src/treeep.cpp

   1 /*  Copyright (C) 2006-2008  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
   5     This file is part of libDAI.
   6
   7     libDAI is free software; you can redistribute it and/or modify
   8     it under the terms of the GNU General Public License as published by
   9     the Free Software Foundation; either version 2 of the License, or
  10     (at your option) any later version.
  11
  12     libDAI is distributed in the hope that it will be useful,
  13     but WITHOUT ANY WARRANTY; without even the implied warranty of
  14     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15     GNU General Public License for more details.
  16
  17     You should have received a copy of the GNU General Public License
  18     along with libDAI; if not, write to the Free Software
  19     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  20 */
  21
  22
  23 #include <iostream>
  24 #include <fstream>
  25 #include <vector>
  26 #include <dai/jtree.h>
  27 #include <dai/treeep.h>
  28 #include <dai/util.h>
  29
  30
  31 namespace dai {
  32
  33
  34 using namespace std;
  35
  36
  37 const char *TreeEP::Name = "TREEEP";
  38
  39
  40 void TreeEP::setProperties( const PropertySet &opts ) {
  41     assert( opts.hasKey("tol") );
  42     assert( opts.hasKey("maxiter") );
  43     assert( opts.hasKey("verbose") );
  44     assert( opts.hasKey("type") );
  45
  46     props.tol = opts.getStringAs<double>("tol");
  47     props.maxiter = opts.getStringAs<size_t>("maxiter");
  48     props.verbose = opts.getStringAs<size_t>("verbose");
  49     props.type = opts.getStringAs<Properties::TypeType>("type");
  50 }
  51
  52
  53 PropertySet TreeEP::getProperties() const {
  54     PropertySet opts;
  55     opts.Set( "tol", props.tol );
  56     opts.Set( "maxiter", props.maxiter );
  57     opts.Set( "verbose", props.verbose );
  58     opts.Set( "type", props.type );
  59     return opts;
  60 }
  61
  62
  63 string TreeEP::printProperties() const {
  64     stringstream s( stringstream::out );
  65     s << "[";
  66     s << "tol=" << props.tol << ",";
  67     s << "maxiter=" << props.maxiter << ",";
  68     s << "verbose=" << props.verbose << ",";
  69     s << "type=" << props.type << "]";
  70     return s.str();
  71 }
  72
  73
  74 TreeEP::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) {
  75     _ns = _I->vars();
  76
  77     // Make _Qa, _Qb, _a and _b corresponding to the subtree
  78     _b.reserve( subRTree.size() );
  79     _Qb.reserve( subRTree.size() );
  80     _RTree.reserve( subRTree.size() );
  81     for( size_t i = 0; i < subRTree.size(); i++ ) {
  82         size_t alpha1 = subRTree[i].n1;     // old index 1
  83         size_t alpha2 = subRTree[i].n2;     // old index 2
  84         size_t beta;                        // old sep index
  85         for( beta = 0; beta < jt_RTree.size(); beta++ )
  86             if( UEdge( jt_RTree[beta].n1, jt_RTree[beta].n2 ) == UEdge( alpha1, alpha2 ) )
  87                 break;
  88         assert( beta != jt_RTree.size() );
  89
  90         size_t newalpha1 = find(_a.begin(), _a.end(), alpha1) - _a.begin();
  91         if( newalpha1 == _a.size() ) {
  92             _Qa.push_back( Factor( jt_Qa[alpha1].vars(), 1.0 ) );
  93             _a.push_back( alpha1 );         // save old index in index conversion table
  94         }
  95
  96         size_t newalpha2 = find(_a.begin(), _a.end(), alpha2) - _a.begin();
  97         if( newalpha2 == _a.size() ) {
