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) 2009 Frederik Eaton
8 */
11 /// \file
12 /// \brief Defines class FBP, which implements Fractional Belief Propagation
15 #ifndef __defined_libdai_fbp_h
16 #define __defined_libdai_fbp_h
19 #include <string>
20 #include <dai/daialg.h>
21 #include <dai/factorgraph.h>
22 #include <dai/properties.h>
23 #include <dai/enum.h>
24 #include <dai/bp.h>
27 namespace dai {
30 /// Approximate inference algorithm "Fractional Belief Propagation" [\ref WiH03]
31 /** The Fractional Belief Propagation algorithm is like Belief
32 * Propagation, but associates each factor with a weight (scale parameter)
33 * which controls the divergence measure being minimized. Standard
34 * Belief Propagation corresponds to the case of FBP where each weight
35 * is 1. When cast as an EP algorithm, BP (and EP) minimize
36 * the inclusive KL-divergence, i.e. \f$\min_q KL(p||q)\f$ (note that the
37 * Bethe free energy is typically derived from \f$KL(q||p) \f$). If each
38 * factor \a I has weight \f$c_I \f$, then FBP minimizes the
39 * alpha-divergence with \f$\alpha=1/c_I \f$ for that factor, which also
40 * corresponds to Power EP [\ref Min05].
41 *
42 * The messages \f$m_{I\to i}(x_i)\f$ are passed from factors \f$I\f$ to variables \f$i\f$.
43 * The update equation is given by:
44 * \f[ m_{I\to i}(x_i) \propto \left( \sum_{x_{N_I\setminus\{i\}}} f_I(x_I)^{1/c_I} \prod_{j\in N_I\setminus\{i\}} m_{I\to j}^{1-1/c_I} \prod_{J\in N_j\setminus\{I\}} m_{J\to j} \right)^{c_I} \f]
45 * After convergence, the variable beliefs are calculated by:
46 * \f[ b_i(x_i) \propto \prod_{I\in N_i} m_{I\to i} \f]
47 * and the factor beliefs are calculated by:
48 * \f[ b_I(x_I) \propto f_I(x_I)^{1/c_I} \prod_{j \in N_I} m_{I\to j}^{1-1/c_I} \prod_{J\in N_j\setminus\{I\}} m_{J\to j} \f]
49 * The logarithm of the partition sum is approximated by:
50 * \f[ \log Z = \sum_{I} \sum_{x_I} b_I(x_I) \big( \log f_I(x_I) - c_I \log b_I(x_I) \big) + \sum_{i} (c_i - 1) \sum_{x_i} b_i(x_i) \log b_i(x_i) \f]
51 * where the variable weights are defined as
52 * \f[ c_i := \sum_{I \in N_i} c_I \f]
53 *
54 * \todo Add nice way to set weights
55 * \todo Merge duplicate code in calcNewMessage() and calcBeliefF()
56 * \author Frederik Eaton
57 */
58 class FBP : public BP {
59 protected:
60 /// Factor weights (indexed by factor ID)
61 std::vector<Real> _weight;
63 public:
64 /// Name of this inference algorithm
65 static const char *Name;
67 public:
68 /// \name Constructors/destructors
69 //@{
70 /// Default constructor
71 FBP() : BP(), _weight() {}
73 /// Construct from FactorGraph \a fg and PropertySet \a opts
74 /** \param opts Parameters @see BP::Properties
75 */
76 FBP( const FactorGraph &fg, const PropertySet &opts ) : BP(fg, opts), _weight() {
77 setProperties( opts );
78 construct();
79 }
80 //@}
82 /// \name General InfAlg interface
83 //@{
84 virtual FBP* clone() const { return new FBP(*this); }
85 virtual std::string identify() const;
86 virtual Real logZ() const;
87 //@}
89 /// \name FBP accessors/mutators for weights
90 //@{
91 /// Returns weight of the \a I 'th factor
92 Real Weight( size_t I ) const { return _weight[I]; }
94 /// Returns constant reference to vector of all factor weights
95 const std::vector<Real>& Weights() const { return _weight; }
97 /// Sets the weight of the \a I 'th factor to \a c
98 void setWeight( size_t I, Real c ) { _weight[I] = c; }
100 /// Sets the weights of all factors simultaenously
101 /** \note Faster than calling setWeight(size_t,Real) for each factor
102 */
103 void setWeights( const std::vector<Real> &c ) { _weight = c; }
105 protected:
106 // Calculate the updated message from the \a _I 'th neighbor of variable \a i to variable \a i
107 virtual void calcNewMessage( size_t i, size_t _I );
109 // Calculates unnormalized belief of factor \a I
110 virtual void calcBeliefF( size_t I, Prob &p ) const;
112 // Helper function for constructors
113 virtual void construct();
114 };
117 } // end of namespace dai
120 #endif