Fixed wrong version number in documentation and README
[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 Replace all Neighbor subclasses with a global Neighbor class, and
15 * introduce global (un)directed edge classes
16 *
17 * \todo Replace all Name members by virtual functions (or add virtual functions returning the Name)
18 *
19 * \idea Adapt (part of the) guidelines in http://www.boost.org/development/requirements.html#Design_and_Programming
20 *
21 * \idea Use "gcc -MM" to generate dependencies for targets: http://make.paulandlesley.org/autodep.html
22 *
23 * \idea Disentangle structures. In particular, ensure that graphical properties are not
24 * entangled with probabilistic properties. For example, a FactorGraph contains several components:
25 * - a BipartiteGraph
26 * - an array of variable labels
27 * - an array of variable state space sizes
28 * - an array of pointers to factor value vectors
29 * In this way, each factor could be implemented differently, e.g., we could have
30 * some sparse factors, some noisy-OR factors, some dense factors, some arbitrary
31 * precision factors, etcetera.
32 *
33 * \idea Use boost::uBLAS framework to deal with matrices, especially, with 2D sparse matrices.
34 * See http://www.boost.org/libs/numeric/ublas/doc/matrix_sparse.htm
35 * However: I read somewhere that boost::uBLAS concentrates more on correct implementation than on performance.
36 **/
37
38
39 /** \mainpage Reference manual for libDAI - A free/open source C++ library for Discrete Approximate Inference methods
40 * \author Joris Mooij, Frederik Eaton
41 * \version 0.2.5
42 * \date May 9, 2010
43 *
44 * <hr size="1">
45 * \section about About libDAI
46 * libDAI is a free/open source C++ library (licensed under GPL 2+) that provides
47 * implementations of various (approximate) inference methods for discrete
48 * graphical models. libDAI supports arbitrary factor graphs with discrete
49 * variables; this includes discrete Markov Random Fields and Bayesian
50 * Networks.
51 *
52 * The library is targeted at researchers. To be able to use the library, a
53 * good understanding of graphical models is needed.
54 *
55 * The best way to use libDAI is by writing C++ code that invokes the library;
56 * in addition, part of the functionality is accessibly by using the
57 * - command line interface
58 * - (limited) MatLab interface
59 * - (experimental) python interface
60 * - (experimental) octave interface.
61 *
62 * libDAI can be used to implement novel (approximate) inference algorithms
63 * and to easily compare the accuracy and performance with existing algorithms
64 * that have been implemented already.
65 *
66 * \section features Features
67 * Currently, libDAI supports the following (approximate) inference methods:
68 * - Exact inference by brute force enumeration;
69 * - Exact inference by junction-tree methods;
70 * - Mean Field;
71 * - Loopy Belief Propagation [\ref KFL01];
72 * - Fractional Belief Propagation [\ref WiH03];
73 * - Tree-Reweighted Belief Propagation [\ref WJW03];
74 * - Tree Expectation Propagation [\ref MiQ04];
75 * - Generalized Belief Propagation [\ref YFW05];
76 * - Double-loop GBP [\ref HAK03];
77 * - Various variants of Loop Corrected Belief Propagation
78 * [\ref MoK07, \ref MoR05];
79 * - Gibbs sampler;
80 * - Conditioned Belief Propagation [\ref EaG09].
81 *
82 * These inference methods can be used to calculate partition sums, marginals
83 * over subsets of variables, and MAP states (the joint state of variables that
84 * has maximum probability).
85 *
86 * In addition, libDAI supports parameter learning of conditional probability
87 * tables by Expectation Maximization.
88 *
89 * \section limitations Limitations
90 * libDAI is not intended to be a complete package for approximate inference.
91 * Instead, it should be considered as an "inference engine", providing
92 * various inference methods. In particular, it contains no GUI, currently
93 * only supports its own file format for input and output (although support
94 * for standard file formats may be added later), and provides very limited
95 * visualization functionalities. The only learning method supported currently
96 * is Expectation Maximization (or Maximum Likelihood if no data is missing)
97 * for learning factor parameters.
98 *
99 * \section rationale Rationale
100 *
101 * In my opinion, the lack of open source "reference" implementations hampers
102 * progress in research on approximate inference. Methods differ widely in terms
103 * of quality and performance characteristics, which also depend in different
104 * ways on various properties of the graphical models. Finding the best
105 * approximate inference method for a particular application therefore often
106 * requires empirical comparisons. However, implementing and debugging these
107 * methods takes a lot of time which could otherwise be spent on research. I hope
108 * that this code will aid researchers to be able to easily compare various
109 * (existing as well as new) approximate inference methods, in this way
110 * accelerating research and stimulating real-world applications of approximate
111 * inference.
112 *
113 * \section language Language
114 * Because libDAI is implemented in C++, it is very fast compared with
115 * implementations in MatLab (a factor 1000 faster is not uncommon).
116 * libDAI does provide a (limited) MatLab interface for easy integration with MatLab.
117 * It also provides a command line interface and experimental python and octave
118 * interfaces (thanks to Patrick Pletscher).
119 *
120 * \section compatibility Compatibility
121 *
122 * The code has been developed under Debian GNU/Linux with the GCC compiler suite.
123 * libDAI compiles successfully with g++ versions 3.4 up to 4.4.
