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 bool JTree::checkProperties() {
  36     if (!HasProperty("verbose") )
  37         return false;
  38     if( !HasProperty("updates") )
  39         return false;
  40
  41     ConvertPropertyTo<size_t>("verbose");
  42     ConvertPropertyTo<UpdateType>("updates");
  43
  44     return true;
  45 }
  46
  47
  48 JTree::JTree( const FactorGraph &fg, const Properties &opts, bool automatic ) : DAIAlgRG(fg, opts), _RTree(), _Qa(), _Qb(), _mes(), _logZ() {
  49     assert( checkProperties() );
  50
  51     if( automatic ) {
  52         // Copy VarSets of factors
  53         vector<VarSet> cl;
  54         cl.reserve( fg.nrFactors() );
  55         for( size_t I = 0; I < nrFactors(); I++ )
  56             cl.push_back( factor(I).vars() );
  57         ClusterGraph _cg( cl );
  58
  59         if( Verbose() >= 3 )
  60             cout << "Initial clusters: " << _cg << endl;
  61
  62         // Retain only maximal clusters
  63         _cg.eraseNonMaximal();
  64         if( Verbose() >= 3 )
  65             cout << "Maximal clusters: " << _cg << endl;
  66
  67         vector<VarSet> ElimVec = _cg.VarElim_MinFill().eraseNonMaximal().toVector();
  68         if( Verbose() >= 3 )
  69             cout << "VarElim_MinFill result: " << ElimVec << endl;
  70
  71         GenerateJT( ElimVec );
  72     }
  73 }
  74
  75
  76 void JTree::GenerateJT( const std::vector<VarSet> &Cliques ) {
  77     // Construct a weighted graph (each edge is weighted with the cardinality
  78     // of the intersection of the nodes, where the nodes are the elements of
  79     // Cliques).
  80     WeightedGraph<int> JuncGraph;
  81     for( size_t i = 0; i < Cliques.size(); i++ )
  82         for( size_t j = i+1; j < Cliques.size(); j++ ) {
  83             size_t w = (Cliques[i] & Cliques[j]).size();
  84             JuncGraph[UEdge(i,j)] = w;
  85         }
  86
  87     // Construct maximal spanning tree using Prim's algorithm
  88     _RTree = MaxSpanningTreePrims( JuncGraph );
  89
  90     // Construct corresponding region graph
  91
  92     // Create outer regions
  93     ORs.reserve( Cliques.size() );
  94     for( size_t i = 0; i < Cliques.size(); i++ )
  95         ORs.push_back( FRegion( Factor(Cliques[i], 1.0), 1.0 ) );
  96
  97     // For each factor, find an outer region that subsumes that factor.
  98     // Then, multiply the outer region with that factor.
  99     for( size_t I = 0; I < nrFactors(); I++ ) {
 100         size_t alpha;
 101         for( alpha = 0; alpha < nrORs(); alpha++ )
 102             if( OR(alpha).vars() >> factor(I).vars() ) {
 103 //              OR(alpha) *= factor(I);
 104                 fac2OR.push_back( alpha );
 105                 break;
 106             }
 107         assert( alpha != nrORs() );
 108     }
 109     RecomputeORs();
 110
 111     // Create inner regions and edges
 112     IRs.reserve( _RTree.size() );
 113     vector<Edge> edges;
 114     edges.reserve( 2 * _RTree.size() );
 115     for( size_t i = 0; i < _RTree.size(); i++ ) {
 116         edges.push_back( Edge( _RTree[i].n1, nrIRs() ) );
 117         edges.push_back( Edge( _RTree[i].n2, nrIRs() ) );
 118         // inner clusters have counting number -1
 119         IRs.push_back( Region( Cliques[_RTree[i].n1] & Cliques[_RTree[i].n2], -1.0 ) );
 120     }
 121
 122     // create bipartite graph
 123     G.create( nrORs(), nrIRs(), edges.begin(), edges.end() );
 124
 125     // Create messages and beliefs
 126     _Qa.clear();
 127     _Qa.reserve( nrORs() );
