Added some functionality to create various standard factors and renamed "Clamped...
[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 * \todo Document utils/createfg (and clean up the code a bit)
15 *
16 * \idea Adapt (part of the) guidelines in http://www.boost.org/development/requirements.html#Design_and_Programming
17 *
18 * \idea Use "gcc -MM" to generate dependencies for targets: http://make.paulandlesley.org/autodep.html
19 *
20 * \idea Disentangle structures. In particular, ensure that graphical properties are not
21 * entangled with probabilistic properties. For example, a FactorGraph contains several components:
22 * - a BipartiteGraph
23 * - an array of variable labels
24 * - an array of variable state space sizes
25 * - an array of pointers to factor value vectors
26 * In this way, each factor could be implemented differently, e.g., we could have
27 * some sparse factors, some noisy-OR factors, some dense factors, some arbitrary
28 * precision factors, etcetera.
29 *
30 * \idea Use boost::uBLAS framework to deal with matrices, especially, with 2D sparse matrices.
31 * See http://www.boost.org/libs/numeric/ublas/doc/matrix_sparse.htm
32 * However: I read somewhere that boost::uBLAS concentrates more on correct implementation than on performance.
33 *
34 * \idea Introduce naming scheme:
35 * - all Vars should be named v_..., e.g. v_i instead of i
36 * - all VarSets should be named vs_..., e.g. v_i instead of i
37 * - all Factors should be named f_..., e.g. f_I instead of I
38 * - all indices should be named _..., e.g. _k instead of k
39 * - all iterators should be named i_, e.g. i_i is an iterator to i
40 * - all const_iterators should be named ci_, e.g. ci_i is an iterator to i
41 **/
42
43
44 /** \mainpage Reference manual for libDAI - A free/open source C++ library for Discrete Approximate Inference methods
45 * \author Joris Mooij
46 * \version git HEAD
47 * \date February 4, 2010 - or later
48 *
49 * <hr size="1">
50 * \section about About libDAI
51 * libDAI is a free/open source C++ library (licensed under GPL 2+) that provides
52 * implementations of various (approximate) inference methods for discrete
53 * graphical models. libDAI supports arbitrary factor graphs with discrete
54 * variables; this includes discrete Markov Random Fields and Bayesian
55 * Networks.
56 *
57 * The library is targeted at researchers. To be able to use the library, a
58 * good understanding of graphical models is needed.
59 *
60 * The best way to use libDAI is by writing C++ code that invokes the library;
61 * in addition, part of the functionality is accessibly by using the
62 * - command line interface
63 * - (limited) MatLab interface
64 * - (experimental) python interface
65 * - (experimental) octave interface.
66 *
67 * libDAI can be used to implement novel (approximate) inference algorithms
68 * and to easily compare the accuracy and performance with existing algorithms
69 * that have been implemented already.
70 *
71 * \section features Features
72 * Currently, libDAI supports the following (approximate) inference methods:
73 * - Exact inference by brute force enumeration;
74 * - Exact inference by junction-tree methods;
75 * - Mean Field;
76 * - Loopy Belief Propagation [\ref KFL01];
77 * - Fractional Belief Propagation [\ref WiH03];
78 * - Tree-Reweighted Belief Propagation [\ref WJW03];
79 * - Tree Expectation Propagation [\ref MiQ04];
80 * - Generalized Belief Propagation [\ref YFW05];
81 * - Double-loop GBP [\ref HAK03];
82 * - Various variants of Loop Corrected Belief Propagation
83 * [\ref MoK07, \ref MoR05];
84 * - Gibbs sampler;
85 * - Conditioned Belief Propagation [\ref EaG09].
86 *
87 * These inference methods can be used to calculate partition sums, marginals
88 * over subsets of variables, and MAP states (the joint state of variables that
89 * has maximum probability).
90 *
91 * In addition, libDAI supports parameter learning of conditional probability
92 * tables by Expectation Maximization.
93 *
94 * \section limitations Limitations
95 * libDAI is not intended to be a complete package for approximate inference.
96 * Instead, it should be considered as an "inference engine", providing
97 * various inference methods. In particular, it contains no GUI, currently
98 * only supports its own file format for input and output (although support
99 * for standard file formats may be added later), and provides very limited
100 * visualization functionalities. The only learning method supported currently
101 * is Expectation Maximization (or Maximum Likelihood if no data is missing)
102 * for learning factor parameters.
103 *
104 * \section rationale Rationale
105 *
106 * In my opinion, the lack of open source "reference" implementations hampers
107 * progress in research on approximate inference. Methods differ widely in terms
108 * of quality and performance characteristics, which also depend in different
109 * ways on various properties of the graphical models. Finding the best
110 * approximate inference method for a particular application therefore often
111 * requires empirical comparisons. However, implementing and debugging these
112 * methods takes a lot of time which could otherwise be spent on research. I hope
113 * that this code will aid researchers to be able to easily compare various
114 * (existing as well as new) approximate inference methods, in this way
115 * accelerating research and stimulating real-world applications of approximate
116 * inference.