124 *
125 * libDAI has also been successfully compiled with MS Visual Studio 2008 under Windows
126 * (but not all build targets are supported yet) and with Cygwin under Windows.
127 *
128 * Finally, libDAI has been compiled successfully on MacOS X.
129 *
130 * \section download Downloading libDAI
131 * The libDAI sources and documentation can be downloaded from the libDAI website:
132 * http://www.libdai.org.
133 *
134 * \section support Mailing list
135 * The Google group "libDAI" (http://groups.google.com/group/libdai)
136 * can be used for getting support and discussing development issues.
137 */
138
139
140 /** \page license License
141 * <hr size="1">
142 * \section license-license License
143 *
144 * libDAI is free software; you can redistribute it and/or modify
145 * it under the terms of the GNU General Public License as published by
146 * the Free Software Foundation; either version 2 of the License, or
147 * (at your option) any later version.
148 *
149 * libDAI is distributed in the hope that it will be useful,
150 * but WITHOUT ANY WARRANTY; without even the implied warranty of
151 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
152 * GNU General Public License for more details.
153 *
154 * <hr size="1">
155 * \section license-gpl GNU General Public License version 2
156 *
157 * \verbinclude COPYING
158 */
159
160
161 /** \page citations Citing libDAI
162 * <hr size="1">
163 * \section citations-citations Citing libDAI
164 *
165 * If you write a scientific paper describing research that made substantive use
166 * of this program, please cite the software appropriately, by mentioning the
167 * fashion in which this software was used, including the version number.
168 *
169 * An appropriate citation would be:\n
170 *
171 * Joris M. Mooij et al. (2010) "libDAI 0.2.5: A free/open source C++ library for Discrete
172 * Approximate Inference", http://www.libdai.org
173 *
174 * or in BiBTeX format:
175 *
176 * <pre>
177 * \@misc{mooij2010libdai,
178 * author = "Joris M. Mooij et al.",
179 * title = "lib{DAI} 0.2.5: A free/open source {C}++ library for {D}iscrete {A}pproximate {I}nference",
180 * howpublished = "http://www.libdai.org/",
181 * year = 2010
182 * }
183 * </pre>
184 *
185 * Moreover, as a personal note, I would appreciate it to be informed about any
186 * publications using libDAI at joris dot mooij at libdai dot org.
187 */
188
189
190 /** \page authors Authors
191 * \section authors-authors People who contributed to libDAI
192 *
193 * \verbinclude AUTHORS
194 */
195
196
197 /** \page build Building libDAI
198 * <hr size="1">
199 * \section build-unix Building libDAI under UNIX variants (Linux / Cygwin / Mac OS X)
200 *
201 * \subsection build-unix-preparations Preparations
202 *
203 * You need:
204 * - a recent version of gcc (at least version 3.4)
205 * - GNU make
206 * - recent boost C++ libraries (at least version 1.37; however,
207 * version 1.37 shipped with Ubuntu 9.04 is known not to work)
208 * - doxygen (only for building the documentation)
209 * - graphviz (only for using some of the libDAI command line utilities)
210 *
211 * On Debian/Ubuntu, you can easily install the required packages with a single command:
212 * <pre> apt-get install g++ make doxygen graphviz libboost-dev libboost-graph-dev libboost-program-options-dev libboost-test-dev</pre>
213 * (root permissions needed).
214 *
215 * On Mac OS X (10.4 is known to work), these packages can be installed easily via MacPorts.
216 * If MacPorts is not already installed, install it according to the instructions at http://www.macports.org/.
217 * Then, a simple
218 * <pre> sudo port install gmake boost doxygen graphviz</pre>
219 * should be enough to install everything that is needed.
220 *
221 * On Cygwin, the prebuilt Cygwin package boost-1.33.1-x is known not to work.
222 * You can however obtain the latest boost version (you need at least 1.37.0)
223 * from http://www.boost.org/ and build it as described in the next subsection.
224 *
225 * \subsubsection build-unix-boost Building boost under Cygwin
226 *
227 * - Download the latest boost libraries from http://www.boost.org
228 * - Build the required boost libraries using:
229 * <pre>
230 * ./bootstrap.sh --with-libraries=program_options,math,graph,test --prefix=/boost_root/
231 * ./bjam</pre>
232 * - In order to use dynamic linking, the boost .dll's should be somewhere in the path.
233 * This can be achieved by a command like:
234 * <pre>
235 * export PATH=$PATH:/boost_root/stage/lib</pre>
236 *
237 *
238 * \subsection build-unix-libdai Building libDAI
239 *
240 * To build the libDAI source, first copy a template Makefile.* to Makefile.conf
241 * (for example, copy Makefile.LINUX to Makefile.conf if you use GNU/Linux).
242 * Then, edit the Makefile.conf template to adapt it to your local setup.
243 * Especially directories may differ from system to system. Platform independent
244 * build options can be set in Makefile.ALL. Finally, run
245 * <pre> make</pre>
246 * The build includes a regression test, which may take a while to complete.
