src/treeep.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 <fstream>
  24 #include <vector>
  25 #include <dai/jtree.h>
  26 #include <dai/treeep.h>
  27 #include <dai/util.h>
  28 #include <dai/diffs.h>
  29
  30
  31 namespace dai {
  32
  33
  34 using namespace std;
  35
  36
  37 const char *TreeEP::Name = "TREEEP";
  38
  39
  40 bool TreeEP::checkProperties() {
  41     if( !HasProperty("type") )
  42         return false;
  43     if( !HasProperty("tol") )
  44         return false;
  45     if (!HasProperty("maxiter") )
  46         return false;
  47     if (!HasProperty("verbose") )
  48         return false;
  49
  50     ConvertPropertyTo<TypeType>("type");
  51     ConvertPropertyTo<double>("tol");
  52     ConvertPropertyTo<size_t>("maxiter");
  53     ConvertPropertyTo<size_t>("verbose");
  54
  55     return true;
  56 }
  57
  58
  59 TreeEPSubTree::TreeEPSubTree( const DEdgeVec &subRTree, const DEdgeVec &jt_RTree, const std::vector<Factor> &jt_Qa, const std::vector<Factor> &jt_Qb, const Factor *I ) : _Qa(), _Qb(), _RTree(), _a(), _b(), _I(I), _ns(), _nsrem(), _logZ(0.0) {
  60     _ns = _I->vars();
  61
  62     // Make _Qa, _Qb, _a and _b corresponding to the subtree
  63     _b.reserve( subRTree.size() );
  64     _Qb.reserve( subRTree.size() );
  65     _RTree.reserve( subRTree.size() );
  66     for( size_t i = 0; i < subRTree.size(); i++ ) {
  67         size_t alpha1 = subRTree[i].n1;     // old index 1
  68         size_t alpha2 = subRTree[i].n2;     // old index 2
  69         size_t beta;                        // old sep index
  70         for( beta = 0; beta < jt_RTree.size(); beta++ )
  71             if( UEdge( jt_RTree[beta].n1, jt_RTree[beta].n2 ) == UEdge( alpha1, alpha2 ) )
  72                 break;
  73         assert( beta != jt_RTree.size() );
  74
  75         size_t newalpha1 = find(_a.begin(), _a.end(), alpha1) - _a.begin();
  76         if( newalpha1 == _a.size() ) {
  77             _Qa.push_back( Factor( jt_Qa[alpha1].vars(), 1.0 ) );
  78             _a.push_back( alpha1 );         // save old index in index conversion table
  79         }
  80
  81         size_t newalpha2 = find(_a.begin(), _a.end(), alpha2) - _a.begin();
  82         if( newalpha2 == _a.size() ) {
  83             _Qa.push_back( Factor( jt_Qa[alpha2].vars(), 1.0 ) );
  84             _a.push_back( alpha2 );         // save old index in index conversion table
  85         }
  86
  87         _RTree.push_back( DEdge( newalpha1, newalpha2 ) );
  88         _Qb.push_back( Factor( jt_Qb[beta].vars(), 1.0 ) );
  89         _b.push_back( beta );
  90     }
  91
  92     // Find remaining variables (which are not in the new root)
  93     _nsrem = _ns / _Qa[0].vars();
  94 };
  95
  96
  97 void TreeEPSubTree::init() {
  98     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
  99         _Qa[alpha].fill( 1.0 );
 100     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 101         _Qb[beta].fill( 1.0 );
 102 }
 103
 104
 105 void TreeEPSubTree::InvertAndMultiply( const std::vector<Factor> &Qa, const std::vector<Factor> &Qb ) {
 106     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 107         _Qa[alpha] = Qa[_a[alpha]].divided_by( _Qa[alpha] );
 108
 109     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 110         _Qb[beta] = Qb[_b[beta]].divided_by( _Qb[beta] );
 111 }
 112
 113
 114 void TreeEPSubTree::HUGIN_with_I( std::vector<Factor> &Qa, std::vector<Factor> &Qb ) {
 115     // Backup _Qa and _Qb
 116     vector<Factor> _Qa_old(_Qa);
 117     vector<Factor> _Qb_old(_Qb);
 118
 119     // Clear Qa and Qb
