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         ClusterGraph _cg;
  53
  54         // Copy factors
  55         for( size_t I = 0; I < nrFactors(); I++ )
  56             _cg.insert( factor(I).vars() );
  57         if( Verbose() >= 3 )
  58             cout << "Initial clusters: " << _cg << endl;
  59
  60         // Retain only maximal clusters
  61         _cg.eraseNonMaximal();
  62         if( Verbose() >= 3 )
  63             cout << "Maximal clusters: " << _cg << endl;
  64
  65         vector<VarSet> ElimVec = _cg.VarElim_MinFill().eraseNonMaximal().toVector();
  66         if( Verbose() >= 3 ) {
  67             cout << "VarElim_MinFill result: {" << endl;
  68             for( size_t i = 0; i < ElimVec.size(); i++ ) {
  69                 if( i != 0 )
  70                     cout << ", ";
  71                 cout << ElimVec[i];
  72             }
  73             cout << "}" << endl;
  74         }
  75
  76         GenerateJT( ElimVec );
  77     }
  78 }
  79
  80
  81 void JTree::GenerateJT( const vector<VarSet> &Cliques ) {
  82     // Construct a weighted graph (each edge is weighted with the cardinality
  83     // of the intersection of the nodes, where the nodes are the elements of
  84     // Cliques).
  85     WeightedGraph<int> JuncGraph;
  86     for( size_t i = 0; i < Cliques.size(); i++ )
  87         for( size_t j = i+1; j < Cliques.size(); j++ ) {
  88             size_t w = (Cliques[i] & Cliques[j]).size();
  89             JuncGraph[UEdge(i,j)] = w;
  90         }
  91
  92     // Construct maximal spanning tree using Prim's algorithm
  93     _RTree = MaxSpanningTreePrim( JuncGraph );
  94
  95     // Construct corresponding region graph
  96
  97     // Create outer regions
  98     ORs().reserve( Cliques.size() );
  99     for( size_t i = 0; i < Cliques.size(); i++ )
 100         ORs().push_back( FRegion( Factor(Cliques[i], 1.0), 1.0 ) );
 101
 102     // For each factor, find an outer region that subsumes that factor.
 103     // Then, multiply the outer region with that factor.
 104     for( size_t I = 0; I < nrFactors(); I++ ) {
 105         size_t alpha;
 106         for( alpha = 0; alpha < nr_ORs(); alpha++ )
 107             if( OR(alpha).vars() >> factor(I).vars() ) {
 108 //              OR(alpha) *= factor(I);
 109                 _fac2OR[I] = alpha;
 110                 break;
 111             }
 112         assert( alpha != nr_ORs() );
 113     }
 114     RecomputeORs();
 115
 116     // Create inner regions and edges
 117     IRs().reserve( _RTree.size() );
 118     Redges().reserve( 2 * _RTree.size() );
 119     for( size_t i = 0; i < _RTree.size(); i++ ) {
 120         Redges().push_back( R_edge_t( _RTree[i].n1, IRs().size() ) );
 121         Redges().push_back( R_edge_t( _RTree[i].n2, IRs().size() ) );
 122         // inner clusters have counting number -1
 123         IRs().push_back( Region( Cliques[_RTree[i].n1] & Cliques[_RTree[i].n2], -1.0 ) );
 124     }
 125
 126     // Regenerate BipartiteGraph internals
 127     Regenerate();
 128
 129     // Create messages and beliefs
 130     _Qa.clear();
 131     _Qa.reserve( nr_ORs() );
 132     for( size_t alpha = 0; alpha < nr_ORs(); alpha++ )
 133         _Qa.push_back( OR(alpha) );
 134
 135     _Qb.clear();
 136     _Qb.reserve( nr_IRs() );
 137     for( size_t beta = 0; beta < nr_IRs(); beta++ )
 138         _Qb.push_back( Factor( IR(beta), 1.0 ) );
 139
 140     _mes.clear();
 141     _mes.reserve( nr_Redges() );
 142     for( size_t e = 0; e < nr_Redges(); e++ )
 143         _mes.push_back( Factor( IR(Redge(e).second), 1.0 ) );
 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 < nr_IRs(); beta++ )