247 *
248 * If the build is successful, you can test the example program:
249 * <pre> examples/example tests/alarm.fg</pre>
250 * or the more extensive test program:
251 * <pre> tests/testdai --aliases tests/aliases.conf --filename tests/alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
252 *
253 *
254 * <hr size="1">
255 * \section build-windows Building libDAI under Windows
256 *
257 * \subsection build-windows-preparations Preparations
258 *
259 * You need:
260 * - A recent version of MicroSoft Visual Studio (2008 is known to work)
261 * - recent boost C++ libraries (version 1.37 or higher)
262 * - GNU make (can be obtained from http://gnuwin32.sourceforge.net)
263 *
264 * For the regression test, you need:
265 * - GNU diff, GNU sed (can be obtained from http://gnuwin32.sourceforge.net)
266 *
267 * \subsubsection build-windows-boost Building boost under Windows
268 *
269 * Because building boost under Windows is tricky, I provide some guidance here.
270 *
271 * - Download the boost zip file from http://www.boost.org/users/download
272 * and unpack it somewhere.
273 * - Download the bjam executable from http://www.boost.org/users/download
274 * and unpack it somewhere else.
275 * - Download Boost.Build (v2) from http://www.boost.org/docs/tools/build/index.html
276 * and unpack it yet somewhere else.
277 * - Edit the file \c boost-build.jam in the main boost directory to change the
278 * \c BOOST_BUILD directory to the place where you put Boost.Build (use UNIX
279 * / instead of Windows \ in pathnames).
280 * - Copy the \c bjam.exe executable into the main boost directory.
281 * Now if you issue <tt>"bjam --version"</tt> you should get a version and no errors.
282 * Issueing <tt>"bjam --show-libraries"</tt> will show the libraries that will be built.
283 * - The following command builds the boost libraries that are relevant for libDAI:
284 * <pre>
285 * bjam --with-graph --with-math --with-program_options --with-test link=static runtime-link=shared</pre>
286 *
287 * \subsection build-windows-libdai Building libDAI
288 *
289 * To build the source, copy Makefile.WINDOWS to Makefile.conf. Then, edit
290 * Makefile.conf to adapt it to your local setup. Platform independent
291 * build options can be set in Makefile.ALL. Finally, run (from the command line)
292 * <pre> make</pre>
293 * The build includes a regression test, which may take a while to complete.
294 *
295 * If the build is successful, you can test the example program:
296 * <pre> examples\\example tests\\alarm.fg</pre>
297 * or the more extensive test program:
298 * <pre> tests\\testdai --aliases tests\\aliases.conf --filename tests\\alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
299 *
300 *
301 * <hr size="1">
302 * \section build-matlab Building the libDAI MatLab interface
303 *
304 * You need:
305 * - MatLab
306 * - The platform-dependent requirements described above
307 *
308 * First, you need to build the libDAI source as described above for your
309 * platform. By default, the MatLab interface is disabled, so before compiling the
310 * source, you have to enable it in Makefile.ALL by setting
311 * <pre> WITH_MATLAB=true</pre>
312 * Also, you have to configure the MatLab-specific parts of
313 * Makefile.conf to match your system (in particular, the Makefile variables ME,
314 * MATLABDIR and MEX). The MEX file extension depends on your platform; for a
315 * 64-bit linux x86_64 system this would be "ME=.mexa64", for a 32-bit linux x86
316 * system "ME=.mexglx". If you are unsure about your MEX file
317 * extension: it needs to be the same as what the MatLab command "mexext" returns.
318 * The required MEX files are built by issuing
319 * <pre> make</pre>
320 * from the command line. The MatLab interface is much less powerful than using
321 * libDAI from C++. There are two reasons for this: (i) it is boring to write MEX
322 * files; (ii) the large performance penalty paid when large data structures (like
323 * factor graphs) have to be converted between their native C++ data structure to
324 * something that MatLab understands.
325 *
326 * A simple example of how to use the MatLab interface is the following (entered
327 * at the MatLab prompt), which performs exact inference by the junction tree
328 * algorithm and approximate inference by belief propagation on the ALARM network:
329 * <pre> cd path_to_libdai/matlab
330 * [psi] = dai_readfg ('../tests/alarm.fg');
331 * [logZ,q,md,qv,qf] = dai (psi, 'JTREE', '[updates=HUGIN,verbose=0]')
332 * [logZ,q,md,qv,qf] = dai (psi, 'BP', '[updates=SEQMAX,tol=1e-9,maxiter=10000,logdomain=0]')</pre>
333 * where "path_to_libdai" has to be replaced with the directory in which libDAI
334 * was installed. For other algorithms and some default parameters, see the file
335 * tests/aliases.conf.
336 *
337 * <hr size="1">
338 * \section build-doxygen Building the documentation
339 *
340 * Install doxygen, graphviz and a TeX distribution and use
341 * <pre> make doc</pre>
342 * to build the documentation. If the documentation is not clear enough, feel free
343 * to send me an email (or even better, to improve the documentation and send a patch!).
344 * The documentation can also be browsed online at http://www.libdai.org.
345 */
346
347
348 /** \page changelog Change Log
349 * \verbinclude ChangeLog
350 */
351
352
353 /** \page terminology Terminology and conventions
354 *
355 * \section terminology-graphicalmodels Graphical models
356 *
357 * Commonly used graphical models are Bayesian networks and Markov random fields.
358 * In libDAI, both types of graphical models are represented by a slightly more
359 * general type of graphical model: a factor graph [\ref KFL01].