117 *
118 * \section language Language
119 * Because libDAI is implemented in C++, it is very fast compared with
120 * implementations in MatLab (a factor 1000 faster is not uncommon).
121 * libDAI does provide a (limited) MatLab interface for easy integration with MatLab.
122 * It also provides a command line interface and experimental python and octave
123 * interfaces (thanks to Patrick Pletscher).
124 *
125 * \section compatibility Compatibility
126 *
127 * The code has been developed under Debian GNU/Linux with the GCC compiler suite.
128 * libDAI compiles successfully with g++ versions 3.4, 4.1, 4.2 and 4.3.
129 *
130 * libDAI has also been successfully compiled with MS Visual Studio 2008 under Windows
131 * (but not all build targets are supported yet) and with Cygwin under Windows.
132 *
133 * Finally, libDAI has been compiled successfully on MacOS X.
134 *
135 * \section download Downloading libDAI
136 * The libDAI sources and documentation can be downloaded from the libDAI website:
137 * http://www.libdai.org.
138 *
139 * \section support Mailing list
140 * The Google group "libDAI" (http://groups.google.com/group/libdai)
141 * can be used for getting support and discussing development issues.
142 */
143
144
145 /** \page license License
146 * <hr size="1">
147 * \section license-license License
148 *
149 * libDAI is free software; you can redistribute it and/or modify
150 * it under the terms of the GNU General Public License as published by
151 * the Free Software Foundation; either version 2 of the License, or
152 * (at your option) any later version.
153 *
154 * libDAI is distributed in the hope that it will be useful,
155 * but WITHOUT ANY WARRANTY; without even the implied warranty of
156 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
157 * GNU General Public License for more details.
158 *
159 * <hr size="1">
160 * \section license-gpl GNU General Public License version 2
161 *
162 * \verbinclude COPYING
163 */
164
165
166 /** \page citations Citing libDAI
167 * <hr size="1">
168 * \section citations-citations Citing libDAI
169 *
170 * If you write a scientific paper describing research that made substantive use
171 * of this program, please:
172 * - mention the fashion in which this software was
173 * used, including the version number, with a citation to the literature,
174 * to allow replication;
175 * - mention this software in the Acknowledgements section.
176 *
177 * An appropriate citation would be:\n
178 * J. M. Mooij (2009) "libDAI 0.2.3: A free/open source C++ library for Discrete
179 * Approximate Inference", http://www.libdai.org
180 *
181 * Moreover, as a personal note, I would appreciate it if you would email
182 * (citations of) papers referencing this work to joris dot mooij at libdai dot org.
183 */
184
185
186 /** \page authors Authors
187 * \section authors-authors People who contributed to libDAI
188 *
189 * \verbinclude AUTHORS
190 */
191
192
193 /** \page build Building libDAI
194 * <hr size="1">
195 * \section build-unix Building libDAI under UNIX variants (Linux / Cygwin / Mac OS X)
196 *
197 * You need:
198 * - a recent version of gcc (at least version 3.4)
199 * - GNU make
200 * - doxygen
201 * - graphviz
202 * - recent boost C++ libraries (at least version 1.34 if you have
203 * a recent version of GCC, otherwise at least version 1.37; however,
204 * version 1.37 shipped with Ubuntu 9.04 is known not to work)
205 *
206 * On Debian/Ubuntu, you can easily install all these packages with a single command:
207 * <pre> apt-get install g++ make doxygen graphviz libboost-dev libboost-graph-dev libboost-program-options-dev</pre>
208 * (root permissions needed).
209 *
210 * On Mac OS X (10.4 is known to work), these packages can be installed easily via MacPorts.
211 * If MacPorts is not already installed, install it according to the instructions at http://www.macports.org/.
212 * Then, a simple
213 * <pre> sudo port install gmake boost doxygen graphviz</pre>
214 * should be enough to install everything that is needed.
215 *
216 * On Cygwin, the prebuilt Cygwin package boost-1.33.1-x is known not to work.
217 * You can however obtain the latest boost version (you need at least 1.37.0)
218 * from http://www.boost.org/ and compile/install it with:
219 *
220 * <pre> ./configure
221 * make
222 * make install
223 * </pre>
224 *
225 * To build the libDAI source, first copy a template Makefile.* to Makefile.conf
226 * (for example, copy Makefile.LINUX to Makefile.conf if you use GNU/Linux).
227 * Then, edit the Makefile.conf template to adapt it to your local setup.
228 * Especially directories may differ from system to system. Platform independent
229 * build options can be set in Makefile.ALL. Finally, run
230 * <pre> make</pre>
231 * The build includes a regression test, which may take a while to complete.
