Merge branch 'master' of git@git.tuebingen.mpg.de:libdai
[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 Name members by virtual functions (or add virtual functions returning the Name)
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, Frederik Eaton
46 * \version git HEAD
47 * \date February 11, 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 *
179 * Joris M. Mooij et al. (2010) "libDAI 0.2.4: A free/open source C++ library for Discrete
180 * Approximate Inference", http://www.libdai.org
181 *
182 * or in BiBTeX format:
183 *
184 * <pre>
185 * \@misc{mooij2010libdai,
186 * author = "Joris M. Mooij et al.",
187 * title = "lib{DAI} 0.2.4: A free/open source {C}++ library for {D}iscrete {A}pproximate {I}nference",
188 * howpublished = "http://www.libdai.org/",
189 * year = 2010
190 * }
191 * </pre>
192 *
193 * Moreover, as a personal note, I would appreciate it if you would email
194 * (citations of) papers referencing this work to joris dot mooij at libdai dot org.
195 */
196
197
198 /** \page authors Authors
199 * \section authors-authors People who contributed to libDAI
200 *
201 * \verbinclude AUTHORS
202 */
203
204
205 /** \page build Building libDAI
206 * <hr size="1">
207 * \section build-unix Building libDAI under UNIX variants (Linux / Cygwin / Mac OS X)
208 *
209 * \subsection build-unix-preparations Preparations
210 *
211 * You need:
212 * - a recent version of gcc (at least version 3.4)
213 * - GNU make
214 * - doxygen
215 * - graphviz
216 * - recent boost C++ libraries (at least version 1.34 if you have
217 * a recent version of GCC, otherwise at least version 1.37; however,
218 * version 1.37 shipped with Ubuntu 9.04 is known not to work)
219 *
220 * On Debian/Ubuntu, you can easily install all these packages with a single command:
221 * <pre> apt-get install g++ make doxygen graphviz libboost-dev libboost-graph-dev libboost-program-options-dev</pre>
222 * (root permissions needed).
223 *
224 * On Mac OS X (10.4 is known to work), these packages can be installed easily via MacPorts.
225 * If MacPorts is not already installed, install it according to the instructions at http://www.macports.org/.
226 * Then, a simple
227 * <pre> sudo port install gmake boost doxygen graphviz</pre>
228 * should be enough to install everything that is needed.
229 *
230 * On Cygwin, the prebuilt Cygwin package boost-1.33.1-x is known not to work.
231 * You can however obtain the latest boost version (you need at least 1.37.0)
232 * from http://www.boost.org/ and compile/install it with:
233 *
234 * <pre> ./configure
235 * make
236 * make install
237 * </pre>
238 *
239 * \subsection build-unix-libdai Building libDAI
240 *
241 * To build the libDAI source, first copy a template Makefile.* to Makefile.conf
242 * (for example, copy Makefile.LINUX to Makefile.conf if you use GNU/Linux).
243 * Then, edit the Makefile.conf template to adapt it to your local setup.
244 * Especially directories may differ from system to system. Platform independent
245 * build options can be set in Makefile.ALL. Finally, run
246 * <pre> make</pre>
247 * The build includes a regression test, which may take a while to complete.
248 *
249 * If the build is successful, you can test the example program:
250 * <pre> examples/example tests/alarm.fg</pre>
251 * or the more extensive test program:
252 * <pre> tests/testdai --aliases tests/aliases.conf --filename tests/alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
253 *
254 *
255 * <hr size="1">
256 * \section build-windows Building libDAI under Windows
257 *
258 * \subsection build-windows-preparations Preparations
259 *
260 * You need:
261 * - A recent version of MicroSoft Visual Studio (2008 is known to work)
262 * - recent boost C++ libraries (version 1.37 or higher)
263 * - GNU make (can be obtained from http://gnuwin32.sourceforge.net)
264 *
265 * For the regression test, you need:
266 * - GNU diff, GNU sed (can be obtained from http://gnuwin32.sourceforge.net)
267 *
268 * \subsection build-windows-libdai Building libDAI
269 *
270 * To build the source, copy Makefile.WINDOWS to Makefile.conf. Then, edit
271 * Makefile.conf to adapt it to your local setup. Platform independent
272 * build options can be set in Makefile.ALL. Finally, run (from the command line)
273 * <pre> make</pre>
274 * The build includes a regression test, which may take a while to complete.