360 *
361 * An example of a Bayesian network is:
362 * \dot
363 * digraph bayesnet {
364 * size="1,1";
365 * x0 [label="0"];
366 * x1 [label="1"];
367 * x2 [label="2"];
368 * x3 [label="3"];
369 * x4 [label="4"];
370 * x0 -> x1;
371 * x0 -> x2;
372 * x1 -> x3;
373 * x1 -> x4;
374 * x2 -> x4;
375 * }
376 * \enddot
377 * The probability distribution of a Bayesian network factorizes as:
378 * \f[ P(\mathbf{x}) = \prod_{i\in\mathcal{V}} P(x_i \,|\, x_{\mathrm{pa}(i)}) \f]
379 * where \f$\mathrm{pa}(i)\f$ are the parents of node \a i in a DAG.
380 *
381 * The same probability distribution can be represented as a Markov random field:
382 * \dot
383 * graph mrf {
384 * size="1.5,1.5";
385 * x0 [label="0"];
386 * x1 [label="1"];
387 * x2 [label="2"];
388 * x3 [label="3"];
389 * x4 [label="4"];
390 * x0 -- x1;
391 * x0 -- x2;
392 * x1 -- x2;
393 * x1 -- x3;
394 * x1 -- x4;
395 * x2 -- x4;
396 * }
397 * \enddot
398 *
399 * The probability distribution of a Markov random field factorizes as:
400 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{C\in\mathcal{C}} \psi_C(x_C) \f]
401 * where \f$ \mathcal{C} \f$ are the cliques of an undirected graph,
402 * \f$ \psi_C(x_C) \f$ are "potentials" or "compatibility functions", and
403 * \f$ Z \f$ is the partition sum which properly normalizes the probability
404 * distribution.
405 *
406 * Finally, the same probability distribution can be represented as a factor graph:
407 * \dot
408 * graph factorgraph {
409 * size="1.8,1";
410 * x0 [label="0"];
411 * x1 [label="1"];
412 * x2 [label="2"];
413 * x3 [label="3"];
414 * x4 [label="4"];
415 * f01 [shape="box",label=""];
416 * f02 [shape="box",label=""];
417 * f13 [shape="box",label=""];
418 * f124 [shape="box",label=""];
419 * x0 -- f01;
420 * x1 -- f01;
421 * x0 -- f02;
422 * x2 -- f02;
423 * x1 -- f13;
424 * x3 -- f13;
425 * x1 -- f124;
426 * x2 -- f124;
427 * x4 -- f124;
428 * }
429 * \enddot
430 *
431 * The probability distribution of a factor graph factorizes as:
432 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{I\in \mathcal{F}} f_I(x_I) \f]
433 * where \f$ \mathcal{F} \f$ are the factor nodes of a factor graph (a
434 * bipartite graph consisting of variable nodes and factor nodes),
435 * \f$ f_I(x_I) \f$ are the factors, and \f$ Z \f$ is the partition sum
436 * which properly normalizes the probability distribution.
437 *
438 * Looking at the expressions for the joint probability distributions,
439 * it is obvious that Bayesian networks and Markov random fields can
440 * both be easily represented as factor graphs. Factor graphs most
441 * naturally express the factorization structure of a probability
442 * distribution, and hence are a convenient representation for approximate
443 * inference algorithms, which all try to exploit this factorization.
444 * This is why libDAI uses a factor graph as representation of a
445 * graphical model, implemented in the dai::FactorGraph class.
446 *
447 * \section terminology-inference Inference tasks
448 *
449 * Given a factor graph, specified by the variable nodes \f$\{x_i\}_{i\in\mathcal{V}}\f$
450 * the factor nodes \f$ \mathcal{F} \f$, the graph structure, and the factors
451 * \f$\{f_I(x_I)\}_{I\in\mathcal{F}}\f$, the following tasks are important:
452 *
453 * - Calculating the partition sum:
454 * \f[ Z = \sum_{\mathbf{x}_{\mathcal{V}}} \prod_{I \in \mathcal{F}} f_I(x_I) \f]
455 * - Calculating the marginal distribution of a subset of variables
456 * \f$\{x_i\}_{i\in A}\f$:
457 * \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]
458 * - Calculating the MAP state which has the maximum probability mass:
459 * \f[ \mathrm{argmax}_{\mathbf{x}}\,\prod_{I\in\mathcal{F}} f_I(x_I) \f]
460 *
461 * libDAI offers several inference algorithms, which solve (a subset of) these tasks either
462 * approximately or exactly, for factor graphs with discrete variables. The following
463 * algorithms are implemented:
464 *
465 * Exact inference:
466 * - Brute force enumeration: dai::ExactInf
467 * - Junction-tree method: dai::JTree
468 *
469 * Approximate inference:
470 * - Mean Field: dai::MF
471 * - (Loopy) Belief Propagation: dai::BP [\ref KFL01]
472 * - Fractional Belief Propagation: dai::FBP [\ref WiH03]
473 * - Tree-Reweighted Belief Propagation: dai::TRWBP [\ref WJW03]
474 * - Tree Expectation Propagation: dai::TreeEP [\ref MiQ04]
475 * - Generalized Belief Propagation: dai::HAK [\ref YFW05]
476 * - Double-loop GBP: dai::HAK [\ref HAK03]
477 * - Loop Corrected Belief Propagation: dai::MR [\ref MoR05] and dai::LC [\ref MoK07]
478 * - Gibbs sampling: dai::Gibbs
479 * - Conditioned Belief Propagation: dai::CBP [\ref EaG09]
480 *
481 * Not all inference tasks are implemented by each method: calculating MAP states
482 * is only possible with dai::JTree and dai::BP, calculating partition sums is
483 * not possible with dai::MR, dai::LC and dai::Gibbs.