 128     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 129         _Qa.push_back( OR(alpha) );
 130
 131     _Qb.clear();
 132     _Qb.reserve( nrIRs() );
 133     for( size_t beta = 0; beta < nrIRs(); beta++ )
 134         _Qb.push_back( Factor( IR(beta), 1.0 ) );
 135
 136     _mes.clear();
 137     _mes.reserve( nrORs() );
 138     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 139         _mes.push_back( vector<Factor>() );
 140         _mes[alpha].reserve( nbOR(alpha).size() );
 141         foreach( const Neighbor &beta, nbOR(alpha) )
 142             _mes[alpha].push_back( Factor( IR(beta), 1.0 ) );
 143     }
 144
 145     // Check counting numbers
 146     Check_Counting_Numbers();
 147
 148     if( Verbose() >= 3 ) {
 149         cout << "Resulting regiongraph: " << *this << endl;
 150     }
 151 }
 152
 153
 154 string JTree::identify() const {
 155     stringstream result (stringstream::out);
 156     result << Name << GetProperties();
 157     return result.str();
 158 }
 159
 160
 161 Factor JTree::belief( const VarSet &ns ) const {
 162     vector<Factor>::const_iterator beta;
 163     for( beta = _Qb.begin(); beta != _Qb.end(); beta++ )
 164         if( beta->vars() >> ns )
 165             break;
 166     if( beta != _Qb.end() )
 167         return( beta->marginal(ns) );
 168     else {
 169         vector<Factor>::const_iterator alpha;
 170         for( alpha = _Qa.begin(); alpha != _Qa.end(); alpha++ )
 171             if( alpha->vars() >> ns )
 172                 break;
 173         assert( alpha != _Qa.end() );
 174         return( alpha->marginal(ns) );
 175     }
 176 }
 177
 178
 179 vector<Factor> JTree::beliefs() const {
 180     vector<Factor> result;
 181     for( size_t beta = 0; beta < nrIRs(); beta++ )
 182         result.push_back( _Qb[beta] );
 183     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 184         result.push_back( _Qa[alpha] );
 185     return result;
 186 }
 187
 188
 189 Factor JTree::belief( const Var &n ) const {
 190     return belief( (VarSet)n );
 191 }
 192
 193
 194 // Needs no init
 195 void JTree::runHUGIN() {
 196     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 197         _Qa[alpha] = OR(alpha);
 198
 199     for( size_t beta = 0; beta < nrIRs(); beta++ )
 200         _Qb[beta].fill( 1.0 );
 201
 202     // CollectEvidence
 203     _logZ = 0.0;
 204     for( size_t i = _RTree.size(); (i--) != 0; ) {
 205 //      Make outer region _RTree[i].n1 consistent with outer region _RTree[i].n2
 206 //      IR(i) = seperator OR(_RTree[i].n1) && OR(_RTree[i].n2)
 207         Factor new_Qb = _Qa[_RTree[i].n2].part_sum( IR( i ) );
 208         _logZ += log(new_Qb.normalize( Prob::NORMPROB ));
 209         _Qa[_RTree[i].n1] *= new_Qb.divided_by( _Qb[i] );
 210         _Qb[i] = new_Qb;
 211     }
 212     if( _RTree.empty() )
 213         _logZ += log(_Qa[0].normalize( Prob::NORMPROB ) );
 214     else
 215         _logZ += log(_Qa[_RTree[0].n1].normalize( Prob::NORMPROB ));
 216
 217     // DistributeEvidence
 218     for( size_t i = 0; i < _RTree.size(); i++ ) {
 219 //      Make outer region _RTree[i].n2 consistent with outer region _RTree[i].n1
 220 //      IR(i) = seperator OR(_RTree[i].n1) && OR(_RTree[i].n2)
 221         Factor new_Qb = _Qa[_RTree[i].n1].marginal( IR( i ) );
 222         _Qa[_RTree[i].n2] *= new_Qb.divided_by( _Qb[i] );
 223         _Qb[i] = new_Qb;
 224     }
 225
 226     // Normalize
 227     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 228         _Qa[alpha].normalize( Prob::NORMPROB );
 229 }
 230
 231
 232 // Really needs no init! Initial messages can be anything.