 120     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 121         Qa[_a[alpha]].fill( 0.0 );
 122     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 123         Qb[_b[beta]].fill( 0.0 );
 124
 125     // For all states of _nsrem
 126     for( State s(_nsrem); s.valid(); s++ ) {
 127         // Multiply root with slice of I
 128         _Qa[0] *= _I->slice( _nsrem, s );
 129
 130         // CollectEvidence
 131         for( size_t i = _RTree.size(); (i--) != 0; ) {
 132             // clamp variables in nsrem
 133             for( VarSet::const_iterator n = _nsrem.begin(); n != _nsrem.end(); n++ )
 134                 if( _Qa[_RTree[i].n2].vars() >> *n ) {
 135                     Factor delta( *n, 0.0 );
 136                     delta[s(*n)] = 1.0;
 137                     _Qa[_RTree[i].n2] *= delta;
 138                 }
 139             Factor new_Qb = _Qa[_RTree[i].n2].part_sum( _Qb[i].vars() );
 140             _Qa[_RTree[i].n1] *= new_Qb.divided_by( _Qb[i] );
 141             _Qb[i] = new_Qb;
 142         }
 143
 144         // DistributeEvidence
 145         for( size_t i = 0; i < _RTree.size(); i++ ) {
 146             Factor new_Qb = _Qa[_RTree[i].n1].part_sum( _Qb[i].vars() );
 147             _Qa[_RTree[i].n2] *= new_Qb.divided_by( _Qb[i] );
 148             _Qb[i] = new_Qb;
 149         }
 150
 151         // Store Qa's and Qb's
 152         for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 153             Qa[_a[alpha]].p() += _Qa[alpha].p();
 154         for( size_t beta = 0; beta < _Qb.size(); beta++ )
 155             Qb[_b[beta]].p() += _Qb[beta].p();
 156
 157         // Restore _Qa and _Qb
 158         _Qa = _Qa_old;
 159         _Qb = _Qb_old;
 160     }
 161
 162     // Normalize Qa and Qb
 163     _logZ = 0.0;
 164     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ ) {
 165         _logZ += log(Qa[_a[alpha]].totalSum());
 166         Qa[_a[alpha]].normalize( Prob::NORMPROB );
 167     }
 168     for( size_t beta = 0; beta < _Qb.size(); beta++ ) {
 169         _logZ -= log(Qb[_b[beta]].totalSum());
 170         Qb[_b[beta]].normalize( Prob::NORMPROB );
 171     }
 172 }
 173
 174
 175 double TreeEPSubTree::logZ( const std::vector<Factor> &Qa, const std::vector<Factor> &Qb ) const {
 176     double sum = 0.0;
 177     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 178         sum += (Qa[_a[alpha]] * _Qa[alpha].log0()).totalSum();
 179     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 180         sum -= (Qb[_b[beta]] * _Qb[beta].log0()).totalSum();
 181     return sum + _logZ;
 182 }
 183
 184
 185 TreeEP::TreeEP( const FactorGraph &fg, const Properties &opts ) : JTree(fg, opts("updates",string("HUGIN")), false) {
 186     assert( checkProperties() );
 187
 188     assert( fg.G.isConnected() );
 189
 190     if( opts.hasKey("tree") ) {
 191         ConstructRG( opts.GetAs<DEdgeVec>("tree") );
 192     } else {
 193         if( Type() == TypeType::ORG ) {
 194             // construct weighted graph with as weights a crude estimate of the
 195             // mutual information between the nodes
 196             WeightedGraph<double> wg;
 197             for( size_t i = 0; i < nrVars(); ++i ) {
 198                 Var v_i = var(i);
 199                 VarSet di = delta(i);
 200                 for( VarSet::const_iterator j = di.begin(); j != di.end(); j++ )
 201                     if( v_i < *j ) {
 202                         Factor piet;
 203                         for( size_t I = 0; I < nrFactors(); I++ ) {
 204                             VarSet Ivars = factor(I).vars();
 205                             if( (Ivars == v_i) || (Ivars == *j) )