484 *
485 * \section terminology-learning Parameter learning
486 *
487 * In addition, libDAI supports parameter learning of conditional probability
488 * tables by Expectation Maximization (or Maximum Likelihood, if there is no
489 * missing data). This is implemented in dai::EMAlg.
490 *
491 * \section terminology-variables-states Variables and states
492 *
493 * Linear states are a concept that is used often in libDAI, for example for storing
494 * and accessing factors, which are functions mapping from states of a set of variables
495 * to the real numbers. Internally, a factor is stored as an array, and the array index
496 * of an entry corresponds with the linear state of the set of variables. Below we will
497 * define variables, states and linear states of (sets of) variables.
498 *
499 * \subsection terminology-variables Variables
500 *
501 * Each (random) \a variable has a unique identifier, its \a label (which has
502 * a non-negative integer value). If two variables have the same
503 * label, they are considered as identical. A variable can take on a finite
504 * number of different values or \a states.
505 *
506 * We use the following notational conventions. The discrete
507 * random variable with label \f$l\f$ is denoted as \f$x_l\f$, and the number
508 * of possible values of this variable as \f$S_{x_l}\f$ or simply \f$S_l\f$.
509 * The set of possible values of variable \f$x_l\f$ is denoted
510 * \f$X_l := \{0,1,\dots,S_l-1\}\f$ and called its \a state \a space.
511 *
512 * \subsection terminology-variable-sets Sets of variables and the canonical ordering
513 *
514 * Let \f$A := \{x_{l_1},x_{l_2},\dots,x_{l_n}\}\f$ be a set of variables.
515 *
516 * The \a canonical \a ordering of the variables in \a A is induced by their labels.
517 * That is: if \f$l_1 < l_2\f$, then \f$x_{l_1}\f$ occurs before \f$x_{l_2}\f$ in the
518 * canonical ordering. Below, we will assume that \f$(l_i)_{i=1}^n\f$ is
519 * ordered according to the canonical ordering, i.e., \f$l_1 < l_2 < \dots < l_n\f$.
520 *
521 * \subsection terminology-variable-states States and linear states of sets of variables
522 *
523 * A \a state of the variables in \a A refers to a joint assignment of the
524 * variables, or in other words, to an element of the Cartesian product
525 * \f$ \prod_{i=1}^n X_{l_i}\f$ of the state spaces of the variables in \a A.
526 * Note that a state can also be interpreted as a mapping from variables (or
527 * variable labels) to the natural numbers, which assigns to a variable (or its
528 * label) the corresponding state of the variable.
529 *
530 * A state of \a n variables can be represented as an n-tuple of
531 * non-negative integers: \f$(s_1,s_2,\dots,s_n)\f$ corresponds to the
532 * joint assignment \f$x_{l_1} = s_1, \dots, x_{l_n} = s_n\f$.
533 * Alternatively, a state can be represented compactly as one non-negative integer;
534 * this representation is called a \a linear \a state. The linear state
535 * \a s corresponding to the state \f$(s_1,s_2,\dots,s_n)\f$ would be:
536 * \f[
537 * s := \sum_{i=1}^n s_i \prod_{j=1}^{i-1} S_{l_j}
538 * = 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}}.
539 * \f]
540 *
541 * Vice versa, given a linear state \a s for the variables \a A, the
542 * corresponding state \f$s_i\f$ of the \a i 'th variable \f$x_{l_i}\f$ (according to
543 * the canonical ordering of the variables in \a A) is given by
544 * \f[
545 * 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.
546 * \f]
547 *
548 * Finally, the \a number \a of \a states of the set of variables \a A is simply the
549 * number of different joint assignments of the variables, that is, \f$\prod_{i=1}^n S_{l_i}\f$.
550 */
551
552
553 /** \page fileformats libDAI file formats
554 *
555 * \section fileformats-factorgraph Factor graph (.fg) file format
556 *
557 * This section describes the .fg file format used in libDAI to store factor graphs.
558 * Markov Random Fields are special cases of factor graphs, as are Bayesian
559 * networks. A factor graph can be specified as follows: for each factor, one has
560 * to specify which variables occur in the factor, what their respective
561 * cardinalities (i.e., number of possible values) are, and a table listing all
562 * the values of that factor for all possible configurations of these variables.
563 *
564 * A .fg file is not much more than that. It starts with a line containing the
565 * number of factors in that graph, followed by an empty line. Then all factors
566 * are specified, using one block for each factor, where the blocks are seperated
567 * by empty lines. Each variable occurring in the factor graph has a unique
568 * identifier, its label (which should be a nonnegative integer). Comment lines
569 * which start with # are ignored.