275 *
276 * If the build is successful, you can test the example program:
277 * <pre> examples\\example tests\\alarm.fg</pre>
278 * or the more extensive test program:
279 * <pre> tests\\testdai --aliases tests\\aliases.conf --filename tests\\alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>
280 *
281 *
282 * <hr size="1">
283 * \section build-matlab Building the libDAI MatLab interface
284 *
285 * You need:
286 * - MatLab
287 * - The platform-dependent requirements described above
288 *
289 * First, you need to build the libDAI source as described above for your
290 * platform. By default, the MatLab interface is disabled, so before compiling the
291 * source, you have to enable it in Makefile.ALL by setting
292 * <pre> WITH_MATLAB=true</pre>
293 * Also, you have to configure the MatLab-specific parts of
294 * Makefile.conf to match your system (in particular, the Makefile variables ME,
295 * MATLABDIR and MEX). The MEX file extension depends on your platform; for a
296 * 64-bit linux x86_64 system this would be "ME=.mexa64", for a 32-bit linux x86
297 * system "ME=.mexglx". If you are unsure about your MEX file
298 * extension: it needs to be the same as what the MatLab command "mexext" returns.
299 * The required MEX files are built by issuing
300 * <pre> make</pre>
301 * from the command line. The MatLab interface is much less powerful than using
302 * libDAI from C++. There are two reasons for this: (i) it is boring to write MEX
303 * files; (ii) the large performance penalty paid when large data structures (like
304 * factor graphs) have to be converted between their native C++ data structure to
305 * something that MatLab understands.
306 *
307 * A simple example of how to use the MatLab interface is the following (entered
308 * at the MatLab prompt), which performs exact inference by the junction tree
309 * algorithm and approximate inference by belief propagation on the ALARM network:
310 * <pre> cd path_to_libdai/matlab
311 * [psi] = dai_readfg ('../tests/alarm.fg');
312 * [logZ,q,md,qv,qf] = dai (psi, 'JTREE', '[updates=HUGIN,verbose=0]')
313 * [logZ,q,md,qv,qf] = dai (psi, 'BP', '[updates=SEQMAX,tol=1e-9,maxiter=10000,logdomain=0]')</pre>
314 * where "path_to_libdai" has to be replaced with the directory in which libDAI
315 * was installed. For other algorithms and some default parameters, see the file
316 * tests/aliases.conf.
317 *
318 * <hr size="1">
319 * \section build-doxygen Building the documentation
320 *
321 * Install doxygen, graphviz and a TeX distribution and use
322 * <pre> make doc</pre>
323 * to build the documentation. If the documentation is not clear enough, feel free
324 * to send me an email (or even better, to improve the documentation and send a patch!).
325 * The documentation can also be browsed online at http://www.libdai.org.
326 */
327
328
329 /** \page changelog Change Log
330 * \verbinclude ChangeLog
331 */
332
333
334 /** \page terminology Terminology and conventions
335 *
336 * \section terminology-graphicalmodels Graphical models
337 *
338 * Commonly used graphical models are Bayesian networks and Markov random fields.
339 * In libDAI, both types of graphical models are represented by a slightly more
340 * general type of graphical model: a factor graph [\ref KFL01].
341 *
342 * An example of a Bayesian network is:
343 * \dot
344 * digraph bayesnet {
345 * size="1,1";
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 -> x3;
354 * x1 -> x4;
355 * x2 -> x4;
356 * }
357 * \enddot
358 * The probability distribution of a Bayesian network factorizes as:
359 * \f[ P(\mathbf{x}) = \prod_{i\in\mathcal{V}} P(x_i \,|\, x_{\mathrm{pa}(i)}) \f]
360 * where \f$\mathrm{pa}(i)\f$ are the parents of node \a i in a DAG.