232 *
233 * If the build is successful, you can test the example program:
234 * <pre> examples/example tests/alarm.fg</pre>
235 * or the more elaborate test program:
236 * <pre> tests/testdai --aliases tests/aliases.conf --filename tests/alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
237 *
238 *
239 * <hr size="1">
240 * \section build-windows Building libDAI under Windows
241 *
242 * You need:
243 * - A recent version of MicroSoft Visual Studio (2008 is known to work)
244 * - recent boost C++ libraries (version 1.37 or higher)
245 * - GNU make (can be obtained from http://gnuwin32.sourceforge.net)
246 *
247 * For the regression test, you need:
248 * - GNU diff, GNU sed (can be obtained from http://gnuwin32.sourceforge.net)
249 *
250 * To build the source, copy Makefile.WINDOWS to Makefile.conf. Then, edit
251 * Makefile.conf to adapt it to your local setup. Platform independent
252 * build options can be set in Makefile.ALL. Finally, run (from the command line)
253 * <pre> make</pre>
254 * The build includes a regression test, which may take a while to complete.
255 *
256 * If the build is successful, you can test the example program:
257 * <pre> examples\\example tests\\alarm.fg</pre>
258 * or the more elaborate test program:
259 * <pre> tests\\testdai --aliases tests\\aliases.conf --filename tests\\alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
260 *
261 *
262 * <hr size="1">
263 * \section build-matlab Building the libDAI MatLab interface
264 *
265 * You need:
266 * - MatLab
267 * - The platform-dependent requirements described above
268 *
269 * First, you need to build the libDAI source as described above for your
270 * platform. By default, the MatLab interface is disabled, so before compiling the
271 * source, you have to enable it in Makefile.ALL by setting
272 * <pre> WITH_MATLAB=true</pre>
273 * Also, you have to configure the MatLab-specific parts of
274 * Makefile.conf to match your system (in particular, the Makefile variables ME,
275 * MATLABDIR and MEX). The MEX file extension depends on your platform; for a
276 * 64-bit linux x86_64 system this would be "ME=.mexa64", for a 32-bit linux x86
277 * system "ME=.mexglx". If you are unsure about your MEX file
278 * extension: it needs to be the same as what the MatLab command "mexext" returns.
279 * The required MEX files are built by issuing
280 * <pre> make</pre>
281 * from the command line. The MatLab interface is much less powerful than using
282 * libDAI from C++. There are two reasons for this: (i) it is boring to write MEX
283 * files; (ii) the large performance penalty paid when large data structures (like
284 * factor graphs) have to be converted between their native C++ data structure to
285 * something that MatLab understands.
286 *
287 * A simple example of how to use the MatLab interface is the following (entered
288 * at the MatLab prompt), which performs exact inference by the junction tree
289 * algorithm and approximate inference by belief propagation on the ALARM network:
290 * <pre> cd path_to_libdai/matlab
291 * [psi] = dai_readfg ('../examples/alarm.fg');
292 * [logZ,q,md,qv,qf] = dai (psi, 'JTREE', '[updates=HUGIN,verbose=0]')
293 * [logZ,q,md,qv,qf] = dai (psi, 'BP', '[updates=SEQMAX,tol=1e-9,maxiter=10000,logdomain=0]')</pre>
294 * where "path_to_libdai" has to be replaced with the directory in which libDAI
295 * was installed. For other algorithms and some default parameters, see the file
296 * tests/aliases.conf.
297 *
298 * <hr size="1">
299 * \section build-doxygen Building the documentation
300 *
301 * Install doxygen, graphviz and a TeX distribution and use
302 * <pre> make doc</pre>
303 * to build the documentation. If the documentation is not clear enough, feel free
304 * to send me an email (or even better, to improve the documentation and send a patch!).
305 * The documentation can also be browsed online at http://www.libdai.org.
306 */
307
308
309 /** \page changelog Change Log
310 * \verbinclude ChangeLog
311 */
312
313
314 /** \page terminology Terminology and conventions
315 *
316 * \section terminology-graphicalmodels Graphical models
317 *
318 * Commonly used graphical models are Bayesian networks and Markov random fields.
319 * In libDAI, both types of graphical models are represented by a slightly more
320 * general type of graphical model: a factor graph [\ref KFL01].
321 *
322 * An example of a Bayesian network is:
323 * \dot
324 * digraph bayesnet {
325 * size="1,1";
326 * x0 [label="0"];
327 * x1 [label="1"];
328 * x2 [label="2"];
329 * x3 [label="3"];
330 * x4 [label="4"];
331 * x0 -> x1;
332 * x0 -> x2;
333 * x1 -> x3;
334 * x1 -> x4;
335 * x2 -> x4;
336 * }
337 * \enddot
338 * The probability distribution of a Bayesian network factorizes as:
339 * \f[ P(\mathbf{x}) = \prod_{i\in\mathcal{V}} P(x_i \,|\, x_{\mathrm{pa}(i)}) \f]
340 * where \f$\mathrm{pa}(i)\f$ are the parents of node \a i in a DAG.
