Rewrote implementation of response propagation in MR
[libdai.git] / include / dai / doc.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) 2008-2010 Joris Mooij [joris dot mooij at libdai dot org]
8 */
9
10
11 /** \file
12 * \brief Contains additional doxygen documentation
13 *
14 * \idea Adapt (part of the) guidelines in http://www.boost.org/development/requirements.html#Design_and_Programming
15 *
16 * \idea Use "gcc -MM" to generate dependencies for targets: http://make.paulandlesley.org/autodep.html
17 *
18 * \idea Disentangle structures. In particular, ensure that graphical properties are not
19 * entangled with probabilistic properties. For example, a FactorGraph contains several components:
20 * - a BipartiteGraph
21 * - an array of variable labels
22 * - an array of variable state space sizes
23 * - an array of pointers to factor value vectors
24 * In this way, each factor could be implemented differently, e.g., we could have
25 * some sparse factors, some noisy-OR factors, some dense factors, some arbitrary
26 * precision factors, etcetera.
27 *
28 * \idea Use boost::uBLAS framework to deal with matrices, especially, with 2D sparse matrices.
29 * See http://www.boost.org/libs/numeric/ublas/doc/matrix_sparse.htm
30 * However: I read somewhere that boost::uBLAS concentrates more on correct implementation than on performance.
31 *
32 * \idea Introduce naming scheme:
33 * - all Vars should be named v_..., e.g. v_i instead of i
34 * - all VarSets should be named vs_..., e.g. v_i instead of i
35 * - all Factors should be named f_..., e.g. f_I instead of I
36 * - all indices should be named _..., e.g. _k instead of k
37 * - all iterators should be named i_, e.g. i_i is an iterator to i
38 * - all const_iterators should be named ci_, e.g. ci_i is an iterator to i
39 **/
40
41
42 /** \mainpage Reference manual for libDAI - A free/open source C++ library for Discrete Approximate Inference methods
43 * \author Joris Mooij, Frederik Eaton
44 * \version git HEAD
45 * \date February 11, 2010 - or later
46 *
47 * <hr size="1">
48 * \section about About libDAI
49 * libDAI is a free/open source C++ library (licensed under GPL 2+) that provides
50 * implementations of various (approximate) inference methods for discrete
51 * graphical models. libDAI supports arbitrary factor graphs with discrete
52 * variables; this includes discrete Markov Random Fields and Bayesian
53 * Networks.
54 *
55 * The library is targeted at researchers. To be able to use the library, a
56 * good understanding of graphical models is needed.
57 *
58 * The best way to use libDAI is by writing C++ code that invokes the library;
59 * in addition, part of the functionality is accessibly by using the
60 * - command line interface
61 * - (limited) MatLab interface
62 * - (experimental) python interface
63 * - (experimental) octave interface.
64 *
65 * libDAI can be used to implement novel (approximate) inference algorithms
66 * and to easily compare the accuracy and performance with existing algorithms
67 * that have been implemented already.
68 *
69 * \section features Features
70 * Currently, libDAI supports the following (approximate) inference methods:
71 * - Exact inference by brute force enumeration;
72 * - Exact inference by junction-tree methods;
73 * - Mean Field;
74 * - Loopy Belief Propagation [\ref KFL01];
75 * - Fractional Belief Propagation [\ref WiH03];
76 * - Tree-Reweighted Belief Propagation [\ref WJW03];
77 * - Tree Expectation Propagation [\ref MiQ04];
78 * - Generalized Belief Propagation [\ref YFW05];
79 * - Double-loop GBP [\ref HAK03];
80 * - Various variants of Loop Corrected Belief Propagation
81 * [\ref MoK07, \ref MoR05];
82 * - Gibbs sampler;
83 * - Conditioned Belief Propagation [\ref EaG09].
84 *
85 * These inference methods can be used to calculate partition sums, marginals
86 * over subsets of variables, and MAP states (the joint state of variables that
87 * has maximum probability).
88 *
89 * In addition, libDAI supports parameter learning of conditional probability
90 * tables by Expectation Maximization.
91 *
92 * \section limitations Limitations
93 * libDAI is not intended to be a complete package for approximate inference.
94 * Instead, it should be considered as an "inference engine", providing
95 * various inference methods. In particular, it contains no GUI, currently
96 * only supports its own file format for input and output (although support
97 * for standard file formats may be added later), and provides very limited
98 * visualization functionalities. The only learning method supported currently
99 * is Expectation Maximization (or Maximum Likelihood if no data is missing)
100 * for learning factor parameters.
101 *
102 * \section rationale Rationale
103 *
104 * In my opinion, the lack of open source "reference" implementations hampers
105 * progress in research on approximate inference. Methods differ widely in terms
106 * of quality and performance characteristics, which also depend in different
107 * ways on various properties of the graphical models. Finding the best
108 * approximate inference method for a particular application therefore often
109 * requires empirical comparisons. However, implementing and debugging these
110 * methods takes a lot of time which could otherwise be spent on research. I hope
111 * that this code will aid researchers to be able to easily compare various
112 * (existing as well as new) approximate inference methods, in this way
113 * accelerating research and stimulating real-world applications of approximate
114 * inference.