361 *
362 * The same probability distribution can be represented as a Markov random field:
363 * \dot
364 * graph mrf {
365 * size="1.5,1.5";
366 * x0 [label="0"];
367 * x1 [label="1"];
368 * x2 [label="2"];
369 * x3 [label="3"];
370 * x4 [label="4"];
371 * x0 -- x1;
372 * x0 -- x2;
373 * x1 -- x2;
374 * x1 -- x3;
375 * x1 -- x4;
376 * x2 -- x4;
377 * }
378 * \enddot
379 *
380 * The probability distribution of a Markov random field factorizes as:
381 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{C\in\mathcal{C}} \psi_C(x_C) \f]
382 * where \f$ \mathcal{C} \f$ are the cliques of an undirected graph,
383 * \f$ \psi_C(x_C) \f$ are "potentials" or "compatibility functions", and
384 * \f$ Z \f$ is the partition sum which properly normalizes the probability
385 * distribution.
386 *
387 * Finally, the same probability distribution can be represented as a factor graph:
388 * \dot
389 * graph factorgraph {
390 * size="1.8,1";
391 * x0 [label="0"];
392 * x1 [label="1"];
393 * x2 [label="2"];
394 * x3 [label="3"];
395 * x4 [label="4"];
396 * f01 [shape="box",label=""];
397 * f02 [shape="box",label=""];
398 * f13 [shape="box",label=""];
399 * f124 [shape="box",label=""];
400 * x0 -- f01;
401 * x1 -- f01;
402 * x0 -- f02;
403 * x2 -- f02;
404 * x1 -- f13;
405 * x3 -- f13;
406 * x1 -- f124;
407 * x2 -- f124;
408 * x4 -- f124;
409 * }
410 * \enddot
411 *
412 * The probability distribution of a factor graph factorizes as:
413 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{I\in \mathcal{F}} f_I(x_I) \f]
414 * where \f$ \mathcal{F} \f$ are the factor nodes of a factor graph (a
415 * bipartite graph consisting of variable nodes and factor nodes),
416 * \f$ f_I(x_I) \f$ are the factors, and \f$ Z \f$ is the partition sum
417 * which properly normalizes the probability distribution.
418 *
419 * Looking at the expressions for the joint probability distributions,
420 * it is obvious that Bayesian networks and Markov random fields can
421 * both be easily represented as factor graphs. Factor graphs most
422 * naturally express the factorization structure of a probability
423 * distribution, and hence are a convenient representation for approximate
424 * inference algorithms, which all try to exploit this factorization.
425 * This is why libDAI uses a factor graph as representation of a
426 * graphical model, implemented in the dai::FactorGraph class.