341 *
342 * The same probability distribution can be represented as a Markov random field:
343 * \dot
344 * graph mrf {
345 * size="1.5,1.5";
346 * x0 [label="0"];
347 * x1 [label="1"];
348 * x2 [label="2"];
349 * x3 [label="3"];
350 * x4 [label="4"];
351 * x0 -- x1;
352 * x0 -- x2;
353 * x1 -- x2;
354 * x1 -- x3;
355 * x1 -- x4;
356 * x2 -- x4;
357 * }
358 * \enddot
359 *
360 * The probability distribution of a Markov random field factorizes as:
361 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{C\in\mathcal{C}} \psi_C(x_C) \f]
362 * where \f$ \mathcal{C} \f$ are the cliques of an undirected graph,
363 * \f$ \psi_C(x_C) \f$ are "potentials" or "compatibility functions", and
364 * \f$ Z \f$ is the partition sum which properly normalizes the probability
365 * distribution.
366 *
367 * Finally, the same probability distribution can be represented as a factor graph:
368 * \dot
369 * graph factorgraph {
370 * size="1.8,1";
371 * x0 [label="0"];
372 * x1 [label="1"];
373 * x2 [label="2"];
374 * x3 [label="3"];
375 * x4 [label="4"];
376 * f01 [shape="box",label=""];
377 * f02 [shape="box",label=""];
378 * f13 [shape="box",label=""];
379 * f124 [shape="box",label=""];
380 * x0 -- f01;
381 * x1 -- f01;
382 * x0 -- f02;
383 * x2 -- f02;
384 * x1 -- f13;
385 * x3 -- f13;
386 * x1 -- f124;
387 * x2 -- f124;
388 * x4 -- f124;
389 * }
390 * \enddot
391 *
392 * The probability distribution of a factor graph factorizes as:
393 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{I\in \mathcal{F}} f_I(x_I) \f]
394 * where \f$ \mathcal{F} \f$ are the factor nodes of a factor graph (a
395 * bipartite graph consisting of variable nodes and factor nodes),
396 * \f$ f_I(x_I) \f$ are the factors, and \f$ Z \f$ is the partition sum
397 * which properly normalizes the probability distribution.
398 *
399 * Looking at the expressions for the joint probability distributions,
400 * it is obvious that Bayesian networks and Markov random fields can
401 * both be easily represented as factor graphs. Factor graphs most
402 * naturally express the factorization structure of a probability
403 * distribution, and hence are a convenient representation for approximate
404 * inference algorithms, which all try to exploit this factorization.
405 * This is why libDAI uses a factor graph as representation of a
406 * graphical model, implemented in the dai::FactorGraph class.
407 *
408 * \section terminology-inference Inference tasks
409 *
410 * Given a factor graph, specified by the variable nodes \f$\{x_i\}_{i\in\mathcal{V}}\f$
411 * the factor nodes \f$ \mathcal{F} \f$, the graph structure, and the factors
412 * \f$\{f_I(x_I)\}_{I\in\mathcal{F}}\f$, the following tasks are important:
413 *
414 * - Calculating the partition sum:
415 * \f[ Z = \sum_{\mathbf{x}_{\mathcal{V}}} \prod_{I \in \mathcal{F}} f_I(x_I) \f]
416 * - Calculating the marginal distribution of a subset of variables
417 * \f$\{x_i\}_{i\in A}\f$:
418 * \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]
419 * - Calculating the MAP state which has the maximum probability mass:
420 * \f[ \mathrm{argmax}_{\mathbf{x}}\,\prod_{I\in\mathcal{F}} f_I(x_I) \f]
421 *
422 * libDAI offers several inference algorithms, which solve (a subset of) these tasks either
423 * approximately or exactly, for factor graphs with discrete variables. The following
424 * algorithms are implemented:
425 *
426 * Exact inference:
427 * - Brute force enumeration: dai::ExactInf
428 * - Junction-tree method: dai::JTree
429 *
430 * Approximate inference:
431 * - Mean Field: dai::MF
432 * - (Loopy) Belief Propagation: dai::BP [\ref KFL01]
433 * - Fractional Belief Propagation: dai::FBP [\ref WiH03]
434 * - Tree-Reweighted Belief Propagation: dai::TRWBP [\ref WJW03]
435 * - Tree Expectation Propagation: dai::TreeEP [\ref MiQ04]
436 * - Generalized Belief Propagation: dai::HAK [\ref YFW05]
437 * - Double-loop GBP: dai::HAK [\ref HAK03]
438 * - Loop Corrected Belief Propagation: dai::MR [\ref MoR05] and dai::LC [\ref MoK07]
439 * - Gibbs sampling: dai::Gibbs
440 * - Conditioned Belief Propagation: dai::CBP [\ref EaG09]
441 *
442 * Not all inference tasks are implemented by each method: calculating MAP states
443 * is only possible with dai::JTree and dai::BP, calculating partition sums is
444 * not possible with dai::MR, dai::LC and dai::Gibbs.
445 *
446 * \section terminology-learning Parameter learning
447 *
448 * In addition, libDAI supports parameter learning of conditional probability
449 * tables by Expectation Maximization (or Maximum Likelihood, if there is no
450 * missing data). This is implemented in dai::EMAlg.