115 *
116 * \section language Language
117 * Because libDAI is implemented in C++, it is very fast compared with
118 * implementations in MatLab (a factor 1000 faster is not uncommon).
119 * libDAI does provide a (limited) MatLab interface for easy integration with MatLab.
120 * It also provides a command line interface and experimental python and octave
121 * interfaces (thanks to Patrick Pletscher).
122 *
123 * \section compatibility Compatibility
124 *
125 * The code has been developed under Debian GNU/Linux with the GCC compiler suite.
126 * libDAI compiles successfully with g++ versions 3.4, 4.1, 4.2 and 4.3.
127 *
128 * libDAI has also been successfully compiled with MS Visual Studio 2008 under Windows
129 * (but not all build targets are supported yet) and with Cygwin under Windows.
130 *
131 * Finally, libDAI has been compiled successfully on MacOS X.
132 *
133 * \section download Downloading libDAI
134 * The libDAI sources and documentation can be downloaded from the libDAI website:
135 * http://www.libdai.org.
136 *
137 * \section support Mailing list
138 * The Google group "libDAI" (http://groups.google.com/group/libdai)
139 * can be used for getting support and discussing development issues.
140 */
141
142
143 /** \page license License
144 * <hr size="1">
145 * \section license-license License
146 *
147 * libDAI is free software; you can redistribute it and/or modify
148 * it under the terms of the GNU General Public License as published by
149 * the Free Software Foundation; either version 2 of the License, or
150 * (at your option) any later version.
151 *
152 * libDAI is distributed in the hope that it will be useful,
153 * but WITHOUT ANY WARRANTY; without even the implied warranty of
154 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
155 * GNU General Public License for more details.
156 *
157 * <hr size="1">
158 * \section license-gpl GNU General Public License version 2
159 *
160 * \verbinclude COPYING
161 */
162
163
164 /** \page citations Citing libDAI
165 * <hr size="1">
166 * \section citations-citations Citing libDAI
167 *
168 * If you write a scientific paper describing research that made substantive use
169 * of this program, please:
170 * - mention the fashion in which this software was
171 * used, including the version number, with a citation to the literature,
172 * to allow replication;
173 * - mention this software in the Acknowledgements section.
174 *
175 * An appropriate citation would be:\n
176 *
177 * Joris M. Mooij et al. (2010) "libDAI 0.2.4: A free/open source C++ library for Discrete
178 * Approximate Inference", http://www.libdai.org
179 *
180 * or in BiBTeX format:
181 *
182 * <pre>
183 * \@misc{mooij2010libdai,
184 * author = "Joris M. Mooij et al.",
185 * title = "lib{DAI} 0.2.4: A free/open source {C}++ library for {D}iscrete {A}pproximate {I}nference",
186 * howpublished = "http://www.libdai.org/",
187 * year = 2010
188 * }
189 * </pre>
190 *
191 * Moreover, as a personal note, I would appreciate it if you would email
192 * (citations of) papers referencing this work to joris dot mooij at libdai dot org.
193 */
194
195
196 /** \page authors Authors
197 * \section authors-authors People who contributed to libDAI
198 *
199 * \verbinclude AUTHORS
200 */
201
202
203 /** \page build Building libDAI
204 * <hr size="1">
205 * \section build-unix Building libDAI under UNIX variants (Linux / Cygwin / Mac OS X)
206 *
207 * \subsection build-unix-preparations Preparations
208 *
209 * You need:
210 * - a recent version of gcc (at least version 3.4)
211 * - GNU make
212 * - doxygen
213 * - graphviz
214 * - recent boost C++ libraries (at least version 1.34 if you have
215 * a recent version of GCC, otherwise at least version 1.37; however,
216 * version 1.37 shipped with Ubuntu 9.04 is known not to work)
217 *
218 * On Debian/Ubuntu, you can easily install all these packages with a single command:
219 * <pre> apt-get install g++ make doxygen graphviz libboost-dev libboost-graph-dev libboost-program-options-dev</pre>
220 * (root permissions needed).
221 *
222 * On Mac OS X (10.4 is known to work), these packages can be installed easily via MacPorts.
223 * If MacPorts is not already installed, install it according to the instructions at http://www.macports.org/.
224 * Then, a simple
225 * <pre> sudo port install gmake boost doxygen graphviz</pre>
226 * should be enough to install everything that is needed.
227 *
228 * On Cygwin, the prebuilt Cygwin package boost-1.33.1-x is known not to work.
229 * You can however obtain the latest boost version (you need at least 1.37.0)
230 * from http://www.boost.org/ and compile/install it with:
231 *
232 * <pre> ./configure
233 * make
234 * make install
235 * </pre>
236 *
237 * \subsection build-unix-libdai Building libDAI
238 *
239 * To build the libDAI source, first copy a template Makefile.* to Makefile.conf
240 * (for example, copy Makefile.LINUX to Makefile.conf if you use GNU/Linux).
241 * Then, edit the Makefile.conf template to adapt it to your local setup.
242 * Especially directories may differ from system to system. Platform independent
243 * build options can be set in Makefile.ALL. Finally, run
244 * <pre> make</pre>
245 * The build includes a regression test, which may take a while to complete.