 206                                 piet *= factor(I);
 207                             else if( Ivars >> (v_i | *j) )
 208                                 piet *= factor(I).marginal( v_i | *j );
 209                         }
 210                         if( piet.vars() >> (v_i | *j) ) {
 211                             piet = piet.marginal( v_i | *j );
 212                             Factor pietf = piet.marginal(v_i) * piet.marginal(*j);
 213                             wg[UEdge(i,findVar(*j))] = real( KL_dist( piet, pietf ) );
 214                         } else
 215                             wg[UEdge(i,findVar(*j))] = 0;
 216                     }
 217             }
 218
 219             // find maximal spanning tree
 220             ConstructRG( MaxSpanningTreePrims( wg ) );
 221
 222 //            cout << "Constructing maximum spanning tree..." << endl;
 223 //            DEdgeVec MST = MaxSpanningTreePrims( wg );
 224 //            cout << "Maximum spanning tree:" << endl;
 225 //            for( DEdgeVec::const_iterator e = MST.begin(); e != MST.end(); e++ )
 226 //                cout << *e << endl;
 227 //            ConstructRG( MST );
 228         } else if( Type() == TypeType::ALT ) {
 229             // construct weighted graph with as weights an upper bound on the
 230             // effective interaction strength between pairs of nodes
 231             WeightedGraph<double> wg;
 232             for( size_t i = 0; i < nrVars(); ++i ) {
 233                 Var v_i = var(i);
 234                 VarSet di = delta(i);
 235                 for( VarSet::const_iterator j = di.begin(); j != di.end(); j++ )
 236                     if( v_i < *j ) {
 237                         Factor piet;
 238                         for( size_t I = 0; I < nrFactors(); I++ ) {
 239                             VarSet Ivars = factor(I).vars();
 240                             if( Ivars >> (v_i | *j) )
 241                                 piet *= factor(I);
 242                         }
 243                         wg[UEdge(i,findVar(*j))] = piet.strength(v_i, *j);
 244                     }
 245             }
 246
 247             // find maximal spanning tree
 248             ConstructRG( MaxSpanningTreePrims( wg ) );
 249         } else {
 250             assert( 0 == 1 );
 251         }
 252     }
 253 }
 254
 255
 256 void TreeEP::ConstructRG( const DEdgeVec &tree ) {
 257     vector<VarSet> Cliques;
 258     for( size_t i = 0; i < tree.size(); i++ )
 259         Cliques.push_back( var(tree[i].n1) | var(tree[i].n2) );
 260
 261     // Construct a weighted graph (each edge is weighted with the cardinality
 262     // of the intersection of the nodes, where the nodes are the elements of
 263     // Cliques).
 264     WeightedGraph<int> JuncGraph;
 265     for( size_t i = 0; i < Cliques.size(); i++ )
 266         for( size_t j = i+1; j < Cliques.size(); j++ ) {
 267             size_t w = (Cliques[i] & Cliques[j]).size();
 268             JuncGraph[UEdge(i,j)] = w;
 269         }
 270
 271     // Construct maximal spanning tree using Prim's algorithm
 272     _RTree = MaxSpanningTreePrims( JuncGraph );
 273
 274     // Construct corresponding region graph
 275
 276     // Create outer regions
 277     ORs.reserve( Cliques.size() );
 278     for( size_t i = 0; i < Cliques.size(); i++ )
 279         ORs.push_back( FRegion( Factor(Cliques[i], 1.0), 1.0 ) );
 280
 281     // For each factor, find an outer region that subsumes that factor.
 282     // Then, multiply the outer region with that factor.
 283     // If no outer region can be found subsuming that factor, label the
 284     // factor as off-tree.