451 *
452 * \section terminology-variables-states Variables and states
453 *
454 * Linear states are a concept that is used often in libDAI, for example for storing
455 * and accessing factors, which are functions mapping from states of a set of variables
456 * to the real numbers. Internally, a factor is stored as an array, and the array index
457 * of an entry corresponds with the linear state of the set of variables. Below we will
458 * define variables, states and linear states of (sets of) variables.
459 *
460 * \subsection terminology-variables Variables
461 *
462 * Each (random) \a variable has a unique identifier, its \a label (which has
463 * a non-negative integer value). If two variables have the same
464 * label, they are considered as identical. A variable can take on a finite
465 * number of different values or \a states.
466 *
467 * We use the following notational conventions. The discrete
468 * random variable with label \f$l\f$ is denoted as \f$x_l\f$, and the number
469 * of possible values of this variable as \f$S_{x_l}\f$ or simply \f$S_l\f$.
470 * The set of possible values of variable \f$x_l\f$ is denoted
471 * \f$X_l := \{0,1,\dots,S_l-1\}\f$ and called its \a state \a space.
472 *
473 * \subsection terminology-variable-sets Sets of variables and the canonical ordering
474 *
475 * Let \f$A := \{x_{l_1},x_{l_2},\dots,x_{l_n}\}\f$ be a set of variables.
476 *
477 * The \a canonical \a ordering of the variables in \a A is induced by their labels.
478 * That is: if \f$l_1 < l_2\f$, then \f$x_{l_1}\f$ occurs before \f$x_{l_2}\f$ in the
479 * canonical ordering. Below, we will assume that \f$(l_i)_{i=1}^n\f$ is
480 * ordered according to the canonical ordering, i.e., \f$l_1 < l_2 < \dots < l_n\f$.
481 *
482 * \subsection terminology-variable-states States and linear states of sets of variables
483 *
484 * A \a state of the variables in \a A refers to a joint assignment of the
485 * variables, or in other words, to an element of the Cartesian product
486 * \f$ \prod_{i=1}^n X_{l_i}\f$ of the state spaces of the variables in \a A.
487 * Note that a state can also be interpreted as a mapping from variables (or
488 * variable labels) to the natural numbers, which assigns to a variable (or its
489 * label) the corresponding state of the variable.
490 *
491 * A state of \a n variables can be represented as an n-tuple of
492 * non-negative integers: \f$(s_1,s_2,\dots,s_n)\f$ corresponds to the
493 * joint assignment \f$x_{l_1} = s_1, \dots, x_{l_n} = s_n\f$.
494 * Alternatively, a state can be represented compactly as one non-negative integer;
495 * this representation is called a \a linear \a state. The linear state
496 * \a s corresponding to the state \f$(s_1,s_2,\dots,s_n)\f$ would be:
497 * \f[
498 * s := \sum_{i=1}^n s_i \prod_{j=1}^{i-1} S_{l_j}
499 * = 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}}.
500 * \f]
501 *
502 * Vice versa, given a linear state \a s for the variables \a A, the
503 * corresponding state \f$s_i\f$ of the \a i 'th variable \f$x_{l_i}\f$ (according to
504 * the canonical ordering of the variables in \a A) is given by
505 * \f[
506 * 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.
507 * \f]
508 *
509 * Finally, the \a number \a of \a states of the set of variables \a A is simply the
510 * number of different joint assignments of the variables, that is, \f$\prod_{i=1}^n S_{l_i}\f$.
511 */
512
513
514 /** \page fileformats libDAI file formats
515 *
516 * \section fileformats-factorgraph Factor graph (.fg) file format
517 *
518 * This section describes the .fg file format used in libDAI to store factor graphs.
519 * Markov Random Fields are special cases of factor graphs, as are Bayesian
520 * networks. A factor graph can be specified as follows: for each factor, one has
521 * to specify which variables occur in the factor, what their respective
522 * cardinalities (i.e., number of possible values) are, and a table listing all
523 * the values of that factor for all possible configurations of these variables.
524 *
525 * A .fg file is not much more than that. It starts with a line containing the
526 * number of factors in that graph, followed by an empty line. Then all factors
527 * are specified, using one block for each factor, where the blocks are seperated
528 * by empty lines. Each variable occurring in the factor graph has a unique
529 * identifier, its label (which should be a nonnegative integer). Comment lines
530 * which start with # are ignored.
531 *
532 * \subsection fileformats-factorgraph-factor Factor block format
533 *
534 * Each block describing a factor starts with a line containing the number of
535 * variables in that factor. The second line contains the labels of these
536 * variables, seperated by spaces (labels are nonnegative integers and to avoid
537 * confusion, it is suggested to start counting at 0). The third line contains
538 * the number of possible values of each of these variables, also seperated by
539 * spaces. Note that there is some redundancy here, since if a variable appears
540 * in more than one factor, the cardinality of that variable appears several
541 * times in the .fg file; obviously, these cardinalities should be consistent.