246 *
247 * If the build is successful, you can test the example program:
248 * <pre> examples/example tests/alarm.fg</pre>
249 * or the more extensive test program:
250 * <pre> tests/testdai --aliases tests/aliases.conf --filename tests/alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
251 *
252 *
253 * <hr size="1">
254 * \section build-windows Building libDAI under Windows
255 *
256 * \subsection build-windows-preparations Preparations
257 *
258 * You need:
259 * - A recent version of MicroSoft Visual Studio (2008 is known to work)
260 * - recent boost C++ libraries (version 1.37 or higher)
261 * - GNU make (can be obtained from http://gnuwin32.sourceforge.net)
262 *
263 * For the regression test, you need:
264 * - GNU diff, GNU sed (can be obtained from http://gnuwin32.sourceforge.net)
265 *
266 * \subsection build-windows-libdai Building libDAI
267 *
268 * To build the source, copy Makefile.WINDOWS to Makefile.conf. Then, edit
269 * Makefile.conf to adapt it to your local setup. Platform independent
270 * build options can be set in Makefile.ALL. Finally, run (from the command line)
271 * <pre> make</pre>
272 * The build includes a regression test, which may take a while to complete.
273 *
274 * If the build is successful, you can test the example program:
275 * <pre> examples\\example tests\\alarm.fg</pre>
276 * or the more extensive test program:
277 * <pre> tests\\testdai --aliases tests\\aliases.conf --filename tests\\alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
278 *
279 *
280 * <hr size="1">
281 * \section build-matlab Building the libDAI MatLab interface
282 *
283 * You need:
284 * - MatLab
285 * - The platform-dependent requirements described above
286 *
287 * First, you need to build the libDAI source as described above for your
288 * platform. By default, the MatLab interface is disabled, so before compiling the
289 * source, you have to enable it in Makefile.ALL by setting
290 * <pre> WITH_MATLAB=true</pre>
291 * Also, you have to configure the MatLab-specific parts of
292 * Makefile.conf to match your system (in particular, the Makefile variables ME,
293 * MATLABDIR and MEX). The MEX file extension depends on your platform; for a
294 * 64-bit linux x86_64 system this would be "ME=.mexa64", for a 32-bit linux x86
295 * system "ME=.mexglx". If you are unsure about your MEX file
296 * extension: it needs to be the same as what the MatLab command "mexext" returns.
297 * The required MEX files are built by issuing
298 * <pre> make</pre>
299 * from the command line. The MatLab interface is much less powerful than using
300 * libDAI from C++. There are two reasons for this: (i) it is boring to write MEX
301 * files; (ii) the large performance penalty paid when large data structures (like
302 * factor graphs) have to be converted between their native C++ data structure to
303 * something that MatLab understands.
304 *
305 * A simple example of how to use the MatLab interface is the following (entered
306 * at the MatLab prompt), which performs exact inference by the junction tree
307 * algorithm and approximate inference by belief propagation on the ALARM network:
308 * <pre> cd path_to_libdai/matlab
309 * [psi] = dai_readfg ('../examples/alarm.fg');
310 * [logZ,q,md,qv,qf] = dai (psi, 'JTREE', '[updates=HUGIN,verbose=0]')
311 * [logZ,q,md,qv,qf] = dai (psi, 'BP', '[updates=SEQMAX,tol=1e-9,maxiter=10000,logdomain=0]')</pre>
312 * where "path_to_libdai" has to be replaced with the directory in which libDAI
313 * was installed. For other algorithms and some default parameters, see the file
314 * tests/aliases.conf.
315 *
316 * <hr size="1">
317 * \section build-doxygen Building the documentation
318 *
319 * Install doxygen, graphviz and a TeX distribution and use
320 * <pre> make doc</pre>
321 * to build the documentation. If the documentation is not clear enough, feel free
322 * to send me an email (or even better, to improve the documentation and send a patch!).
323 * The documentation can also be browsed online at http://www.libdai.org.
324 */
325
326
327 /** \page changelog Change Log
328 * \verbinclude ChangeLog
329 */
330
331
332 /** \page terminology Terminology and conventions
333 *
334 * \section terminology-graphicalmodels Graphical models
335 *
336 * Commonly used graphical models are Bayesian networks and Markov random fields.
337 * In libDAI, both types of graphical models are represented by a slightly more
338 * general type of graphical model: a factor graph [\ref KFL01].
339 *
340 * An example of a Bayesian network is:
341 * \dot
342 * digraph bayesnet {
343 * size="1,1";
344 * x0 [label="0"];
345 * x1 [label="1"];
346 * x2 [label="2"];
347 * x3 [label="3"];
348 * x4 [label="4"];
349 * x0 -> x1;
350 * x0 -> x2;
351 * x1 -> x3;
352 * x1 -> x4;
353 * x2 -> x4;
354 * }
355 * \enddot
356 * The probability distribution of a Bayesian network factorizes as:
357 * \f[ P(\mathbf{x}) = \prod_{i\in\mathcal{V}} P(x_i \,|\, x_{\mathrm{pa}(i)}) \f]
358 * where \f$\mathrm{pa}(i)\f$ are the parents of node \a i in a DAG.