 285     fac2OR.clear();
 286     fac2OR.resize( nrFactors(), -1U );
 287     for( size_t I = 0; I < nrFactors(); I++ ) {
 288         size_t alpha;
 289         for( alpha = 0; alpha < nrORs(); alpha++ )
 290             if( OR(alpha).vars() >> factor(I).vars() ) {
 291                 fac2OR[I] = alpha;
 292                 break;
 293             }
 294     // DIFF WITH JTree::GenerateJT:      assert
 295     }
 296     RecomputeORs();
 297
 298     // Create inner regions and edges
 299     IRs.reserve( _RTree.size() );
 300     vector<Edge> edges;
 301     edges.reserve( 2 * _RTree.size() );
 302     for( size_t i = 0; i < _RTree.size(); i++ ) {
 303         edges.push_back( Edge( _RTree[i].n1, IRs.size() ) );
 304         edges.push_back( Edge( _RTree[i].n2, IRs.size() ) );
 305         // inner clusters have counting number -1
 306         IRs.push_back( Region( Cliques[_RTree[i].n1] & Cliques[_RTree[i].n2], -1.0 ) );
 307     }
 308
 309     // create bipartite graph
 310     G.create( nrORs(), nrIRs(), edges.begin(), edges.end() );
 311
 312     // Check counting numbers
 313     Check_Counting_Numbers();
 314
 315     // Create messages and beliefs
 316     _Qa.clear();
 317     _Qa.reserve( nrORs() );
 318     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 319         _Qa.push_back( OR(alpha) );
 320
 321     _Qb.clear();
 322     _Qb.reserve( nrIRs() );
 323     for( size_t beta = 0; beta < nrIRs(); beta++ )
 324         _Qb.push_back( Factor( IR(beta), 1.0 ) );
 325
 326     // DIFF with JTree::GenerateJT:  no messages
 327
 328     // DIFF with JTree::GenerateJT:
 329     // Create factor approximations
 330     _Q.clear();
 331     size_t PreviousRoot = (size_t)-1;
 332     for( size_t I = 0; I < nrFactors(); I++ )
 333         if( offtree(I) ) {
 334             // find efficient subtree
 335             DEdgeVec subTree;
 336             /*size_t subTreeSize =*/ findEfficientTree( factor(I).vars(), subTree, PreviousRoot );
 337             PreviousRoot = subTree[0].n1;
 338             //subTree.resize( subTreeSize );  // FIXME
 339 //          cout << "subtree " << I << " has size " << subTreeSize << endl;
 340
 341 /*
 342             char fn[30];
 343             sprintf( fn, "/tmp/subtree_%d.dot", I );
 344             std::ofstream dots(fn);
 345             dots << "graph G {" << endl;
 346             dots << "graph[size=\"9,9\"];" << endl;
 347             dots << "node[shape=circle,width=0.4,fixedsize=true];" << endl;
 348             for( size_t i = 0; i < nrVars(); i++ )
 349                 dots << "\tx" << var(i).label() << ((factor(I).vars() >> var(i)) ? "[color=blue];" : ";") << endl;
 350             dots << "node[shape=box,style=filled,color=lightgrey,width=0.3,height=0.3,fixedsize=true];" << endl;
 351             for( size_t J = 0; J < nrFactors(); J++ )
 352                 dots << "\tp" << J << ";" << endl;
 353             for( size_t iI = 0; iI < FactorGraph::nr_edges(); iI++ )
 354                 dots << "\tx" << var(FactorGraph::edge(iI).first).label() << " -- p" << FactorGraph::edge(iI).second << ";" << endl;
 355             for( size_t a = 0; a < tree.size(); a++ )
 356                 dots << "\tx" << var(tree[a].n1).label() << " -- x" << var(tree[a].n2).label() << " [color=red];" << endl;
 357             dots << "}" << endl;
 358             dots.close();
 359 */
 360
 361             TreeEPSubTree QI( subTree, _RTree, _Qa, _Qb, &factor(I) );
 362             _Q[I] = QI;
 363         }
 364     // Previous root of first off-tree factor should be the root of the last off-tree factor
 365     for( size_t I = 0; I < nrFactors(); I++ )
 366         if( offtree(I) ) {
 367             DEdgeVec subTree;
 368             /*size_t subTreeSize =*/ findEfficientTree( factor(I).vars(), subTree, PreviousRoot );