 233 void JTree::runShaferShenoy() {
 234     // First pass
 235     _logZ = 0.0;
 236     for( size_t e = nrIRs(); (e--) != 0; ) {
 237         // send a message from _RTree[e].n2 to _RTree[e].n1
 238         // or, actually, from the seperator IR(e) to _RTree[e].n1
 239
 240         size_t i = nbIR(e)[1].node; // = _RTree[e].n2
 241         size_t j = nbIR(e)[0].node; // = _RTree[e].n1
 242         size_t _e = nbIR(e)[0].dual;
 243
 244         Factor piet = OR(i);
 245         foreach( const Neighbor &k, nbOR(i) )
 246             if( k != e )
 247                 piet *= message( i, k.iter );
 248         message( j, _e ) = piet.part_sum( IR(e) );
 249         _logZ += log( message(j,_e).normalize( Prob::NORMPROB ) );
 250     }
 251
 252     // Second pass
 253     for( size_t e = 0; e < nrIRs(); e++ ) {
 254         size_t i = nbIR(e)[0].node; // = _RTree[e].n1
 255         size_t j = nbIR(e)[1].node; // = _RTree[e].n2
 256         size_t _e = nbIR(e)[1].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.marginal( IR(e) );
 263     }
 264
 265     // Calculate beliefs
 266     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 267         Factor piet = OR(alpha);
 268         foreach( const Neighbor &k, nbOR(alpha) )
 269             piet *= message( alpha, k.iter );
 270         if( nrIRs() == 0 ) {
 271             _logZ += log( piet.normalize( Prob::NORMPROB ) );
 272             _Qa[alpha] = piet;
 273         } else if( alpha == nbIR(0)[0].node /*_RTree[0].n1*/ ) {
 274             _logZ += log( piet.normalize( Prob::NORMPROB ) );
 275             _Qa[alpha] = piet;
 276         } else
 277             _Qa[alpha] = piet.normalized( Prob::NORMPROB );
 278     }
 279
 280     // Only for logZ (and for belief)...
 281     for( size_t beta = 0; beta < nrIRs(); beta++ )
 282         _Qb[beta] = _Qa[nbIR(beta)[0].node].marginal( IR(beta) );
 283 }
 284
 285
 286 double JTree::run() {
 287     if( Updates() == UpdateType::HUGIN )
 288         runHUGIN();
 289     else if( Updates() == UpdateType::SHSH )
 290         runShaferShenoy();
 291     return 0.0;
 292 }
 293
 294
 295 Complex JTree::logZ() const {
 296     Complex sum = 0.0;
 297     for( size_t beta = 0; beta < nrIRs(); beta++ )
 298         sum += Complex(IR(beta).c()) * _Qb[beta].entropy();
 299     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 300         sum += Complex(OR(alpha).c()) * _Qa[alpha].entropy();
 301         sum += (OR(alpha).log0() * _Qa[alpha]).totalSum();
 302     }
 303     return sum;
 304 }
 305
 306
 307
 308 size_t JTree::findEfficientTree( const VarSet& ns, DEdgeVec &Tree, size_t PreviousRoot ) const {
 309     // find new root clique (the one with maximal statespace overlap with ns)
 310     size_t maxval = 0, maxalpha = 0;
 311     for( size_t alpha = 0; alpha < nrORs(); alpha++ ) {
 312         size_t val = (ns & OR(alpha).vars()).states();
 313         if( val > maxval ) {
 314             maxval = val;
 315             maxalpha = alpha;
 316         }
 317     }
 318
 319 //  for( size_t e = 0; e < _RTree.size(); e++ )
 320 //      cout << OR(_RTree[e].n1).vars() << "->" << OR(_RTree[e].n2).vars() << ",  ";
 321 //  cout << endl;
 322     // grow new tree
 323     Graph oldTree;
 324     for( DEdgeVec::const_iterator e = _RTree.begin(); e != _RTree.end(); e++ )
 325         oldTree.insert( UEdge(e->n1, e->n2) );
 326     DEdgeVec newTree = GrowRootedTree( oldTree, maxalpha );
 327 //  cout << ns << ": ";
 328 //  for( size_t e = 0; e < newTree.size(); e++ )
 329 //      cout << OR(newTree[e].n1).vars() << "->" << OR(newTree[e].n2).vars() << ",  ";
 330 //  cout << endl;
 331
 332     // identify subtree that contains variables of ns which are not in the new root
 333     VarSet nsrem = ns / OR(maxalpha).vars();