359 *
360 * The same probability distribution can be represented as a Markov random field:
361 * \dot
362 * graph mrf {
363 * size="1.5,1.5";
364 * x0 [label="0"];
365 * x1 [label="1"];
366 * x2 [label="2"];
367 * x3 [label="3"];
368 * x4 [label="4"];
369 * x0 -- x1;
370 * x0 -- x2;
371 * x1 -- x2;
372 * x1 -- x3;
373 * x1 -- x4;
374 * x2 -- x4;
375 * }
376 * \enddot
377 *
378 * The probability distribution of a Markov random field factorizes as:
379 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{C\in\mathcal{C}} \psi_C(x_C) \f]
380 * where \f$ \mathcal{C} \f$ are the cliques of an undirected graph,
381 * \f$ \psi_C(x_C) \f$ are "potentials" or "compatibility functions", and
382 * \f$ Z \f$ is the partition sum which properly normalizes the probability
383 * distribution.
384 *
385 * Finally, the same probability distribution can be represented as a factor graph:
386 * \dot
387 * graph factorgraph {
388 * size="1.8,1";
389 * x0 [label="0"];
390 * x1 [label="1"];
391 * x2 [label="2"];
392 * x3 [label="3"];
393 * x4 [label="4"];
394 * f01 [shape="box",label=""];
395 * f02 [shape="box",label=""];
396 * f13 [shape="box",label=""];
397 * f124 [shape="box",label=""];
398 * x0 -- f01;
399 * x1 -- f01;
400 * x0 -- f02;
401 * x2 -- f02;
402 * x1 -- f13;
403 * x3 -- f13;
404 * x1 -- f124;
405 * x2 -- f124;
406 * x4 -- f124;
407 * }
408 * \enddot
409 *
410 * The probability distribution of a factor graph factorizes as:
411 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{I\in \mathcal{F}} f_I(x_I) \f]
412 * where \f$ \mathcal{F} \f$ are the factor nodes of a factor graph (a
413 * bipartite graph consisting of variable nodes and factor nodes),
414 * \f$ f_I(x_I) \f$ are the factors, and \f$ Z \f$ is the partition sum
415 * which properly normalizes the probability distribution.
416 *
417 * Looking at the expressions for the joint probability distributions,
418 * it is obvious that Bayesian networks and Markov random fields can
419 * both be easily represented as factor graphs. Factor graphs most
420 * naturally express the factorization structure of a probability
421 * distribution, and hence are a convenient representation for approximate
422 * inference algorithms, which all try to exploit this factorization.
423 * This is why libDAI uses a factor graph as representation of a
424 * graphical model, implemented in the dai::FactorGraph class.
425 *
426 * \section terminology-inference Inference tasks
427 *
428 * Given a factor graph, specified by the variable nodes \f$\{x_i\}_{i\in\mathcal{V}}\f$
429 * the factor nodes \f$ \mathcal{F} \f$, the graph structure, and the factors
430 * \f$\{f_I(x_I)\}_{I\in\mathcal{F}}\f$, the following tasks are important:
431 *
432 * - Calculating the partition sum:
433 * \f[ Z = \sum_{\mathbf{x}_{\mathcal{V}}} \prod_{I \in \mathcal{F}} f_I(x_I) \f]
434 * - Calculating the marginal distribution of a subset of variables
435 * \f$\{x_i\}_{i\in A}\f$:
436 * \f[ P(\mathbf{x}_{A}) = \frac{1}{Z} \sum_{\mathbf{x}_{\mathcal{V}\setminus A}} \prod_{I \in \mathcal{F}} f_I(x_I) \f]
437 * - Calculating the MAP state which has the maximum probability mass:
438 * \f[ \mathrm{argmax}_{\mathbf{x}}\,\prod_{I\in\mathcal{F}} f_I(x_I) \f]
439 *
440 * libDAI offers several inference algorithms, which solve (a subset of) these tasks either
441 * approximately or exactly, for factor graphs with discrete variables. The following
442 * algorithms are implemented:
443 *
444 * Exact inference:
445 * - Brute force enumeration: dai::ExactInf
446 * - Junction-tree method: dai::JTree
447 *
448 * Approximate inference:
449 * - Mean Field: dai::MF
450 * - (Loopy) Belief Propagation: dai::BP [\ref KFL01]
451 * - Fractional Belief Propagation: dai::FBP [\ref WiH03]
452 * - Tree-Reweighted Belief Propagation: dai::TRWBP [\ref WJW03]
453 * - Tree Expectation Propagation: dai::TreeEP [\ref MiQ04]
454 * - Generalized Belief Propagation: dai::HAK [\ref YFW05]
455 * - Double-loop GBP: dai::HAK [\ref HAK03]
456 * - Loop Corrected Belief Propagation: dai::MR [\ref MoR05] and dai::LC [\ref MoK07]
457 * - Gibbs sampling: dai::Gibbs
458 * - Conditioned Belief Propagation: dai::CBP [\ref EaG09]
459 *
460 * Not all inference tasks are implemented by each method: calculating MAP states
461 * is only possible with dai::JTree and dai::BP, calculating partition sums is
462 * not possible with dai::MR, dai::LC and dai::Gibbs.
