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