include/dai/bp.h

   1 /*  This file is part of libDAI - http://www.libdai.org/
   2  *
   3  *  libDAI is licensed under the terms of the GNU General Public License version
   4  *  2, or (at your option) any later version. libDAI is distributed without any
   5  *  warranty. See the file COPYING for more details.
   6  *
   7  *  Copyright (C) 2006-2010  Joris Mooij  [joris dot mooij at libdai dot org]
   8  *  Copyright (C) 2006-2007  Radboud University Nijmegen, The Netherlands
   9  */
  10
  11
  12 /// \file
  13 /// \brief Defines class BP, which implements (Loopy) Belief Propagation
  14 /// \todo Consider using a priority_queue for maximum residual schedule
  15
  16
  17 #ifndef __defined_libdai_bp_h
  18 #define __defined_libdai_bp_h
  19
  20
  21 #include <string>
  22 #include <dai/daialg.h>
  23 #include <dai/factorgraph.h>
  24 #include <dai/properties.h>
  25 #include <dai/enum.h>
  26
  27
  28 namespace dai {
  29
  30
  31 /// Approximate inference algorithm "(Loopy) Belief Propagation"
  32 /** The Loopy Belief Propagation algorithm uses message passing
  33  *  to approximate marginal probability distributions ("beliefs") for variables
  34  *  and factors (more precisely, for the subset of variables depending on the factor).
  35  *  There are two variants, the sum-product algorithm (corresponding to
  36  *  finite temperature) and the max-product algorithm (corresponding to
  37  *  zero temperature).
  38  *
  39  *  The messages \f$m_{I\to i}(x_i)\f$ are passed from factors \f$I\f$ to variables \f$i\f$.
  40  *  In case of the sum-product algorith, the update equation is:
  41  *    \f[ m_{I\to i}(x_i) \propto \sum_{x_{N_I\setminus\{i\}}} f_I(x_I) \prod_{j\in N_I\setminus\{i\}} \prod_{J\in N_j\setminus\{I\}} m_{J\to j}\f]
  42  *  and in case of the max-product algorithm:
  43  *    \f[ m_{I\to i}(x_i) \propto \max_{x_{N_I\setminus\{i\}}} f_I(x_I) \prod_{j\in N_I\setminus\{i\}} \prod_{J\in N_j\setminus\{I\}} m_{J\to j}\f]
  44  *  In order to improve convergence, the updates can be damped. For improved numerical stability,
  45  *  the updates can be done in the log-domain alternatively.
  46  *
  47  *  After convergence, the variable beliefs are calculated by:
  48  *    \f[ b_i(x_i) \propto \prod_{I\in N_i} m_{I\to i}(x_i)\f]
  49  *  and the factor beliefs are calculated by:
  50  *    \f[ b_I(x_I) \propto f_I(x_I) \prod_{j\in N_I} \prod_{J\in N_j\setminus\{I\}} m_{J\to j}(x_j) \f]
  51  *  The logarithm of the partition sum is calculated by:
  52  *    \f[ \log Z = \sum_i (1 - |N_i|) \sum_{x_i} b_i(x_i) \log b_i(x_i) - \sum_I \sum_{x_I} b_I(x_I) \log \frac{b_I(x_I)}{f_I(x_I)} \f]
  53  *
  54  *  For the max-product algorithm, a heuristic way of finding the MAP state (the
  55  *  joint configuration of all variables which has maximum probability) is provided
  56  *  by the findMaximum() method, which can be called after convergence.
  57  *
  58  *  \note There are two implementations, an optimized one (the default) which caches IndexFor objects,
  59  *  and a slower, less complicated one which is easier to maintain/understand. The slower one can be
  60  *  enabled by defining DAI_BP_FAST as false in the source file.