463 *
464 * \section terminology-learning Parameter learning
465 *
466 * In addition, libDAI supports parameter learning of conditional probability
467 * tables by Expectation Maximization (or Maximum Likelihood, if there is no
468 * missing data). This is implemented in dai::EMAlg.
469 *
470 * \section terminology-variables-states Variables and states
471 *
472 * Linear states are a concept that is used often in libDAI, for example for storing
473 * and accessing factors, which are functions mapping from states of a set of variables
474 * to the real numbers. Internally, a factor is stored as an array, and the array index
475 * of an entry corresponds with the linear state of the set of variables. Below we will
476 * define variables, states and linear states of (sets of) variables.
477 *
478 * \subsection terminology-variables Variables
479 *
480 * Each (random) \a variable has a unique identifier, its \a label (which has
481 * a non-negative integer value). If two variables have the same
482 * label, they are considered as identical. A variable can take on a finite
483 * number of different values or \a states.
484 *
485 * We use the following notational conventions. The discrete
486 * random variable with label \f$l\f$ is denoted as \f$x_l\f$, and the number
487 * of possible values of this variable as \f$S_{x_l}\f$ or simply \f$S_l\f$.
488 * The set of possible values of variable \f$x_l\f$ is denoted
489 * \f$X_l := \{0,1,\dots,S_l-1\}\f$ and called its \a state \a space.
490 *
491 * \subsection terminology-variable-sets Sets of variables and the canonical ordering
492 *
493 * Let \f$A := \{x_{l_1},x_{l_2},\dots,x_{l_n}\}\f$ be a set of variables.
494 *
495 * The \a canonical \a ordering of the variables in \a A is induced by their labels.
496 * That is: if \f$l_1 < l_2\f$, then \f$x_{l_1}\f$ occurs before \f$x_{l_2}\f$ in the
497 * canonical ordering. Below, we will assume that \f$(l_i)_{i=1}^n\f$ is
498 * ordered according to the canonical ordering, i.e., \f$l_1 < l_2 < \dots < l_n\f$.
499 *
500 * \subsection terminology-variable-states States and linear states of sets of variables
501 *
502 * A \a state of the variables in \a A refers to a joint assignment of the
503 * variables, or in other words, to an element of the Cartesian product
504 * \f$ \prod_{i=1}^n X_{l_i}\f$ of the state spaces of the variables in \a A.
505 * Note that a state can also be interpreted as a mapping from variables (or
506 * variable labels) to the natural numbers, which assigns to a variable (or its
507 * label) the corresponding state of the variable.
508 *
509 * A state of \a n variables can be represented as an n-tuple of
510 * non-negative integers: \f$(s_1,s_2,\dots,s_n)\f$ corresponds to the
511 * joint assignment \f$x_{l_1} = s_1, \dots, x_{l_n} = s_n\f$.
512 * Alternatively, a state can be represented compactly as one non-negative integer;
513 * this representation is called a \a linear \a state. The linear state
514 * \a s corresponding to the state \f$(s_1,s_2,\dots,s_n)\f$ would be:
515 * \f[
516 * s := \sum_{i=1}^n s_i \prod_{j=1}^{i-1} S_{l_j}
517 * = s_1 + s_2 S_{l_1} + s_3 S_{l_1} S_{l_2} + \dots + s_n S_{l_1} \cdots S_{l_{n-1}}.
518 * \f]
519 *
520 * Vice versa, given a linear state \a s for the variables \a A, the
521 * corresponding state \f$s_i\f$ of the \a i 'th variable \f$x_{l_i}\f$ (according to
522 * the canonical ordering of the variables in \a A) is given by
523 * \f[
524 * s_i = \left\lfloor\frac{s \mbox { mod } \prod_{j=1}^i S_{l_j}}{\prod_{j=1}^{i-1} S_{l_j}}\right\rfloor.
525 * \f]
526 *
527 * Finally, the \a number \a of \a states of the set of variables \a A is simply the
528 * number of different joint assignments of the variables, that is, \f$\prod_{i=1}^n S_{l_i}\f$.
529 */
530
531
532 /** \page fileformats libDAI file formats
533 *
534 * \section fileformats-factorgraph Factor graph (.fg) file format
535 *
536 * This section describes the .fg file format used in libDAI to store factor graphs.
537 * Markov Random Fields are special cases of factor graphs, as are Bayesian
538 * networks. A factor graph can be specified as follows: for each factor, one has
539 * to specify which variables occur in the factor, what their respective
540 * cardinalities (i.e., number of possible values) are, and a table listing all
541 * the values of that factor for all possible configurations of these variables.
542 *
543 * A .fg file is not much more than that. It starts with a line containing the
544 * number of factors in that graph, followed by an empty line. Then all factors
545 * are specified, using one block for each factor, where the blocks are seperated
546 * by empty lines. Each variable occurring in the factor graph has a unique
547 * identifier, its label (which should be a nonnegative integer). Comment lines
548 * which start with # are ignored.