427 *
428 * \section terminology-inference Inference tasks
429 *
430 * Given a factor graph, specified by the variable nodes \f$\{x_i\}_{i\in\mathcal{V}}\f$
431 * the factor nodes \f$ \mathcal{F} \f$, the graph structure, and the factors
432 * \f$\{f_I(x_I)\}_{I\in\mathcal{F}}\f$, the following tasks are important:
433 *
434 * - Calculating the partition sum:
435 * \f[ Z = \sum_{\mathbf{x}_{\mathcal{V}}} \prod_{I \in \mathcal{F}} f_I(x_I) \f]
436 * - Calculating the marginal distribution of a subset of variables
437 * \f$\{x_i\}_{i\in A}\f$:
438 * \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]
439 * - Calculating the MAP state which has the maximum probability mass:
440 * \f[ \mathrm{argmax}_{\mathbf{x}}\,\prod_{I\in\mathcal{F}} f_I(x_I) \f]
441 *
442 * libDAI offers several inference algorithms, which solve (a subset of) these tasks either
443 * approximately or exactly, for factor graphs with discrete variables. The following
444 * algorithms are implemented:
445 *
446 * Exact inference:
447 * - Brute force enumeration: dai::ExactInf
448 * - Junction-tree method: dai::JTree
449 *
450 * Approximate inference:
451 * - Mean Field: dai::MF
452 * - (Loopy) Belief Propagation: dai::BP [\ref KFL01]
453 * - Fractional Belief Propagation: dai::FBP [\ref WiH03]
454 * - Tree-Reweighted Belief Propagation: dai::TRWBP [\ref WJW03]
455 * - Tree Expectation Propagation: dai::TreeEP [\ref MiQ04]
456 * - Generalized Belief Propagation: dai::HAK [\ref YFW05]
457 * - Double-loop GBP: dai::HAK [\ref HAK03]
458 * - Loop Corrected Belief Propagation: dai::MR [\ref MoR05] and dai::LC [\ref MoK07]
459 * - Gibbs sampling: dai::Gibbs
460 * - Conditioned Belief Propagation: dai::CBP [\ref EaG09]
461 *
462 * Not all inference tasks are implemented by each method: calculating MAP states
463 * is only possible with dai::JTree and dai::BP, calculating partition sums is
464 * not possible with dai::MR, dai::LC and dai::Gibbs.
465 *
466 * \section terminology-learning Parameter learning
467 *
468 * In addition, libDAI supports parameter learning of conditional probability
469 * tables by Expectation Maximization (or Maximum Likelihood, if there is no
470 * missing data). This is implemented in dai::EMAlg.
471 *
472 * \section terminology-variables-states Variables and states
473 *
474 * Linear states are a concept that is used often in libDAI, for example for storing
475 * and accessing factors, which are functions mapping from states of a set of variables
476 * to the real numbers. Internally, a factor is stored as an array, and the array index
477 * of an entry corresponds with the linear state of the set of variables. Below we will
478 * define variables, states and linear states of (sets of) variables.
479 *
480 * \subsection terminology-variables Variables
481 *
482 * Each (random) \a variable has a unique identifier, its \a label (which has
483 * a non-negative integer value). If two variables have the same
484 * label, they are considered as identical. A variable can take on a finite
485 * number of different values or \a states.
486 *
487 * We use the following notational conventions. The discrete
488 * random variable with label \f$l\f$ is denoted as \f$x_l\f$, and the number
489 * of possible values of this variable as \f$S_{x_l}\f$ or simply \f$S_l\f$.
490 * The set of possible values of variable \f$x_l\f$ is denoted
491 * \f$X_l := \{0,1,\dots,S_l-1\}\f$ and called its \a state \a space.
492 *
493 * \subsection terminology-variable-sets Sets of variables and the canonical ordering
494 *
495 * Let \f$A := \{x_{l_1},x_{l_2},\dots,x_{l_n}\}\f$ be a set of variables.
496 *
497 * The \a canonical \a ordering of the variables in \a A is induced by their labels.
498 * That is: if \f$l_1 < l_2\f$, then \f$x_{l_1}\f$ occurs before \f$x_{l_2}\f$ in the
499 * canonical ordering. Below, we will assume that \f$(l_i)_{i=1}^n\f$ is
500 * ordered according to the canonical ordering, i.e., \f$l_1 < l_2 < \dots < l_n\f$.
501 *
502 * \subsection terminology-variable-states States and linear states of sets of variables
503 *
504 * A \a state of the variables in \a A refers to a joint assignment of the
505 * variables, or in other words, to an element of the Cartesian product
506 * \f$ \prod_{i=1}^n X_{l_i}\f$ of the state spaces of the variables in \a A.
507 * Note that a state can also be interpreted as a mapping from variables (or
508 * variable labels) to the natural numbers, which assigns to a variable (or its
509 * label) the corresponding state of the variable.
510 *
511 * A state of \a n variables can be represented as an n-tuple of
512 * non-negative integers: \f$(s_1,s_2,\dots,s_n)\f$ corresponds to the
513 * joint assignment \f$x_{l_1} = s_1, \dots, x_{l_n} = s_n\f$.