 334 //  cout << "nsrem:" << nsrem << endl;
 335     set<DEdge> subTree;
 336     // for each variable in ns that is not in the root clique
 337     for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ ) {
 338         // find first occurence of *n in the tree, which is closest to the root
 339         size_t e = 0;
 340         for( ; e != newTree.size(); e++ ) {
 341             if( OR(newTree[e].n2).vars() && *n )
 342                 break;
 343         }
 344         assert( e != newTree.size() );
 345
 346         // track-back path to root and add edges to subTree
 347         subTree.insert( newTree[e] );
 348         size_t pos = newTree[e].n1;
 349         for( ; e > 0; e-- )
 350             if( newTree[e-1].n2 == pos ) {
 351                 subTree.insert( newTree[e-1] );
 352                 pos = newTree[e-1].n1;
 353             }
 354     }
 355     if( PreviousRoot != (size_t)-1 && PreviousRoot != maxalpha) {
 356         // find first occurence of PreviousRoot in the tree, which is closest to the new root
 357         size_t e = 0;
 358         for( ; e != newTree.size(); e++ ) {
 359             if( newTree[e].n2 == PreviousRoot )
 360                 break;
 361         }
 362         assert( e != newTree.size() );
 363
 364         // track-back path to root and add edges to subTree
 365         subTree.insert( newTree[e] );
 366         size_t pos = newTree[e].n1;
 367         for( ; e > 0; e-- )
 368             if( newTree[e-1].n2 == pos ) {
 369                 subTree.insert( newTree[e-1] );
 370                 pos = newTree[e-1].n1;
 371             }
 372     }
 373 //  cout << "subTree: " << endl;
 374 //  for( set<DEdge>::const_iterator sTi = subTree.begin(); sTi != subTree.end(); sTi++ )
 375 //      cout << OR(sTi->n1).vars() << "->" << OR(sTi->n2).vars() << ",  ";
 376 //  cout << endl;
 377
 378     // Resulting Tree is a reordered copy of newTree
 379     // First add edges in subTree to Tree
 380     Tree.clear();
 381     for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 382         if( subTree.count( *e ) ) {
 383             Tree.push_back( *e );
 384 //          cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 385         }
 386 //  cout << endl;
 387     // Then add edges pointing away from nsrem
 388     // FIXME
 389 /*  for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 390         for( set<DEdge>::const_iterator sTi = subTree.begin(); sTi != subTree.end(); sTi++ )
 391             if( *e != *sTi ) {
 392                 if( e->n1 == sTi->n1 || e->n1 == sTi->n2 ||
 393                     e->n2 == sTi->n1 || e->n2 == sTi->n2 ) {
 394                     Tree.push_back( *e );
 395 //                  cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 396                 }
 397             }*/
 398     // FIXME
 399 /*  for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 400         if( find( Tree.begin(), Tree.end(), *e) == Tree.end() ) {
 401             bool found = false;
 402             for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ )
 403                 if( (OR(e->n1).vars() && *n) ) {
 404                     found = true;
 405                     break;
 406                 }
 407             if( found ) {
 408                 Tree.push_back( *e );
 409                 cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 410             }
 411         }
 412     cout << endl;*/
 413     size_t subTreeSize = Tree.size();
 414     // Then add remaining edges
 415     for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 416         if( find( Tree.begin(), Tree.end(), *e ) == Tree.end() )
 417             Tree.push_back( *e );
 418
 419     return subTreeSize;
 420 }
 421
 422
 423 // Cutset conditioning
 424 // assumes that run() has been called already