549 *
550 * \subsection fileformats-factorgraph-factor Factor block format
551 *
552 * Each block describing a factor starts with a line containing the number of
553 * variables in that factor. The second line contains the labels of these
554 * variables, seperated by spaces (labels are nonnegative integers and to avoid
555 * confusion, it is suggested to start counting at 0). The third line contains
556 * the number of possible values of each of these variables, also seperated by
557 * spaces. Note that there is some redundancy here, since if a variable appears
558 * in more than one factor, the cardinality of that variable appears several
559 * times in the .fg file; obviously, these cardinalities should be consistent.
560 * The fourth line contains the number of nonzero entries
561 * in the factor table. The rest of the lines contain these nonzero entries;
562 * each line consists of a table index, followed by white-space, followed by the
563 * value corresponding to that table index. The most difficult part is getting
564 * the indexing right. The convention that is used is that the left-most
565 * variables cycle through their values the fastest (similar to MatLab indexing
566 * of multidimensional arrays).
567 *
568 * \subsubsection fileformats-factorgraph-factor-example Example
569 *
570 * An example block describing one factor is:
571 *
572 * <pre>
573 * 3
574 * 4 8 7
575 * 3 2 2
576 * 11
577 * 0 0.1
578 * 1 3.5
579 * 2 2.8
580 * 3 6.3
581 * 4 8.4
582 * 6 7.4
583 * 7 2.4
584 * 8 8.9
585 * 9 1.3
586 * 10 1.6
587 * 12 6.4
588 * 11 2.6
589 * </pre>
590 *
591 * which corresponds to the following factor:
592 *
593 * \f[
594 * \begin{array}{ccc|c}
595 * x_4 & x_8 & x_7 & \mbox{value}\\
596 * \hline
597 * 0 & 0 & 0 & 0.1\\
598 * 1 & 0 & 0 & 3.5\\
599 * 2 & 0 & 0 & 2.8\\
600 * 0 & 1 & 0 & 6.3\\
601 * 1 & 1 & 0 & 8.4\\
602 * 2 & 1 & 0 & 0.0\\
603 * 0 & 0 & 1 & 7.4\\
604 * 1 & 0 & 1 & 2.4\\
605 * 2 & 0 & 1 & 8.9\\
606 * 0 & 1 & 1 & 1.3\\
607 * 1 & 1 & 1 & 1.6\\
608 * 2 & 1 & 1 & 2.6
609 * \end{array}
610 * \f]
611 *
612 * Note that the value of \f$x_4\f$ changes fastest, followed by that of \f$x_8\f$, and \f$x_7\f$
613 * varies the slowest, corresponding to the second line of the block ("4 8 7").
614 * Further, \f$x_4\f$ can take on three values, and \f$x_8\f$ and \f$x_7\f$ each have two possible
615 * values, as described in the third line of the block ("3 2 2"). The table
616 * contains 11 non-zero entries (all except for the fifth entry). Note that the
617 * eleventh and twelveth entries are interchanged.
618 *
619 * A final note: the internal representation in libDAI of the factor above is
620 * different, because the variables are ordered according to their indices
621 * (i.e., the ordering would be \f$x_4 x_7 x_8\f$) and the values of the table are
622 * stored accordingly, with the variable having the smallest index changing
623 * fastest:
624 *
625 * \f[
626 * \begin{array}{ccc|c}
627 * x_4 & x_7 & x_8 & \mbox{value}\\
628 * \hline
629 * 0 & 0 & 0 & 0.1\\
630 * 1 & 0 & 0 & 3.5\\
631 * 2 & 0 & 0 & 2.8\\
632 * 0 & 1 & 0 & 7.4\\
633 * 1 & 1 & 0 & 2.4\\
634 * 2 & 1 & 0 & 8.9\\
635 * 0 & 0 & 1 & 6.3\\
636 * 1 & 0 & 1 & 8.4\\
637 * 2 & 0 & 1 & 0.0\\
638 * 0 & 1 & 1 & 1.3\\
639 * 1 & 1 & 1 & 1.6\\
640 * 2 & 1 & 1 & 2.6
641 * \end{array}
642 * \f]
643 *
644 *
645 * \section fileformats-evidence Evidence (.tab) file format
646 *
647 * This section describes the .tab fileformat used in libDAI to store "evidence",
648 * i.e., a data set consisting of multiple samples, where each sample is the
649 * observed joint state of some variables.
650 *
651 * A .tab file is a tabular data file, consisting of a header line, followed by
652 * an empty line, followed by the data points, with one line for each data point.
653 * Each line (apart from the empty one) should have the same number of columns,
654 * where columns are separated by one tab character. Each column corresponds to
655 * a variable. The header line consists of the variable labels (corresponding to
656 * dai::Var::label()). The other lines are observed joint states of the variables, i.e.,
657 * each line corresponds to a joint observation of the variables, and each column
658 * of a line contains the state of the variable associated with that column.
659 * Missing data is handled simply by having two consecutive tab characters,
660 * without any characters in between.