542 * The fourth line contains the number of nonzero entries
543 * in the factor table. The rest of the lines contain these nonzero entries;
544 * each line consists of a table index, followed by white-space, followed by the
545 * value corresponding to that table index. The most difficult part is getting
546 * the indexing right. The convention that is used is that the left-most
547 * variables cycle through their values the fastest (similar to MatLab indexing
548 * of multidimensional arrays).
549 *
550 * \subsubsection fileformats-factorgraph-factor-example Example
551 *
552 * An example block describing one factor is:
553 *
554 * <pre>
555 * 3
556 * 4 8 7
557 * 3 2 2
558 * 11
559 * 0 0.1
560 * 1 3.5
561 * 2 2.8
562 * 3 6.3
563 * 4 8.4
564 * 6 7.4
565 * 7 2.4
566 * 8 8.9
567 * 9 1.3
568 * 10 1.6
569 * 12 6.4
570 * 11 2.6
571 * </pre>
572 *
573 * which corresponds to the following factor:
574 *
575 * \f[
576 * \begin{array}{ccc|c}
577 * x_4 & x_8 & x_7 & \mbox{value}\\
578 * \hline
579 * 0 & 0 & 0 & 0.1\\
580 * 1 & 0 & 0 & 3.5\\
581 * 2 & 0 & 0 & 2.8\\
582 * 0 & 1 & 0 & 6.3\\
583 * 1 & 1 & 0 & 8.4\\
584 * 2 & 1 & 0 & 0.0\\
585 * 0 & 0 & 1 & 7.4\\
586 * 1 & 0 & 1 & 2.4\\
587 * 2 & 0 & 1 & 8.9\\
588 * 0 & 1 & 1 & 1.3\\
589 * 1 & 1 & 1 & 1.6\\
590 * 2 & 1 & 1 & 2.6
591 * \end{array}
592 * \f]
593 *
594 * Note that the value of \f$x_4\f$ changes fastest, followed by that of \f$x_8\f$, and \f$x_7\f$
595 * varies the slowest, corresponding to the second line of the block ("4 8 7").
596 * Further, \f$x_4\f$ can take on three values, and \f$x_8\f$ and \f$x_7\f$ each have two possible
597 * values, as described in the third line of the block ("3 2 2"). The table
598 * contains 11 non-zero entries (all except for the fifth entry). Note that the
599 * eleventh and twelveth entries are interchanged.
600 *
601 * A final note: the internal representation in libDAI of the factor above is
602 * different, because the variables are ordered according to their indices
603 * (i.e., the ordering would be \f$x_4 x_7 x_8\f$) and the values of the table are
604 * stored accordingly, with the variable having the smallest index changing
605 * fastest:
606 *
607 * \f[
608 * \begin{array}{ccc|c}
609 * x_4 & x_7 & x_8 & \mbox{value}\\
610 * \hline
611 * 0 & 0 & 0 & 0.1\\
612 * 1 & 0 & 0 & 3.5\\
613 * 2 & 0 & 0 & 2.8\\
614 * 0 & 1 & 0 & 7.4\\
615 * 1 & 1 & 0 & 2.4\\
616 * 2 & 1 & 0 & 8.9\\
617 * 0 & 0 & 1 & 6.3\\
618 * 1 & 0 & 1 & 8.4\\
619 * 2 & 0 & 1 & 0.0\\
620 * 0 & 1 & 1 & 1.3\\
621 * 1 & 1 & 1 & 1.6\\
622 * 2 & 1 & 1 & 2.6
623 * \end{array}
624 * \f]
625 *
626 *
627 * \section fileformats-evidence Evidence (.tab) file format
628 *
629 * This section describes the .tab fileformat used in libDAI to store "evidence",
630 * i.e., a data set consisting of multiple samples, where each sample is the
631 * observed joint state of some variables.
632 *
633 * A .tab file is a tabular data file, consisting of a header line, followed by
634 * an empty line, followed by the data points, with one line for each data point.
635 * Each line (apart from the empty one) should have the same number of columns,
636 * where columns are separated by one tab character. Each column corresponds to
637 * a variable. The header line consists of the variable labels (corresponding to
638 * dai::Var::label()). The other lines are observed joint states of the variables, i.e.,
639 * each line corresponds to a joint observation of the variables, and each column
640 * of a line contains the state of the variable associated with that column.
641 * Missing data is handled simply by having two consecutive tab characters,
642 * without any characters in between.
643 *
644 * \subsection fileformats-evidence-example Example
645 *
646 * <pre>
647 * 1 3 2
648 *
649 * 0 0 1
650 * 1 0 1
651 * 1 1
652 * </pre>
653 *
654 * This would correspond to a data set consisting of three observations concerning
655 * the variables with labels 1, 3 and 2; the first observation being
656 * \f$x_1 = 0, x_3 = 0, x_2 = 1\f$, the second observation being
657 * \f$x_1 = 1, x_3 = 0, x_2 = 1\f$, and the third observation being
658 * \f$x_1 = 1, x_2 = 1\f$ (where the state of \f$x_3\f$ is missing).