 425 Factor JTree::calcMarginal( const VarSet& ns ) {
 426     vector<Factor>::const_iterator beta;
 427     for( beta = _Qb.begin(); beta != _Qb.end(); beta++ )
 428         if( beta->vars() >> ns )
 429             break;
 430     if( beta != _Qb.end() )
 431         return( beta->marginal(ns) );
 432     else {
 433         vector<Factor>::const_iterator alpha;
 434         for( alpha = _Qa.begin(); alpha != _Qa.end(); alpha++ )
 435             if( alpha->vars() >> ns )
 436                 break;
 437         if( alpha != _Qa.end() )
 438             return( alpha->marginal(ns) );
 439         else {
 440             // Find subtree to do efficient inference
 441             DEdgeVec T;
 442             size_t Tsize = findEfficientTree( ns, T );
 443
 444             // Find remaining variables (which are not in the new root)
 445             VarSet nsrem = ns / OR(T.front().n1).vars();
 446             Factor Pns (ns, 0.0);
 447
 448             // Save _Qa and _Qb on the subtree
 449             map<size_t,Factor> _Qa_old;
 450             map<size_t,Factor> _Qb_old;
 451             vector<size_t> b(Tsize, 0);
 452             for( size_t i = Tsize; (i--) != 0; ) {
 453                 size_t alpha1 = T[i].n1;
 454                 size_t alpha2 = T[i].n2;
 455                 size_t beta;
 456                 for( beta = 0; beta < nrIRs(); beta++ )
 457                     if( UEdge( _RTree[beta].n1, _RTree[beta].n2 ) == UEdge( alpha1, alpha2 ) )
 458                         break;
 459                 assert( beta != nrIRs() );
 460                 b[i] = beta;
 461
 462                 if( !_Qa_old.count( alpha1 ) )
 463                     _Qa_old[alpha1] = _Qa[alpha1];
 464                 if( !_Qa_old.count( alpha2 ) )
 465                     _Qa_old[alpha2] = _Qa[alpha2];
 466                 if( !_Qb_old.count( beta ) )
 467                     _Qb_old[beta] = _Qb[beta];
 468             }
 469
 470             // For all states of nsrem
 471             for( State s(nsrem); s.valid(); s++ ) {
 472
 473                 // CollectEvidence
 474                 double logZ = 0.0;
 475                 for( size_t i = Tsize; (i--) != 0; ) {
 476                 // Make outer region T[i].n1 consistent with outer region T[i].n2
 477                 // IR(i) = seperator OR(T[i].n1) && OR(T[i].n2)
 478
 479                     for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ )
 480                         if( _Qa[T[i].n2].vars() >> *n ) {
 481                             Factor piet( *n, 0.0 );
 482                             piet[s(*n)] = 1.0;
 483                             _Qa[T[i].n2] *= piet;
 484                         }
 485
 486                     Factor new_Qb = _Qa[T[i].n2].part_sum( IR( b[i] ) );
 487                     logZ += log(new_Qb.normalize( Prob::NORMPROB ));
 488                     _Qa[T[i].n1] *= new_Qb.divided_by( _Qb[b[i]] );
 489                     _Qb[b[i]] = new_Qb;
 490                 }
 491                 logZ += log(_Qa[T[0].n1].normalize( Prob::NORMPROB ));
 492
 493                 Factor piet( nsrem, 0.0 );
 494                 piet[s] = exp(logZ);
 495                 Pns += piet * _Qa[T[0].n1].part_sum( ns / nsrem );      // OPTIMIZE ME
 496
 497                 // Restore clamped beliefs
 498                 for( map<size_t,Factor>::const_iterator alpha = _Qa_old.begin(); alpha != _Qa_old.end(); alpha++ )
 499                     _Qa[alpha->first] = alpha->second;
 500                 for( map<size_t,Factor>::const_iterator beta = _Qb_old.begin(); beta != _Qb_old.end(); beta++ )
 501                     _Qb[beta->first] = beta->second;
 502             }
 503
 504             return( Pns.normalized(Prob::NORMPROB) );
 505         }
 506     }
 507 }
 508
 509
 510 } // end of namespace dai