 182         result.push_back( _Qb[beta] );
 183     for( size_t alpha = 0; alpha < nr_ORs(); 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 < nr_ORs(); alpha++ )
 197         _Qa[alpha] = OR(alpha);
 198
 199     for( size_t beta = 0; beta < nr_IRs(); 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 < nr_ORs(); 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 = _RTree.size(); (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 = _RTree[e].n2;
 241         size_t j = _RTree[e].n1;
 242
 243         Factor piet = OR(i);
 244         for( R_nb_cit k = nbOR(i).begin(); k != nbOR(i).end(); k++ )
 245             if( *k != e )
 246                 piet *= message( i, *k );
 247         message( j, e ) = piet.part_sum( IR(e) );
 248         _logZ += log( message(j,e).normalize( Prob::NORMPROB ) );
 249     }
 250
 251     // Second pass
 252     for( size_t e = 0; e < _RTree.size(); e++ ) {
 253         size_t i = _RTree[e].n1;
 254         size_t j = _RTree[e].n2;
 255
 256         Factor piet = OR(i);
 257         for( R_nb_cit k = nbOR(i).begin(); k != nbOR(i).end(); k++ )
 258             if( *k != e )
 259                 piet *= message( i, *k );
 260         message( j, e ) = piet.marginal( IR(e) );
 261     }
 262
 263     // Calculate beliefs
 264     for( size_t alpha = 0; alpha < nr_ORs(); alpha++ ) {
 265         Factor piet = OR(alpha);
 266         for( R_nb_cit k = nbOR(alpha).begin(); k != nbOR(alpha).end(); k++ )
 267             piet *= message( alpha, *k );
 268         if( _RTree.empty() ) {
 269             _logZ += log( piet.normalize( Prob::NORMPROB ) );
 270             _Qa[alpha] = piet;
 271         } else if( alpha == _RTree[0].n1 ) {
 272             _logZ += log( piet.normalize( Prob::NORMPROB ) );
 273             _Qa[alpha] = piet;
 274         } else
 275             _Qa[alpha] = piet.normalized( Prob::NORMPROB );
 276     }
 277
 278     // Only for logZ (and for belief)...
 279     for( size_t beta = 0; beta < nr_IRs(); beta++ )
 280         _Qb[beta] = _Qa[nbIR(beta)[0]].marginal( IR(beta) );
 281 }
 282
 283
 284 double JTree::run() {
 285     if( Updates() == UpdateType::HUGIN )
 286         runHUGIN();
 287     else if( Updates() == UpdateType::SHSH )
 288         runShaferShenoy();
 289     return 0.0;
 290 }
 291
 292
 293 Complex JTree::logZ() const {
 294     Complex sum = 0.0;
 295     for( size_t beta = 0; beta < nr_IRs(); beta++ )
 296         sum += Complex(IR(beta).c()) * _Qb[beta].entropy();
 297     for( size_t alpha = 0; alpha < nr_ORs(); alpha++ ) {
 298         sum += Complex(OR(alpha).c()) * _Qa[alpha].entropy();
 299         sum += (OR(alpha).log0() * _Qa[alpha]).totalSum();
 300     }
 301     return sum;
 302 }
 303
 304
 305
 306 size_t JTree::findEfficientTree( const VarSet& ns, DEdgeVec &Tree, size_t PreviousRoot ) const {
 307     // find new root clique (the one with maximal statespace overlap with ns)
 308     size_t maxval = 0, maxalpha = 0;
 309     for( size_t alpha = 0; alpha < nr_ORs(); alpha++ ) {
 310         size_t val = (ns & OR(alpha).vars()).stateSpace();
 311         if( val > maxval ) {
 312             maxval = val;
 313             maxalpha = alpha;
 314         }
 315     }
 316
 317 //  for( size_t e = 0; e < _RTree.size(); e++ )
 318 //      cout << OR(_RTree[e].n1).vars() << "->" << OR(_RTree[e].n2).vars() << ",  ";
 319 //  cout << endl;
 320     // grow new tree
 321     Graph oldTree;
 322     for( DEdgeVec::const_iterator e = _RTree.begin(); e != _RTree.end(); e++ )
 323         oldTree.insert( UEdge(e->n1, e->n2) );
 324     DEdgeVec newTree = GrowRootedTree( oldTree, maxalpha );
 325 //  cout << ns << ": ";