659 *
660 * \section fileformats-emalg Expectation Maximization (.em) file format
661 *
662 * This section describes the file format of .em files, which are used
663 * to specify a particular EM algorithm. The .em files are complementary
664 * to .fg files; in other words, an .em file without a corresponding .fg
665 * file is useless. Furthermore, one also needs a corresponding .tab file
666 * containing the data used for parameter learning.
667 *
668 * An .em file starts with a line specifying the number of maximization steps,
669 * followed by an empty line. Then, each maximization step is described in a
670 * block, which should satisfy the format described in the next subsection.
671 *
672 * \subsection fileformats-emalg-maximizationstep Maximization Step block format
673 *
674 * A maximization step block of an .em file starts with a single line
675 * describing the number of shared parameters blocks that will follow.
676 * Then, each shared parameters block follows, in the format described in
677 * the next subsection.
678 *
679 * \subsection fileformats-emalg-sharedparameters Shared parameters block format
680 *
681 * A shared parameters block of an .em file starts with a single line
682 * consisting of the name of a ParameterEstimation subclass
683 * and its parameters in the format of a PropertySet. For example:
684 * <pre> CondProbEstimation [target_dim=2,total_dim=4,pseudo_count=1]</pre>
685 * The next line contains the number of factors that share their parameters.
686 * Then, each of these factors is specified on separate lines (possibly
687 * seperated by empty lines), where each line consists of several fields
688 * seperated by a space or a tab character. The first field contains
689 * the index of the factor in the factor graph. The following fields should
690 * contain the variable labels of the variables on which that factor depends,
691 * in a specific ordering. This ordering can be different from the canonical
692 * ordering of the variables used internally in libDAI (which would be sorted
693 * ascendingly according to the variable labels). The ordering of the variables
694 * specifies the implicit ordering of the shared parameters: when iterating
695 * over all shared parameters, the corresponding index of the first variable
696 * changes fastest (in the inner loop), and the corresponding index of the
697 * last variable changes slowest (in the outer loop). By choosing the right
698 * ordering, it is possible to let different factors (depending on different
699 * variables) share parameters in parameter learning using EM. This convention
700 * is similar to the convention used in factor blocks in a factor graph .fg
701 * file (see \ref fileformats-factorgraph-factor).
702 *
703 * \section fileformats-aliases Aliases file format
704 *
705 * An aliases file is basically a list of "macros" and the strings that they
706 * should be substituted with.
707 *
708 * Each line of the aliases file can be either empty, contain a comment
709 * (if the first character is a '#') or contain an alias. In the latter case,
710 * the line should contain a colon; the part before the colon contains the
711 * name of the alias, the part after the colon the string that it should be
712 * substituted with. Any whitespace before and after the colon is ignored.
713 *
714 * For example, the following line would define the alias \c BP_SEQFIX
715 * as a shorthand for "BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]":
716 * <pre>
717 * BP_SEQFIX: BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]
718 * </pre>
719 *
720 * Aliases files can be used to store default options for algorithms.
721 */
722
723 /** \page bibliography Bibliography
724 * \anchor EaG09 \ref EaG09
725 * F. Eaton and Z. Ghahramani (2009):
726 * "Choosing a Variable to Clamp",
727 * <em>Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS 2009)</em> 5:145-152,
728 * http://jmlr.csail.mit.edu/proceedings/papers/v5/eaton09a/eaton09a.pdf
729 *
730 * \anchor EMK06 \ref EMK06
731 * G. Elidan and I. McGraw and D. Koller (2006):
732 * "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing",
733 * <em>Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)</em>,
734 * http://uai.sis.pitt.edu/papers/06/UAI2006_0091.pdf
735 *
736 * \anchor HAK03 \ref HAK03
737 * T. Heskes and C. A. Albers and H. J. Kappen (2003):
738 * "Approximate Inference and Constrained Optimization",
739 * <em>Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03)</em> pp. 313-320,
740 * http://www.snn.ru.nl/reports/Heskes.uai2003.ps.gz
741 *
742 * \anchor KFL01 \ref KFL01
743 * F. R. Kschischang and B. J. Frey and H.-A. Loeliger (2001):
744 * "Factor Graphs and the Sum-Product Algorithm",
745 * <em>IEEE Transactions on Information Theory</em> 47(2):498-519,
746 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=910572
747 *
748 * \anchor KoF09 \ref KoF09
749 * D. Koller and N. Friedman (2009):
750 * <em>Probabilistic Graphical Models - Principles and Techniques</em>,
751 * The MIT Press, Cambridge, Massachusetts, London, England.