570 *
571 * \subsection fileformats-factorgraph-factor Factor block format
572 *
573 * Each block describing a factor starts with a line containing the number of
574 * variables in that factor. The second line contains the labels of these
575 * variables, seperated by spaces (labels are nonnegative integers and to avoid
576 * confusion, it is suggested to start counting at 0). The third line contains
577 * the number of possible values of each of these variables, also seperated by
578 * spaces. Note that there is some redundancy here, since if a variable appears
579 * in more than one factor, the cardinality of that variable appears several
580 * times in the .fg file; obviously, these cardinalities should be consistent.
581 * The fourth line contains the number of nonzero entries
582 * in the factor table. The rest of the lines contain these nonzero entries;
583 * each line consists of a table index, followed by white-space, followed by the
584 * value corresponding to that table index. The most difficult part is getting
585 * the indexing right. The convention that is used is that the left-most
586 * variables cycle through their values the fastest (similar to MatLab indexing
587 * of multidimensional arrays).
588 *
589 * \subsubsection fileformats-factorgraph-factor-example Example
590 *
591 * An example block describing one factor is:
592 *
593 * <pre>
594 * 3
595 * 4 8 7
596 * 3 2 2
597 * 11
598 * 0 0.1
599 * 1 3.5
600 * 2 2.8
601 * 3 6.3
602 * 4 8.4
603 * 6 7.4
604 * 7 2.4
605 * 8 8.9
606 * 9 1.3
607 * 10 1.6
608 * 12 6.4
609 * 11 2.6
610 * </pre>
611 *
612 * which corresponds to the following factor:
613 *
614 * \f[
615 * \begin{array}{ccc|c}
616 * x_4 & x_8 & x_7 & \mbox{value}\\
617 * \hline
618 * 0 & 0 & 0 & 0.1\\
619 * 1 & 0 & 0 & 3.5\\
620 * 2 & 0 & 0 & 2.8\\
621 * 0 & 1 & 0 & 6.3\\
622 * 1 & 1 & 0 & 8.4\\
623 * 2 & 1 & 0 & 0.0\\
624 * 0 & 0 & 1 & 7.4\\
625 * 1 & 0 & 1 & 2.4\\
626 * 2 & 0 & 1 & 8.9\\
627 * 0 & 1 & 1 & 1.3\\
628 * 1 & 1 & 1 & 1.6\\
629 * 2 & 1 & 1 & 2.6
630 * \end{array}
631 * \f]
632 *
633 * Note that the value of \f$x_4\f$ changes fastest, followed by that of \f$x_8\f$, and \f$x_7\f$
634 * varies the slowest, corresponding to the second line of the block ("4 8 7").
635 * Further, \f$x_4\f$ can take on three values, and \f$x_8\f$ and \f$x_7\f$ each have two possible
636 * values, as described in the third line of the block ("3 2 2"). The table
637 * contains 11 non-zero entries (all except for the fifth entry). Note that the
638 * eleventh and twelveth entries are interchanged.
639 *
640 * A final note: the internal representation in libDAI of the factor above is
641 * different, because the variables are ordered according to their indices
642 * (i.e., the ordering would be \f$x_4 x_7 x_8\f$) and the values of the table are
643 * stored accordingly, with the variable having the smallest index changing
644 * fastest:
645 *
646 * \f[
647 * \begin{array}{ccc|c}
648 * x_4 & x_7 & x_8 & \mbox{value}\\
649 * \hline
650 * 0 & 0 & 0 & 0.1\\
651 * 1 & 0 & 0 & 3.5\\
652 * 2 & 0 & 0 & 2.8\\
653 * 0 & 1 & 0 & 7.4\\
654 * 1 & 1 & 0 & 2.4\\
655 * 2 & 1 & 0 & 8.9\\
656 * 0 & 0 & 1 & 6.3\\
657 * 1 & 0 & 1 & 8.4\\
658 * 2 & 0 & 1 & 0.0\\
659 * 0 & 1 & 1 & 1.3\\
660 * 1 & 1 & 1 & 1.6\\
661 * 2 & 1 & 1 & 2.6
662 * \end{array}
663 * \f]
664 *
665 *
666 * \section fileformats-evidence Evidence (.tab) file format
667 *
668 * This section describes the .tab fileformat used in libDAI to store "evidence",
669 * i.e., a data set consisting of multiple samples, where each sample is the
670 * observed joint state of some variables.
671 *
672 * A .tab file is a tabular data file, consisting of a header line, followed by
673 * an empty line, followed by the data points, with one line for each data point.
674 * Each line (apart from the empty one) should have the same number of columns,
675 * where columns are separated by one tab character. Each column corresponds to
676 * a variable. The header line consists of the variable labels (corresponding to
677 * dai::Var::label()). The other lines are observed joint states of the variables, i.e.,
678 * each line corresponds to a joint observation of the variables, and each column
679 * of a line contains the state of the variable associated with that column.
680 * Missing data is handled simply by having two consecutive tab characters,
681 * without any characters in between.
682 *
683 * \subsection fileformats-evidence-example Example
684 *
685 * <pre>
686 * 1 3 2
687 *
688 * 0 0 1
689 * 1 0 1
690 * 1 1
691 * </pre>
692 *
693 * This would correspond to a data set consisting of three observations concerning
694 * the variables with labels 1, 3 and 2; the first observation being
695 * \f$x_1 = 0, x_3 = 0, x_2 = 1\f$, the second observation being
696 * \f$x_1 = 1, x_3 = 0, x_2 = 1\f$, and the third observation being
697 * \f$x_1 = 1, x_2 = 1\f$ (where the state of \f$x_3\f$ is missing).