  98             _Qa.push_back( Factor( jt_Qa[alpha2].vars(), 1.0 ) );
  99             _a.push_back( alpha2 );         // save old index in index conversion table
 100         }
 101
 102         _RTree.push_back( DEdge( newalpha1, newalpha2 ) );
 103         _Qb.push_back( Factor( jt_Qb[beta].vars(), 1.0 ) );
 104         _b.push_back( beta );
 105     }
 106
 107     // Find remaining variables (which are not in the new root)
 108     _nsrem = _ns / _Qa[0].vars();
 109 }
 110
 111
 112 void TreeEP::TreeEPSubTree::init() {
 113     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 114         _Qa[alpha].fill( 1.0 );
 115     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 116         _Qb[beta].fill( 1.0 );
 117 }
 118
 119
 120 void TreeEP::TreeEPSubTree::InvertAndMultiply( const std::vector<Factor> &Qa, const std::vector<Factor> &Qb ) {
 121     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 122         _Qa[alpha] = Qa[_a[alpha]].divided_by( _Qa[alpha] );
 123
 124     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 125         _Qb[beta] = Qb[_b[beta]].divided_by( _Qb[beta] );
 126 }
 127
 128
 129 void TreeEP::TreeEPSubTree::HUGIN_with_I( std::vector<Factor> &Qa, std::vector<Factor> &Qb ) {
 130     // Backup _Qa and _Qb
 131     vector<Factor> _Qa_old(_Qa);
 132     vector<Factor> _Qb_old(_Qb);
 133
 134     // Clear Qa and Qb
 135     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 136         Qa[_a[alpha]].fill( 0.0 );
 137     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 138         Qb[_b[beta]].fill( 0.0 );
 139
 140     // For all states of _nsrem
 141     for( State s(_nsrem); s.valid(); s++ ) {
 142         // Multiply root with slice of I
 143         _Qa[0] *= _I->slice( _nsrem, s );
 144
 145         // CollectEvidence
 146         for( size_t i = _RTree.size(); (i--) != 0; ) {
 147             // clamp variables in nsrem
 148             for( VarSet::const_iterator n = _nsrem.begin(); n != _nsrem.end(); n++ )
 149                 if( _Qa[_RTree[i].n2].vars() >> *n ) {
 150                     Factor delta( *n, 0.0 );
 151                     delta[s(*n)] = 1.0;
 152                     _Qa[_RTree[i].n2] *= delta;
 153                 }
 154             Factor new_Qb = _Qa[_RTree[i].n2].partSum( _Qb[i].vars() );
 155             _Qa[_RTree[i].n1] *= new_Qb.divided_by( _Qb[i] );
 156             _Qb[i] = new_Qb;
 157         }
 158
 159         // DistributeEvidence
 160         for( size_t i = 0; i < _RTree.size(); i++ ) {
 161             Factor new_Qb = _Qa[_RTree[i].n1].partSum( _Qb[i].vars() );
 162             _Qa[_RTree[i].n2] *= new_Qb.divided_by( _Qb[i] );
 163             _Qb[i] = new_Qb;
 164         }
 165
 166         // Store Qa's and Qb's
 167         for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 168             Qa[_a[alpha]].p() += _Qa[alpha].p();
 169         for( size_t beta = 0; beta < _Qb.size(); beta++ )
 170             Qb[_b[beta]].p() += _Qb[beta].p();
 171
 172         // Restore _Qa and _Qb
 173         _Qa = _Qa_old;
 174         _Qb = _Qb_old;
 175     }
 176
 177     // Normalize Qa and Qb
 178     _logZ = 0.0;
 179     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ ) {
 180         _logZ += log(Qa[_a[alpha]].totalSum());
 181         Qa[_a[alpha]].normalize();
 182     }
 183     for( size_t beta = 0; beta < _Qb.size(); beta++ ) {
 184         _logZ -= log(Qb[_b[beta]].totalSum());
 185         Qb[_b[beta]].normalize();
 186     }
 187 }
 188
 189
 190 double TreeEP::TreeEPSubTree::logZ( const std::vector<Factor> &Qa, const std::vector<Factor> &Qb ) const {
