( IR( b[i] ) );
 500                     logZ += log(new_Qb.normalize());
 501                     _Qa[T[i].n1] *= new_Qb.divided_by( _Qb[b[i]] );
 502                     _Qb[b[i]] = new_Qb;
 503                 }
 504                 logZ += log(_Qa[T[0].n1].normalize());
 505
 506                 Factor piet( nsrem, 0.0 );
 507                 piet[s] = exp(logZ);
 508                 Pns += piet * _Qa[T[0].n1].partSum( ns / nsrem );      // OPTIMIZE ME
 509
 510                 // Restore clamped beliefs
 511                 for( map<size_t,Factor>::const_iterator alpha = _Qa_old.begin(); alpha != _Qa_old.end(); alpha++ )
 512                     _Qa[alpha->first] = alpha->second;
 513                 for( map<size_t,Factor>::const_iterator beta = _Qb_old.begin(); beta != _Qb_old.end(); beta++ )
 514                     _Qb[beta->first] = beta->second;
 515             }
 516
 517             return( Pns.normalized() );
 518         }
 519     }
 520 }
 521
 522
 523 // first return value is treewidth
 524 // second return value is number of states in largest clique
 525 pair<size_t,size_t> treewidth( const FactorGraph & fg ) {
 526     ClusterGraph _cg;
 527
 528     // Copy factors
 529     for( size_t I = 0; I < fg.nrFactors(); I++ )
 530         _cg.insert( fg.factor(I).vars() );
 531
 532     // Retain only maximal clusters
 533     _cg.eraseNonMaximal();
 534
 535     // Obtain elimination sequence
 536     vector<VarSet> ElimVec = _cg.VarElim_MinFill().eraseNonMaximal().toVector();
 537
 538     // Calculate treewidth
 539     size_t treewidth = 0;
 540     size_t nrstates = 0;
 541     for( size_t i = 0; i < ElimVec.size(); i++ ) {
 542         if( ElimVec[i].size() > treewidth )
 543             treewidth = ElimVec[i].size();
 544         if( ElimVec[i].states() > nrstates )
 545             nrstates = ElimVec[i].states();
 546     }
 547
 548     return pair<size_t,size_t>(treewidth, nrstates);
 549 }
 550
 551
 552 } // end of namespace dai