661 *
662 * \subsection fileformats-evidence-example Example
663 *
664 * <pre>
665 * 1 3 2
666 *
667 * 0 0 1
668 * 1 0 1
669 * 1 1
670 * </pre>
671 *
672 * This would correspond to a data set consisting of three observations concerning
673 * the variables with labels 1, 3 and 2; the first observation being
674 * \f$x_1 = 0, x_3 = 0, x_2 = 1\f$, the second observation being
675 * \f$x_1 = 1, x_3 = 0, x_2 = 1\f$, and the third observation being
676 * \f$x_1 = 1, x_2 = 1\f$ (where the state of \f$x_3\f$ is missing).
677 *
678 * \section fileformats-emalg Expectation Maximization (.em) file format
679 *
680 * This section describes the file format of .em files, which are used
681 * to specify a particular EM algorithm. The .em files are complementary
682 * to .fg files; in other words, an .em file without a corresponding .fg
683 * file is useless. Furthermore, one also needs a corresponding .tab file
684 * containing the data used for parameter learning.
685 *
686 * An .em file starts with a line specifying the number of maximization steps,
687 * followed by an empty line. Then, each maximization step is described in a
688 * block, which should satisfy the format described in the next subsection.
689 *
690 * \subsection fileformats-emalg-maximizationstep Maximization Step block format
691 *
692 * A maximization step block of an .em file starts with a single line
693 * describing the number of shared parameters blocks that will follow.
694 * Then, each shared parameters block follows, in the format described in
695 * the next subsection.
696 *
697 * \subsection fileformats-emalg-sharedparameters Shared parameters block format
698 *
699 * A shared parameters block of an .em file starts with a single line
700 * consisting of the name of a ParameterEstimation subclass
701 * and its parameters in the format of a PropertySet. For example:
702 * <pre> CondProbEstimation [target_dim=2,total_dim=4,pseudo_count=1]</pre>
703 * The next line contains the number of factors that share their parameters.
704 * Then, each of these factors is specified on separate lines (possibly
705 * seperated by empty lines), where each line consists of several fields
706 * seperated by a space or a tab character. The first field contains
707 * the index of the factor in the factor graph. The following fields should
708 * contain the variable labels of the variables on which that factor depends,
709 * in a specific ordering. This ordering can be different from the canonical
710 * ordering of the variables used internally in libDAI (which would be sorted
711 * ascendingly according to the variable labels). The ordering of the variables
712 * specifies the implicit ordering of the shared parameters: when iterating
713 * over all shared parameters, the corresponding index of the first variable
714 * changes fastest (in the inner loop), and the corresponding index of the
715 * last variable changes slowest (in the outer loop). By choosing the right
716 * ordering, it is possible to let different factors (depending on different
717 * variables) share parameters in parameter learning using EM. This convention
718 * is similar to the convention used in factor blocks in a factor graph .fg
719 * file (see \ref fileformats-factorgraph-factor).
720 *
721 * \section fileformats-aliases Aliases file format
722 *
723 * An aliases file is basically a list of "macros" and the strings that they
724 * should be substituted with.
725 *
726 * Each line of the aliases file can be either empty, contain a comment
727 * (if the first character is a '#') or contain an alias. In the latter case,
728 * the line should contain a colon; the part before the colon contains the
729 * name of the alias, the part after the colon the string that it should be
730 * substituted with. Any whitespace before and after the colon is ignored.
731 *
732 * For example, the following line would define the alias \c BP_SEQFIX
733 * as a shorthand for "BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]":
734 * <pre>
735 * BP_SEQFIX: BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]
736 * </pre>
737 *
738 * Aliases files can be used to store default options for algorithms.
739 */
740
741 /** \page bibliography Bibliography
742 * \anchor EaG09 \ref EaG09
743 * F. Eaton and Z. Ghahramani (2009):
744 * "Choosing a Variable to Clamp",
745 * <em>Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS 2009)</em> 5:145-152,
746 * http://jmlr.csail.mit.edu/proceedings/papers/v5/eaton09a/eaton09a.pdf
747 *
748 * \anchor EMK06 \ref EMK06
749 * G. Elidan and I. McGraw and D. Koller (2006):
750 * "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing",
751 * <em>Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)</em>,
752 * http://uai.sis.pitt.edu/papers/06/UAI2006_0091.pdf
753 *
754 * \anchor HAK03 \ref HAK03
755 * T. Heskes and C. A. Albers and H. J. Kappen (2003):
756 * "Approximate Inference and Constrained Optimization",
757 * <em>Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03)</em> pp. 313-320,
758 * http://www.snn.ru.nl/reports/Heskes.uai2003.ps.gz
759 *
760 * \anchor KFL01 \ref KFL01
761 * F. R. Kschischang and B. J. Frey and H.-A. Loeliger (2001):
762 * "Factor Graphs and the Sum-Product Algorithm",
763 * <em>IEEE Transactions on Information Theory</em> 47(2):498-519,
764 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=910572
765 *
766 * \anchor KoF09 \ref KoF09
767 * D. Koller and N. Friedman (2009):
768 * <em>Probabilistic Graphical Models - Principles and Techniques</em>,
769 * The MIT Press, Cambridge, Massachusetts, London, England.