 191     double sum = 0.0;
 192     for( size_t alpha = 0; alpha < _Qa.size(); alpha++ )
 193         sum += (Qa[_a[alpha]] * _Qa[alpha].log0()).totalSum();
 194     for( size_t beta = 0; beta < _Qb.size(); beta++ )
 195         sum -= (Qb[_b[beta]] * _Qb[beta].log0()).totalSum();
 196     return sum + _logZ;
 197 }
 198
 199
 200 TreeEP::TreeEP( const FactorGraph &fg, const PropertySet &opts ) : JTree(fg, opts("updates",string("HUGIN")), false), _maxdiff(0.0), _iters(0), props(), _Q() {
 201     setProperties( opts );
 202
 203     assert( fg.isConnected() );
 204
 205     if( opts.hasKey("tree") ) {
 206         ConstructRG( opts.GetAs<DEdgeVec>("tree") );
 207     } else {
 208         if( props.type == Properties::TypeType::ORG || props.type == Properties::TypeType::ALT ) {
 209             // ORG: construct weighted graph with as weights a crude estimate of the
 210             // mutual information between the nodes
 211             // ALT: construct weighted graph with as weights an upper bound on the
 212             // effective interaction strength between pairs of nodes
 213
 214             WeightedGraph<double> wg;
 215             for( size_t i = 0; i < nrVars(); ++i ) {
 216                 Var v_i = var(i);
 217                 VarSet di = delta(i);
 218                 for( VarSet::const_iterator j = di.begin(); j != di.end(); j++ )
 219                     if( v_i < *j ) {
 220                         VarSet ij(v_i,*j);
 221                         Factor piet;
 222                         for( size_t I = 0; I < nrFactors(); I++ ) {
 223                             VarSet Ivars = factor(I).vars();
 224                             if( props.type == Properties::TypeType::ORG ) {
 225                                 if( (Ivars == v_i) || (Ivars == *j) )
 226                                     piet *= factor(I);
 227                                 else if( Ivars >> ij )
 228                                     piet *= factor(I).marginal( ij );
 229                             } else {
 230                                 if( Ivars >> ij )
 231                                     piet *= factor(I);
 232                             }
 233                         }
 234                         if( props.type == Properties::TypeType::ORG ) {
 235                             if( piet.vars() >> ij ) {
 236                                 piet = piet.marginal( ij );
 237                                 Factor pietf = piet.marginal(v_i) * piet.marginal(*j);
 238                                 wg[UEdge(i,findVar(*j))] = dist( piet, pietf, Prob::DISTKL );
 239                             } else
 240                                 wg[UEdge(i,findVar(*j))] = 0;
 241                         } else {
 242                             wg[UEdge(i,findVar(*j))] = piet.strength(v_i, *j);
 243                         }
 244                     }
 245             }
 246
 247             // find maximal spanning tree
 248             ConstructRG( MaxSpanningTreePrims( wg ) );
 249         } else
 250             DAI_THROW(INTERNAL_ERROR);
 251     }
 252 }
 253
 254
 255 void TreeEP::ConstructRG( const DEdgeVec &tree ) {
 256     vector<VarSet> Cliques;
 257     for( size_t i = 0; i < tree.size(); i++ )
 258         Cliques.push_back( VarSet( var(tree[i].n1), var(tree[i].n2) ) );
 259
 260     // Construct a weighted graph (each edge is weighted with the cardinality
 261     // of the intersection of the nodes, where the nodes are the elements of
 262     // Cliques).