 369             PreviousRoot = subTree[0].n1;
 370             //subTree.resize( subTreeSize ); // FIXME
 371 //          cout << "subtree " << I << " has size " << subTreeSize << endl;
 372
 373             TreeEPSubTree QI( subTree, _RTree, _Qa, _Qb, &factor(I) );
 374             _Q[I] = QI;
 375             break;
 376         }
 377
 378     if( Verbose() >= 3 ) {
 379         cout << "Resulting regiongraph: " << *this << endl;
 380     }
 381 }
 382
 383
 384 string TreeEP::identify() const {
 385     stringstream result (stringstream::out);
 386     result << Name << GetProperties();
 387     return result.str();
 388 }
 389
 390
 391 void TreeEP::init() {
 392     assert( checkProperties() );
 393
 394     runHUGIN();
 395
 396     // Init factor approximations
 397     for( size_t I = 0; I < nrFactors(); I++ )
 398         if( offtree(I) )
 399             _Q[I].init();
 400 }
 401
 402
 403 double TreeEP::run() {
 404     if( Verbose() >= 1 )
 405         cout << "Starting " << identify() << "...";
 406     if( Verbose() >= 3)
 407         cout << endl;
 408
 409     double tic = toc();
 410     Diffs diffs(nrVars(), 1.0);
 411
 412     vector<Factor> old_beliefs;
 413     old_beliefs.reserve( nrVars() );
 414     for( size_t i = 0; i < nrVars(); i++ )
 415         old_beliefs.push_back(belief(var(i)));
 416
 417     size_t iter = 0;
 418
 419     // do several passes over the network until maximum number of iterations has
 420     // been reached or until the maximum belief difference is smaller than tolerance
 421     for( iter=0; iter < MaxIter() && diffs.maxDiff() > Tol(); iter++ ) {
 422         for( size_t I = 0; I < nrFactors(); I++ )
 423             if( offtree(I) ) {
 424                 _Q[I].InvertAndMultiply( _Qa, _Qb );
 425                 _Q[I].HUGIN_with_I( _Qa, _Qb );
 426                 _Q[I].InvertAndMultiply( _Qa, _Qb );
 427             }
 428
 429         // calculate new beliefs and compare with old ones
 430         for( size_t i = 0; i < nrVars(); i++ ) {
 431             Factor nb( belief(var(i)) );
 432             diffs.push( dist( nb, old_beliefs[i], Prob::DISTLINF ) );
 433             old_beliefs[i] = nb;
 434         }
 435
 436         if( Verbose() >= 3 )
 437             cout << "TreeEP::run:  maxdiff " << diffs.maxDiff() << " after " << iter+1 << " passes" << endl;
 438     }
 439
 440     updateMaxDiff( diffs.maxDiff() );
 441
 442     if( Verbose() >= 1 ) {
 443         if( diffs.maxDiff() > Tol() ) {
 444             if( Verbose() == 1 )
 445                 cout << endl;
 446             cout << "TreeEP::run:  WARNING: not converged within " << MaxIter() << " passes (" << toc() - tic << " clocks)...final maxdiff:" << diffs.maxDiff() << endl;
 447         } else {
 448             if( Verbose() >= 3 )
 449                 cout << "TreeEP::run:  ";
 450             cout << "converged in " << iter << " passes (" << toc() - tic << " clocks)." << endl;
 451         }
 452     }
 453
 454     return diffs.maxDiff();
 455 }
 456
 457
 458 Complex TreeEP::logZ() const {
 459     double sum = 0.0;
 460
 461     // entropy of the tree
 462     for( size_t beta = 0; beta < nrIRs(); beta++ )
 463         sum -= real(_Qb[beta].entropy());
 464     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 465         sum += real(_Qa[alpha].entropy());
 466
 467     // energy of the on-tree factors
 468     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 469         sum += (OR(alpha).log0() * _Qa[alpha]).totalSum();
 470
 471     // energy of the off-tree factors
 472     for( size_t I = 0; I < nrFactors(); I++ )
 473         if( offtree(I) )
 474             sum += (_Q.find(I))->second.logZ( _Qa, _Qb );
 475
 476     return sum;
 477 }
 478
 479
 480 } // end of namespace dai