770
771 * \anchor Min05 \ref Min05
772 * T. Minka (2005):
773 * "Divergence measures and message passing",
774 * <em>MicroSoft Research Technical Report</em> MSR-TR-2005-173,
775 * http://research.microsoft.com/en-us/um/people/minka/papers/message-passing/minka-divergence.pdf
776 *
777 * \anchor MiQ04 \ref MiQ04
778 * T. Minka and Y. Qi (2004):
779 * "Tree-structured Approximations by Expectation Propagation",
780 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 16,
781 * http://books.nips.cc/papers/files/nips16/NIPS2003_AA25.pdf
782 *
783 * \anchor MoK07 \ref MoK07
784 * J. M. Mooij and H. J. Kappen (2007):
785 * "Loop Corrections for Approximate Inference on Factor Graphs",
786 * <em>Journal of Machine Learning Research</em> 8:1113-1143,
787 * http://www.jmlr.org/papers/volume8/mooij07a/mooij07a.pdf
788 *
789 * \anchor MoK07b \ref MoK07b
790 * J. M. Mooij and H. J. Kappen (2007):
791 * "Sufficient Conditions for Convergence of the Sum-Product Algorithm",
792 * <em>IEEE Transactions on Information Theory</em> 53(12):4422-4437,
793 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4385778
794 *
795 * \anchor MoR05 \ref MoR05
796 * A. Montanari and T. Rizzo (2005):
797 * "How to Compute Loop Corrections to the Bethe Approximation",
798 * <em>Journal of Statistical Mechanics: Theory and Experiment</em> 2005(10)-P10011,
799 * http://stacks.iop.org/1742-5468/2005/P10011
800 *
801 * \anchor StW99 \ref StW99
802 * A. Steger and N. C. Wormald (1999):
803 * "Generating Random Regular Graphs Quickly",
804 * <em>Combinatorics, Probability and Computing</em> Vol 8, Issue 4, pp. 377-396,
805 * http://www.math.uwaterloo.ca/~nwormald/papers/randgen.pdf
806 *
807 * \anchor WiH03 \ref WiH03
808 * W. Wiegerinck and T. Heskes (2003):
809 * "Fractional Belief Propagation",
810 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 15, pp. 438-445,
811 * http://books.nips.cc/papers/files/nips15/LT16.pdf
812 *
813 * \anchor WJW03 \ref WJW03
814 * M. J. Wainwright, T. S. Jaakkola and A. S. Willsky (2003):
815 * "Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching",
816 * <em>9th Workshop on Artificial Intelligence and Statistics</em>,
817 * http://www.eecs.berkeley.edu/~wainwrig/Papers/WJW_AIStat03.pdf
818 *
819 * \anchor YFW05 \ref YFW05
820 * J. S. Yedidia and W. T. Freeman and Y. Weiss (2005):
821 * "Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms",
822 * <em>IEEE Transactions on Information Theory</em> 51(7):2282-2312,
823 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1459044
824 */
825
826
827 /** \page discussion Ideas not worth exploring
828 * \section discuss_extendedgraphs Extended factorgraphs/regiongraphs
829 *
830 * A FactorGraph and a RegionGraph are often equipped with
831 * additional properties for nodes and edges. The code to initialize those
832 * is often quite similar. Maybe one could abstract this, e.g.:
833 * \code
834 * template <typename Node1Properties, typename Node2Properties, typename EdgeProperties>
835 * class ExtFactorGraph : public FactorGraph {
836 * public:
837 * std::vector<Node1Properties> node1Props;
838 * std::vector<Node2Properties> node2Props;
839 * std::vector<std::vector<EdgeProperties> > edgeProps;
840 * // ...
841 * }
842 * \endcode
843 *
844 * Advantages:
845 * - Less code duplication.
846 * - Easier maintainability.
847 * - Easier to write new inference algorithms.
848 *
849 * Disadvantages:
850 * - Cachability may be worse.
851 * - A problem is the case where there are no properties for either type of nodes or for edges.
852 * Maybe this can be solved using specializations, or using variadac template arguments?
853 * Another possible solution would be to define a "class Empty {}", and add some code
854 * that checks for the typeid, comparing it with Empty, and doing something special in that case
855 * (e.g., not allocating memory).
856 * - The main disadvantage of this approach seems to be that it leads to even more entanglement.
857 * Therefore this is probably a bad idea.
858 *
859 * \section discuss_templates Polymorphism by template parameterization
860 *
861 * Instead of polymorphism by inheritance, use polymorphism by template parameterization.
862 * For example, the real reason for introducing the complicated inheritance scheme of dai::InfAlg
863 * was for functions like dai::calcMarginal. Instead, one could use a template function:
864 * \code
865 * template<typename InfAlg>
866 * Factor calcMarginal( const InfAlg &obj, const VarSet &ns, bool reInit );
867 * \endcode
868 * This would assume that the type InfAlg supports certain methods. Ideally, one would use
869 * concepts to define different classes of inference algorithms with different capabilities,
870 * for example the ability to calculate logZ, the ability to calculate marginals, the ability to
871 * calculate bounds, the ability to calculate MAP states, etc. Then, one would use traits
872 * classes in order to be able to query the capabilities of the model. For example, one would be
873 * able to query whether the inference algorithm supports calculation of logZ. Unfortunately,
874 * this is compile-time polymorphism, whereas tests/testdai needs runtime polymorphism.
875 * Therefore this is probably a bad idea.
876 */