752
753 * \anchor Min05 \ref Min05
754 * T. Minka (2005):
755 * "Divergence measures and message passing",
756 * <em>MicroSoft Research Technical Report</em> MSR-TR-2005-173,
757 * http://research.microsoft.com/en-us/um/people/minka/papers/message-passing/minka-divergence.pdf
758 *
759 * \anchor MiQ04 \ref MiQ04
760 * T. Minka and Y. Qi (2004):
761 * "Tree-structured Approximations by Expectation Propagation",
762 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 16,
763 * http://books.nips.cc/papers/files/nips16/NIPS2003_AA25.pdf
764 *
765 * \anchor MoK07 \ref MoK07
766 * J. M. Mooij and H. J. Kappen (2007):
767 * "Loop Corrections for Approximate Inference on Factor Graphs",
768 * <em>Journal of Machine Learning Research</em> 8:1113-1143,
769 * http://www.jmlr.org/papers/volume8/mooij07a/mooij07a.pdf
770 *
771 * \anchor MoK07b \ref MoK07b
772 * J. M. Mooij and H. J. Kappen (2007):
773 * "Sufficient Conditions for Convergence of the Sum-Product Algorithm",
774 * <em>IEEE Transactions on Information Theory</em> 53(12):4422-4437,
775 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4385778
776 *
777 * \anchor MoR05 \ref MoR05
778 * A. Montanari and T. Rizzo (2005):
779 * "How to Compute Loop Corrections to the Bethe Approximation",
780 * <em>Journal of Statistical Mechanics: Theory and Experiment</em> 2005(10)-P10011,
781 * http://stacks.iop.org/1742-5468/2005/P10011
782 *
783 * \anchor StW99 \ref StW99
784 * A. Steger and N. C. Wormald (1999):
785 * "Generating Random Regular Graphs Quickly",
786 * <em>Combinatorics, Probability and Computing</em> Vol 8, Issue 4, pp. 377-396,
787 * http://www.math.uwaterloo.ca/~nwormald/papers/randgen.pdf
788 *
789 * \anchor WiH03 \ref WiH03
790 * W. Wiegerinck and T. Heskes (2003):
791 * "Fractional Belief Propagation",
792 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 15, pp. 438-445,
793 * http://books.nips.cc/papers/files/nips15/LT16.pdf
794 *
795 * \anchor WJW03 \ref WJW03
796 * M. J. Wainwright, T. S. Jaakkola and A. S. Willsky (2003):
797 * "Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching",
798 * <em>9th Workshop on Artificial Intelligence and Statistics</em>,
799 * http://www.eecs.berkeley.edu/~wainwrig/Papers/WJW_AIStat03.pdf
800 *
801 * \anchor YFW05 \ref YFW05
802 * J. S. Yedidia and W. T. Freeman and Y. Weiss (2005):
803 * "Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms",
804 * <em>IEEE Transactions on Information Theory</em> 51(7):2282-2312,
805 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1459044
806 */
807
808
809 /** \page discussion Ideas not worth exploring
810 * \section discuss_extendedgraphs Extended factorgraphs/regiongraphs
811 *
812 * A FactorGraph and a RegionGraph are often equipped with
813 * additional properties for nodes and edges. The code to initialize those
814 * is often quite similar. Maybe one could abstract this, e.g.:
815 * \code
816 * template <typename Node1Properties, typename Node2Properties, typename EdgeProperties>
817 * class ExtFactorGraph : public FactorGraph {
818 * public:
819 * std::vector<Node1Properties> node1Props;
820 * std::vector<Node2Properties> node2Props;
821 * std::vector<std::vector<EdgeProperties> > edgeProps;
822 * // ...
823 * }
824 * \endcode
825 *
826 * Advantages:
827 * - Less code duplication.
828 * - Easier maintainability.
829 * - Easier to write new inference algorithms.
830 *
831 * Disadvantages:
832 * - Cachability may be worse.
833 * - A problem is the case where there are no properties for either type of nodes or for edges.
834 * Maybe this can be solved using specializations, or using variadac template arguments?
835 * Another possible solution would be to define a "class Empty {}", and add some code
836 * that checks for the typeid, comparing it with Empty, and doing something special in that case
837 * (e.g., not allocating memory).
838 * - The main disadvantage of this approach seems to be that it leads to even more entanglement.
839 * Therefore this is probably a bad idea.
840 *
841 * \section discuss_templates Polymorphism by template parameterization
842 *
843 * Instead of polymorphism by inheritance, use polymorphism by template parameterization.
844 * For example, the real reason for introducing the complicated inheritance scheme of dai::InfAlg
845 * was for functions like dai::calcMarginal. Instead, one could use a template function:
846 * \code
847 * template<typename InfAlg>
848 * Factor calcMarginal( const InfAlg &obj, const VarSet &ns, bool reInit );
849 * \endcode
850 * This would assume that the type InfAlg supports certain methods. Ideally, one would use
851 * concepts to define different classes of inference algorithms with different capabilities,
852 * for example the ability to calculate logZ, the ability to calculate marginals, the ability to
853 * calculate bounds, the ability to calculate MAP states, etc. Then, one would use traits
854 * classes in order to be able to query the capabilities of the model. For example, one would be
855 * able to query whether the inference algorithm supports calculation of logZ. Unfortunately,
856 * this is compile-time polymorphism, whereas tests/testdai needs runtime polymorphism.
857 * Therefore this is probably a bad idea.
858 */