  61  */
  62 class BP : public DAIAlgFG {
  63     protected:
  64         /// Type used for index cache
  65         typedef std::vector<size_t> ind_t;
  66         /// Type used for storing edge properties
  67         struct EdgeProp {
  68             /// Index cached for this edge
  69             ind_t  index;
  70             /// Old message living on this edge
  71             Prob   message;
  72             /// New message living on this edge
  73             Prob   newMessage;
  74             /// Residual for this edge
  75             Real   residual;
  76         };
  77         /// Stores all edge properties
  78         std::vector<std::vector<EdgeProp> > _edges;
  79         /// Type of lookup table (only used for maximum-residual BP)
  80         typedef std::multimap<Real, std::pair<std::size_t, std::size_t> > LutType;
  81         /// Lookup table (only used for maximum-residual BP)
  82         std::vector<std::vector<LutType::iterator> > _edge2lut;
  83         /// Lookup table (only used for maximum-residual BP)
  84         LutType _lut;
  85         /// Maximum difference between variable beliefs encountered so far
  86         Real _maxdiff;
  87         /// Number of iterations needed
  88         size_t _iters;
  89         /// The history of message updates (only recorded if \a recordSentMessages is \c true)
  90         std::vector<std::pair<std::size_t, std::size_t> > _sentMessages;
  91
  92     public:
  93         /// Parameters for BP
  94         struct Properties {
  95             /// Enumeration of possible update schedules
  96             /** The following update schedules have been defined:
  97              *  - PARALL parallel updates
  98              *  - SEQFIX sequential updates using a fixed sequence
  99              *  - SEQRND sequential updates using a random sequence
 100              *  - SEQMAX maximum-residual updates [\ref EMK06]
 101              */
 102             DAI_ENUM(UpdateType,SEQFIX,SEQRND,SEQMAX,PARALL);
 103
 104             /// Enumeration of inference variants
 105             /** There are two inference variants:
 106              *  - SUMPROD Sum-Product
 107              *  - MAXPROD Max-Product (equivalent to Min-Sum)
 108              */
 109             DAI_ENUM(InfType,SUMPROD,MAXPROD);
 110
 111             /// Verbosity (amount of output sent to stderr)
 112             size_t verbose;
 113
 114             /// Maximum number of iterations
 115             size_t maxiter;
 116
 117             /// Maximum time (in seconds)
 118             double maxtime;
 119
 120             /// Tolerance for convergence test
 121             Real tol;
 122
 123             /// Whether updates should be done in logarithmic domain or not
 124             bool logdomain;
 125
 126             /// Damping constant (0.0 means no damping, 1.0 is maximum damping)
 127             Real damping;
 128
 129             /// Message update schedule
 130             UpdateType updates;
 131
 132             /// Inference variant
 133             InfType inference;
 134         } props;
 135
 136         /// Name of this inference algorithm
 137         static const char *Name;
 138
 139         /// Specifies whether the history of message updates should be recorded
 140         bool recordSentMessages;
 141
 142         /// Stores variable beliefs of previous iteration
 143         std::vector<Factor> oldBeliefsV;
 144
 145         /// Stores factor beliefs of previous iteration
 146         std::vector<Factor> oldBeliefsF;
 147
 148         /// Stores the update schedule
 149         std::vector<Edge> updateSeq;
 150
 151     public:
 152     /// \name Constructors/destructors
 153     //@{
 154         /// Default constructor
 155         BP() : DAIAlgFG(), _edges(), _edge2lut(), _lut(), _maxdiff(0.0), _iters(0U), _sentMessages(), props(), recordSentMessages(false) {}
 156
 157         /// Construct from FactorGraph \a fg and PropertySet \a opts
 158         /** \param fg Factor graph.
 159          *  \param opts Parameters @see Properties
 160          */
 161         BP( const FactorGraph & fg, const PropertySet &opts ) : DAIAlgFG(fg), _edges(), _maxdiff(0.0), _iters(0U), _sentMessages(), props(), recordSentMessages(false) {
 162             setProperties( opts );
 163             construct();
 164         }
 165
 166         /// Copy constructor
 167         BP( const BP &x ) : DAIAlgFG(x), _edges(x._edges), _edge2lut(x._edge2lut),
 168             _lut(x._lut), _maxdiff(x._maxdiff), _iters(x._iters), _sentMessages(x._sentMessages),
 169             props(x.props), recordSentMessages(x.recordSentMessages)
 170         {
 171             for( LutType::iterator l = _lut.begin(); l != _lut.end(); ++l )
 172                 _edge2lut[l->second.first][l->second.second] = l;
 173         }
 174
 175         /// Assignment operator
 176         BP& operator=( const BP &x ) {
 177             if( this != &x ) {
 178                 DAIAlgFG::operator=( x );
 179                 _edges = x._edges;
 180                 _lut = x._lut;
 181                 for( LutType::iterator l = _lut.begin(); l != _lut.end(); ++l )
 182                     _edge2lut[l->second.first][l->second.second] = l;
 183                 _maxdiff = x._maxdiff;