 326 //  for( size_t e = 0; e < newTree.size(); e++ )
 327 //      cout << OR(newTree[e].n1).vars() << "->" << OR(newTree[e].n2).vars() << ",  ";
 328 //  cout << endl;
 329
 330     // identify subtree that contains variables of ns which are not in the new root
 331     VarSet nsrem = ns / OR(maxalpha).vars();
 332 //  cout << "nsrem:" << nsrem << endl;
 333     set<DEdge> subTree;
 334     // for each variable in ns that is not in the root clique
 335     for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ ) {
 336         // find first occurence of *n in the tree, which is closest to the root
 337         size_t e = 0;
 338         for( ; e != newTree.size(); e++ ) {
 339             if( OR(newTree[e].n2).vars() && *n )
 340                 break;
 341         }
 342         assert( e != newTree.size() );
 343
 344         // track-back path to root and add edges to subTree
 345         subTree.insert( newTree[e] );
 346         size_t pos = newTree[e].n1;
 347         for( ; e > 0; e-- )
 348             if( newTree[e-1].n2 == pos ) {
 349                 subTree.insert( newTree[e-1] );
 350                 pos = newTree[e-1].n1;
 351             }
 352     }
 353     if( PreviousRoot != (size_t)-1 && PreviousRoot != maxalpha) {
 354         // find first occurence of PreviousRoot in the tree, which is closest to the new root
 355         size_t e = 0;
 356         for( ; e != newTree.size(); e++ ) {
 357             if( newTree[e].n2 == PreviousRoot )
 358                 break;
 359         }
 360         assert( e != newTree.size() );
 361
 362         // track-back path to root and add edges to subTree
 363         subTree.insert( newTree[e] );
 364         size_t pos = newTree[e].n1;
 365         for( ; e > 0; e-- )
 366             if( newTree[e-1].n2 == pos ) {
 367                 subTree.insert( newTree[e-1] );
 368                 pos = newTree[e-1].n1;
 369             }
 370     }
 371 //  cout << "subTree: " << endl;
 372 //  for( set<DEdge>::const_iterator sTi = subTree.begin(); sTi != subTree.end(); sTi++ )
 373 //      cout << OR(sTi->n1).vars() << "->" << OR(sTi->n2).vars() << ",  ";
 374 //  cout << endl;
 375
 376     // Resulting Tree is a reordered copy of newTree
 377     // First add edges in subTree to Tree
 378     Tree.clear();
 379     for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 380         if( subTree.count( *e ) ) {
 381             Tree.push_back( *e );
 382 //          cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 383         }
 384 //  cout << endl;
 385     // Then add edges pointing away from nsrem
 386     // FIXME
 387 /*  for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 388         for( set<DEdge>::const_iterator sTi = subTree.begin(); sTi != subTree.end(); sTi++ )
 389             if( *e != *sTi ) {
 390                 if( e->n1 == sTi->n1 || e->n1 == sTi->n2 ||
 391                     e->n2 == sTi->n1 || e->n2 == sTi->n2 ) {
 392                     Tree.push_back( *e );
 393 //                  cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 394                 }
 395             }*/
 396     // FIXME
 397 /*  for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 398         if( find( Tree.begin(), Tree.end(), *e) == Tree.end() ) {
 399             bool found = false;
 400             for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++ )
 401                 if( (OR(e->n1).vars() && *n) ) {
 402                     found = true;
 403                     break;
 404                 }
 405             if( found ) {
 406                 Tree.push_back( *e );
 407                 cout << OR(e->n1).vars() << "->" << OR(e->n2).vars() << ",  ";