698 *
699 * \section fileformats-emalg Expectation Maximization (.em) file format
700 *
701 * This section describes the file format of .em files, which are used
702 * to specify a particular EM algorithm. The .em files are complementary
703 * to .fg files; in other words, an .em file without a corresponding .fg
704 * file is useless. Furthermore, one also needs a corresponding .tab file
705 * containing the data used for parameter learning.
706 *
707 * An .em file starts with a line specifying the number of maximization steps,
708 * followed by an empty line. Then, each maximization step is described in a
709 * block, which should satisfy the format described in the next subsection.
710 *
711 * \subsection fileformats-emalg-maximizationstep Maximization Step block format
712 *
713 * A maximization step block of an .em file starts with a single line
714 * describing the number of shared parameters blocks that will follow.
715 * Then, each shared parameters block follows, in the format described in
716 * the next subsection.
717 *
718 * \subsection fileformats-emalg-sharedparameters Shared parameters block format
719 *
720 * A shared parameters block of an .em file starts with a single line
721 * consisting of the name of a ParameterEstimation subclass
722 * and its parameters in the format of a PropertySet. For example:
723 * <pre> CondProbEstimation [target_dim=2,total_dim=4,pseudo_count=1]</pre>
724 * The next line contains the number of factors that share their parameters.
725 * Then, each of these factors is specified on separate lines (possibly
726 * seperated by empty lines), where each line consists of several fields
727 * seperated by a space or a tab character. The first field contains
728 * the index of the factor in the factor graph. The following fields should
729 * contain the variable labels of the variables on which that factor depends,
730 * in a specific ordering. This ordering can be different from the canonical
731 * ordering of the variables used internally in libDAI (which would be sorted
732 * ascendingly according to the variable labels). The ordering of the variables
733 * specifies the implicit ordering of the shared parameters: when iterating
734 * over all shared parameters, the corresponding index of the first variable
735 * changes fastest (in the inner loop), and the corresponding index of the
736 * last variable changes slowest (in the outer loop). By choosing the right
737 * ordering, it is possible to let different factors (depending on different
738 * variables) share parameters in parameter learning using EM. This convention
739 * is similar to the convention used in factor blocks in a factor graph .fg
740 * file (see \ref fileformats-factorgraph-factor).
741 *
742 * \section fileformats-aliases Aliases file format
743 *
744 * An aliases file is basically a list of "macros" and the strings that they
745 * should be substituted with.
746 *
747 * Each line of the aliases file can be either empty, contain a comment
748 * (if the first character is a '#') or contain an alias. In the latter case,
749 * the line should contain a colon; the part before the colon contains the
750 * name of the alias, the part after the colon the string that it should be
751 * substituted with. Any whitespace before and after the colon is ignored.
752 *
753 * For example, the following line would define the alias \c BP_SEQFIX
754 * as a shorthand for "BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]":
755 * <pre>
756 * BP_SEQFIX: BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]
757 * </pre>
758 *
759 * Aliases files can be used to store default options for algorithms.
760 */
761
762 /** \page bibliography Bibliography
763 * \anchor EaG09 \ref EaG09
764 * F. Eaton and Z. Ghahramani (2009):
765 * "Choosing a Variable to Clamp",
766 * <em>Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS 2009)</em> 5:145-152,
767 * http://jmlr.csail.mit.edu/proceedings/papers/v5/eaton09a/eaton09a.pdf
768 *
769 * \anchor EMK06 \ref EMK06
770 * G. Elidan and I. McGraw and D. Koller (2006):
771 * "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing",
772 * <em>Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)</em>,
773 * http://uai.sis.pitt.edu/papers/06/UAI2006_0091.pdf
774 *
775 * \anchor HAK03 \ref HAK03
776 * T. Heskes and C. A. Albers and H. J. Kappen (2003):
777 * "Approximate Inference and Constrained Optimization",
778 * <em>Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03)</em> pp. 313-320,
779 * http://www.snn.ru.nl/reports/Heskes.uai2003.ps.gz
780 *
781 * \anchor KFL01 \ref KFL01
782 * F. R. Kschischang and B. J. Frey and H.-A. Loeliger (2001):
783 * "Factor Graphs and the Sum-Product Algorithm",
784 * <em>IEEE Transactions on Information Theory</em> 47(2):498-519,
785 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=910572
786 *
787 * \anchor KoF09 \ref KoF09
788 * D. Koller and N. Friedman (2009):
789 * <em>Probabilistic Graphical Models - Principles and Techniques</em>,
790 * The MIT Press, Cambridge, Massachusetts, London, England.