 263     WeightedGraph<int> JuncGraph;
 264     for( size_t i = 0; i < Cliques.size(); i++ )
 265         for( size_t j = i+1; j < Cliques.size(); j++ ) {
 266             size_t w = (Cliques[i] & Cliques[j]).size();
 267             if( w )
 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.construct( 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             TreeEPSubTree QI( subTree, RTree, Qa, Qb, &factor(I) );
 342             _Q[I] = QI;
 343         }
 344     // Previous root of first off-tree factor should be the root of the last off-tree factor
 345     for( size_t I = 0; I < nrFactors(); I++ )
 346         if( offtree(I) ) {
 347             DEdgeVec subTree;
 348             /*size_t subTreeSize =*/ findEfficientTree( factor(I).vars(), subTree, PreviousRoot );
 349             PreviousRoot = subTree[0].n1;
 350             //subTree.resize( subTreeSize ); // FIXME
 351 //          cout << "subtree " << I << " has size " << subTreeSize << endl;
 352
 353             TreeEPSubTree QI( subTree, RTree, Qa, Qb, &factor(I) );
 354             _Q[I] = QI;
 355             break;
 356         }
 357
 358     if( props.verbose >= 3 ) {
 359         cout << "Resulting regiongraph: " << *this << endl;
 360     }
 361 }
 362
 363
 364 string TreeEP::identify() const {
 365     return string(Name) + printProperties();
 366 }
 367
 368
 369 void TreeEP::init() {
 370     runHUGIN();
 371
 372     // Init factor approximations
 373     for( size_t I = 0; I < nrFactors(); I++ )
 374         if( offtree(I) )
 375             _Q[I].init();
 376 }
 377
 378
 379 double TreeEP::run() {
 380     if( props.verbose >= 1 )
 381         cout << "Starting " << identify() << "...";
 382     if( props.verbose >= 3)
 383         cout << endl;
 384
 385     double tic = toc();
 386     Diffs diffs(nrVars(), 1.0);
 387
 388     vector<Factor> old_beliefs;
 389     old_beliefs.reserve( nrVars() );
 390     for( size_t i = 0; i < nrVars(); i++ )
 391         old_beliefs.push_back(belief(var(i)));
 392
 393     // do several passes over the network until maximum number of iterations has
 394     // been reached or until the maximum belief difference is smaller than tolerance
 395     for( _iters=0; _iters < props.maxiter && diffs.maxDiff() > props.tol; _iters++ ) {
 396         for( size_t I = 0; I < nrFactors(); I++ )
 397             if( offtree(I) ) {
 398                 _Q[I].InvertAndMultiply( Qa, Qb );
 399                 _Q[I].HUGIN_with_I( Qa, Qb );
 400                 _Q[I].InvertAndMultiply( Qa, Qb );
 401             }
 402
 403         // calculate new beliefs and compare with old ones
 404         for( size_t i = 0; i < nrVars(); i++ ) {
 405             Factor nb( belief(var(i)) );
 406             diffs.push( dist( nb, old_beliefs[i], Prob::DISTLINF ) );
 407             old_beliefs[i] = nb;
 408         }
 409
 410         if( props.verbose >= 3 )
 411             cout << Name << "::run:  maxdiff " << diffs.maxDiff() << " after " << _iters+1 << " passes" << endl;
 412     }
 413
 414     if( diffs.maxDiff() > _maxdiff )
 415         _maxdiff = diffs.maxDiff();
 416
 417     if( props.verbose >= 1 ) {
 418         if( diffs.maxDiff() > props.tol ) {
 419             if( props.verbose == 1 )
 420                 cout << endl;
 421             cout << Name << "::run:  WARNING: not converged within " << props.maxiter << " passes (" << toc() - tic << " seconds)...final maxdiff:" << diffs.maxDiff() << endl;
 422         } else {
 423             if( props.verbose >= 3 )
 424                 cout << Name << "::run:  ";
 425             cout << "converged in " << _iters << " passes (" << toc() - tic << " seconds)." << endl;
 426         }
 427     }
 428
 429     return diffs.maxDiff();
 430 }
 431
 432
 433 Real TreeEP::logZ() const {
 434     double sum = 0.0;
 435
 436     // entropy of the tree
 437     for( size_t beta = 0; beta < nrIRs(); beta++ )
 438         sum -= Qb[beta].entropy();
 439     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 440         sum += Qa[alpha].entropy();
 441
 442     // energy of the on-tree factors
 443     for( size_t alpha = 0; alpha < nrORs(); alpha++ )
 444         sum += (OR(alpha).log0() * Qa[alpha]).totalSum();
 445
 446     // energy of the off-tree factors
 447     for( size_t I = 0; I < nrFactors(); I++ )
 448         if( offtree(I) )
 449             sum += (_Q.find(I))->second.logZ( Qa, Qb );
 450
 451     return sum;
 452 }
 453
 454
 455 } // end of namespace dai