 408             }
 409         }
 410     cout << endl;*/
 411     size_t subTreeSize = Tree.size();
 412     // Then add remaining edges
 413     for( DEdgeVec::const_iterator e = newTree.begin(); e != newTree.end(); e++ )
 414         if( find( Tree.begin(), Tree.end(), *e ) == Tree.end() )
 415             Tree.push_back( *e );
 416
 417     return subTreeSize;
 418 }
 419
 420
 421 // Cutset conditioning
 422 // assumes that run() has been called already
 423 Factor JTree::calcMarginal( const VarSet& ns ) {
 424     vector<Factor>::const_iterator beta;
 425     for( beta = _Qb.begin(); beta != _Qb.end(); beta++ )
 426         if( beta->vars() >> ns )
 427             break;
 428     if( beta != _Qb.end() )
 429         return( beta->marginal(ns) );
 430     else {
 431         vector<Factor>::const_iterator alpha;
 432         for( alpha = _Qa.begin(); alpha != _Qa.end(); alpha++ )
 433             if( alpha->vars() >> ns )
 434                 break;
 435         if( alpha != _Qa.end() )
 436             return( alpha->marginal(ns) );
 437         else {
 438             // Find subtree to do efficient inference
 439             DEdgeVec T;
 440             size_t Tsize = findEfficientTree( ns, T );
 441
 442             // Find remaining variables (which are not in the new root)
 443             VarSet nsrem = ns / OR(T.front().n1).vars();
 444             Factor Pns (ns, 0.0);
 445
 446             multind mi( nsrem );
 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 < nr_IRs(); beta++ )
 457                     if( UEdge( _RTree[beta].n1, _RTree[beta].n2 ) == UEdge( alpha1, alpha2 ) )
 458                         break;
 459                 assert( beta != nr_IRs() );
 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( size_t j = 0; j < mi.max(); j++ ) {
 472                 vector<size_t> vi = mi.vi( j );
 473
 474                 // CollectEvidence
 475                 double logZ = 0.0;
 476                 for( size_t i = Tsize; (i--) != 0; ) {
 477             //      Make outer region T[i].n1 consistent with outer region T[i].n2
 478             //      IR(i) = seperator OR(T[i].n1) && OR(T[i].n2)
 479
 480                     size_t k = 0;
 481                     for( VarSet::const_iterator n = nsrem.begin(); n != nsrem.end(); n++, k++ )
 482                         if( _Qa[T[i].n2].vars() >> *n ) {
 483                             Factor piet( *n, 0.0 );
 484                             piet[vi[k]] = 1.0;
 485                             _Qa[T[i].n2] *= piet;
 486                         }
 487
 488                     Factor new_Qb = _Qa[T[i].n2].part_sum( IR( b[i] ) );
 489                     logZ += log(new_Qb.normalize( Prob::NORMPROB ));
 490                     _Qa[T[i].n1] *= new_Qb.divided_by( _Qb[b[i]] );
 491                     _Qb[b[i]] = new_Qb;
 492                 }
 493                 logZ += log(_Qa[T[0].n1].normalize( Prob::NORMPROB ));
 494
 495                 Factor piet( nsrem, 0.0 );
 496                 piet[j] = exp(logZ);
 497                 Pns += piet * _Qa[T[0].n1].part_sum( ns / nsrem );      // OPTIMIZE ME
 498
 499                 // Restore clamped beliefs
 500                 for( map<size_t,Factor>::const_iterator alpha = _Qa_old.begin(); alpha != _Qa_old.end(); alpha++ )
 501                     _Qa[alpha->first] = alpha->second;
 502                 for( map<size_t,Factor>::const_iterator beta = _Qb_old.begin(); beta != _Qb_old.end(); beta++ )
 503                     _Qb[beta->first] = beta->second;
 504             }
 505
 506             return( Pns.normalized(Prob::NORMPROB) );
 507         }
 508     }
 509 }
 510
 511
 512 } // end of namespace dai