791
792 * \anchor Min05 \ref Min05
793 * T. Minka (2005):
794 * "Divergence measures and message passing",
795 * <em>MicroSoft Research Technical Report</em> MSR-TR-2005-173,
796 * http://research.microsoft.com/en-us/um/people/minka/papers/message-passing/minka-divergence.pdf
797 *
798 * \anchor MiQ04 \ref MiQ04
799 * T. Minka and Y. Qi (2004):
800 * "Tree-structured Approximations by Expectation Propagation",
801 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 16,
802 * http://books.nips.cc/papers/files/nips16/NIPS2003_AA25.pdf
803 *
804 * \anchor MoK07 \ref MoK07
805 * J. M. Mooij and H. J. Kappen (2007):
806 * "Loop Corrections for Approximate Inference on Factor Graphs",
807 * <em>Journal of Machine Learning Research</em> 8:1113-1143,
808 * http://www.jmlr.org/papers/volume8/mooij07a/mooij07a.pdf
809 *
810 * \anchor MoK07b \ref MoK07b
811 * J. M. Mooij and H. J. Kappen (2007):
812 * "Sufficient Conditions for Convergence of the Sum-Product Algorithm",
813 * <em>IEEE Transactions on Information Theory</em> 53(12):4422-4437,
814 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4385778
815 *
816 * \anchor Moo08 \ref Moo08
817 * J. M. Mooij (2008):
818 * "Understanding and Improving Belief Propagation",
819 * <em>Ph.D. Thesis</em> Radboud University Nijmegen
820 * http://webdoc.ubn.ru.nl/mono/m/mooij_j/undeanimb.pdf
821 *
822 * \anchor MoR05 \ref MoR05
823 * A. Montanari and T. Rizzo (2005):
824 * "How to Compute Loop Corrections to the Bethe Approximation",
825 * <em>Journal of Statistical Mechanics: Theory and Experiment</em> 2005(10)-P10011,
826 * http://stacks.iop.org/1742-5468/2005/P10011
827 *
828 * \anchor StW99 \ref StW99
829 * A. Steger and N. C. Wormald (1999):
830 * "Generating Random Regular Graphs Quickly",
831 * <em>Combinatorics, Probability and Computing</em> Vol 8, Issue 4, pp. 377-396,
832 * http://www.math.uwaterloo.ca/~nwormald/papers/randgen.pdf
833 *
834 * \anchor WiH03 \ref WiH03
835 * W. Wiegerinck and T. Heskes (2003):
836 * "Fractional Belief Propagation",
837 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 15, pp. 438-445,
838 * http://books.nips.cc/papers/files/nips15/LT16.pdf
839 *
840 * \anchor WJW03 \ref WJW03
841 * M. J. Wainwright, T. S. Jaakkola and A. S. Willsky (2003):
842 * "Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching",
843 * <em>9th Workshop on Artificial Intelligence and Statistics</em>,
844 * http://www.eecs.berkeley.edu/~wainwrig/Papers/WJW_AIStat03.pdf
845 *
846 * \anchor YFW05 \ref YFW05
847 * J. S. Yedidia and W. T. Freeman and Y. Weiss (2005):
848 * "Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms",
849 * <em>IEEE Transactions on Information Theory</em> 51(7):2282-2312,
850 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1459044
851 */
852
853
854 /** \page discussion Ideas not worth exploring
855 * \section discuss_extendedgraphs Extended factorgraphs/regiongraphs
856 *
857 * A FactorGraph and a RegionGraph are often equipped with
858 * additional properties for nodes and edges. The code to initialize those
859 * is often quite similar. Maybe one could abstract this, e.g.:
860 * \code
861 * template <typename Node1Properties, typename Node2Properties, typename EdgeProperties>
862 * class ExtFactorGraph : public FactorGraph {
863 * public:
864 * std::vector<Node1Properties> node1Props;
865 * std::vector<Node2Properties> node2Props;
866 * std::vector<std::vector<EdgeProperties> > edgeProps;
867 * // ...
868 * }
869 * \endcode
870 *
871 * Advantages:
872 * - Less code duplication.
873 * - Easier maintainability.
874 * - Easier to write new inference algorithms.
875 *
876 * Disadvantages:
877 * - Cachability may be worse.
878 * - A problem is the case where there are no properties for either type of nodes or for edges.
879 * Maybe this can be solved using specializations, or using variadac template arguments?
880 * Another possible solution would be to define a "class Empty {}", and add some code
881 * that checks for the typeid, comparing it with Empty, and doing something special in that case
882 * (e.g., not allocating memory).
883 * - The main disadvantage of this approach seems to be that it leads to even more entanglement.
884 * Therefore this is probably a bad idea.
885 *
886 * \section discuss_templates Polymorphism by template parameterization
887 *
888 * Instead of polymorphism by inheritance, use polymorphism by template parameterization.
889 * For example, the real reason for introducing the complicated inheritance scheme of dai::InfAlg
890 * was for functions like dai::calcMarginal. Instead, one could use a template function:
891 * \code
892 * template<typename InfAlg>
893 * Factor calcMarginal( const InfAlg &obj, const VarSet &ns, bool reInit );
894 * \endcode
895 * This would assume that the type InfAlg supports certain methods. Ideally, one would use
896 * concepts to define different classes of inference algorithms with different capabilities,
897 * for example the ability to calculate logZ, the ability to calculate marginals, the ability to
898 * calculate bounds, the ability to calculate MAP states, etc. Then, one would use traits
899 * classes in order to be able to query the capabilities of the model. For example, one would be
900 * able to query whether the inference algorithm supports calculation of logZ. Unfortunately,
901 * this is compile-time polymorphism, whereas tests/testdai needs runtime polymorphism.
902 * Therefore this is probably a bad idea.
903 */