 184                 _iters = x._iters;
 185                 _sentMessages = x._sentMessages;
 186                 props = x.props;
 187                 recordSentMessages = x.recordSentMessages;
 188             }
 189             return *this;
 190         }
 191     //@}
 192
 193     /// \name General InfAlg interface
 194     //@{
 195         virtual BP* clone() const { return new BP(*this); }
 196         virtual std::string identify() const;
 197         virtual Factor belief( const Var &v ) const { return beliefV( findVar( v ) ); }
 198         virtual Factor belief( const VarSet &vs ) const;
 199         virtual Factor beliefV( size_t i ) const;
 200         virtual Factor beliefF( size_t I ) const;
 201         virtual std::vector<Factor> beliefs() const;
 202         virtual Real logZ() const;
 203         virtual void init();
 204         virtual void init( const VarSet &ns );
 205         virtual Real run();
 206         virtual Real maxDiff() const { return _maxdiff; }
 207         virtual size_t Iterations() const { return _iters; }
 208         virtual void setProperties( const PropertySet &opts );
 209         virtual PropertySet getProperties() const;
 210         virtual std::string printProperties() const;
 211     //@}
 212
 213     /// \name Additional interface specific for BP
 214     //@{
 215         /// Calculates the joint state of all variables that has maximum probability
 216         /** \pre Assumes that run() has been called and that \a props.inference == \c MAXPROD
 217          */
 218         std::vector<std::size_t> findMaximum() const;
 219
 220         /// Returns history of which messages have been updated
 221         const std::vector<std::pair<std::size_t, std::size_t> >& getSentMessages() const {
 222             return _sentMessages;
 223         }
 224
 225         /// Clears history of which messages have been updated
 226         void clearSentMessages() { _sentMessages.clear(); }
 227     //@}
 228
 229     protected:
 230         /// Returns constant reference to message from the \a _I 'th neighbor of variable \a i to variable \a i
 231         const Prob & message(size_t i, size_t _I) const { return _edges[i][_I].message; }
 232         /// Returns reference to message from the \a _I 'th neighbor of variable \a i to variable \a i
 233         Prob & message(size_t i, size_t _I) { return _edges[i][_I].message; }
 234         /// Returns constant reference to updated message from the \a _I 'th neighbor of variable \a i to variable \a i
 235         const Prob & newMessage(size_t i, size_t _I) const { return _edges[i][_I].newMessage; }
 236         /// Returns reference to updated message from the \a _I 'th neighbor of variable \a i to variable \a i
 237         Prob & newMessage(size_t i, size_t _I) { return _edges[i][_I].newMessage; }
 238         /// Returns constant reference to cached index for the edge between variable \a i and its \a _I 'th neighbor
 239         const ind_t & index(size_t i, size_t _I) const { return _edges[i][_I].index; }
 240         /// Returns reference to cached index for the edge between variable \a i and its \a _I 'th neighbor
 241         ind_t & index(size_t i, size_t _I) { return _edges[i][_I].index; }
 242         /// Returns constant reference to residual for the edge between variable \a i and its \a _I 'th neighbor
 243         const Real & residual(size_t i, size_t _I) const { return _edges[i][_I].residual; }
 244         /// Returns reference to residual for the edge between variable \a i and its \a _I 'th neighbor
 245         Real & residual(size_t i, size_t _I) { return _edges[i][_I].residual; }
 246
 247         /// Calculate the product of factor \a I and the incoming messages
 248         /** If \a without_i == \c true, the message coming from variable \a i is omitted from the product
 249          *  \note This function is used by calcNewMessage() and calcBeliefF()
 250          */
 251         virtual Prob calcIncomingMessageProduct( size_t I, bool without_i, size_t i ) const;
 252         /// Calculate the updated message from the \a _I 'th neighbor of variable \a i to variable \a i
 253         virtual void calcNewMessage( size_t i, size_t _I );
 254         /// Replace the "old" message from the \a _I 'th neighbor of variable \a i to variable \a i by the "new" (updated) message
 255         void updateMessage( size_t i, size_t _I );
 256         /// Set the residual (difference between new and old message) for the edge between variable \a i and its \a _I 'th neighbor to \a r
 257         void updateResidual( size_t i, size_t _I, Real r );
 258         /// Finds the edge which has the maximum residual (difference between new and old message)
 259         void findMaxResidual( size_t &i, size_t &_I );
 260         /// Calculates unnormalized belief of variable \a i
 261         virtual void calcBeliefV( size_t i, Prob &p ) const;
 262         /// Calculates unnormalized belief of factor \a I
 263         virtual void calcBeliefF( size_t I, Prob &p ) const {
 264             p = calcIncomingMessageProduct( I, false, 0 );
 265         }
 266
 267         /// Helper function for constructors
 268         virtual void construct();
 269 };
 270
 271
 272 } // end of namespace dai
 273
 274
 275 #endif