514 * Alternatively, a state can be represented compactly as one non-negative integer;
515 * this representation is called a \a linear \a state. The linear state
516 * \a s corresponding to the state \f$(s_1,s_2,\dots,s_n)\f$ would be:
517 * \f[
518 * s := \sum_{i=1}^n s_i \prod_{j=1}^{i-1} S_{l_j}
519 * = 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}}.
520 * \f]
521 *
522 * Vice versa, given a linear state \a s for the variables \a A, the
523 * corresponding state \f$s_i\f$ of the \a i 'th variable \f$x_{l_i}\f$ (according to
524 * the canonical ordering of the variables in \a A) is given by
525 * \f[
526 * 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.
527 * \f]
528 *
529 * Finally, the \a number \a of \a states of the set of variables \a A is simply the
530 * number of different joint assignments of the variables, that is, \f$\prod_{i=1}^n S_{l_i}\f$.
531 */
532
533
534 /** \page fileformats libDAI file formats
535 *
536 * \section fileformats-factorgraph Factor graph (.fg) file format
537 *
538 * This section describes the .fg file format used in libDAI to store factor graphs.
539 * Markov Random Fields are special cases of factor graphs, as are Bayesian
540 * networks. A factor graph can be specified as follows: for each factor, one has
541 * to specify which variables occur in the factor, what their respective
542 * cardinalities (i.e., number of possible values) are, and a table listing all
543 * the values of that factor for all possible configurations of these variables.
544 *
545 * A .fg file is not much more than that. It starts with a line containing the
546 * number of factors in that graph, followed by an empty line. Then all factors
547 * are specified, using one block for each factor, where the blocks are seperated
548 * by empty lines. Each variable occurring in the factor graph has a unique
549 * identifier, its label (which should be a nonnegative integer). Comment lines
550 * which start with # are ignored.
551 *
552 * \subsection fileformats-factorgraph-factor Factor block format
553 *
554 * Each block describing a factor starts with a line containing the number of
555 * variables in that factor. The second line contains the labels of these
556 * variables, seperated by spaces (labels are nonnegative integers and to avoid
557 * confusion, it is suggested to start counting at 0). The third line contains
558 * the number of possible values of each of these variables, also seperated by
559 * spaces. Note that there is some redundancy here, since if a variable appears
560 * in more than one factor, the cardinality of that variable appears several
561 * times in the .fg file; obviously, these cardinalities should be consistent.
562 * The fourth line contains the number of nonzero entries
563 * in the factor table. The rest of the lines contain these nonzero entries;
564 * each line consists of a table index, followed by white-space, followed by the
565 * value corresponding to that table index. The most difficult part is getting
566 * the indexing right. The convention that is used is that the left-most
567 * variables cycle through their values the fastest (similar to MatLab indexing
568 * of multidimensional arrays).
569 *
570 * \subsubsection fileformats-factorgraph-factor-example Example
571 *
572 * An example block describing one factor is:
573 *
574 * <pre>
575 * 3
576 * 4 8 7
577 * 3 2 2
578 * 11
579 * 0 0.1
580 * 1 3.5
581 * 2 2.8
582 * 3 6.3
583 * 4 8.4
584 * 6 7.4
585 * 7 2.4
586 * 8 8.9
587 * 9 1.3
588 * 10 1.6
589 * 12 6.4
590 * 11 2.6
591 * </pre>
592 *
593 * which corresponds to the following factor:
594 *
595 * \f[
596 * \begin{array}{ccc|c}
597 * x_4 & x_8 & x_7 & \mbox{value}\\
598 * \hline
599 * 0 & 0 & 0 & 0.1\\
600 * 1 & 0 & 0 & 3.5\\
601 * 2 & 0 & 0 & 2.8\\
602 * 0 & 1 & 0 & 6.3\\
603 * 1 & 1 & 0 & 8.4\\
604 * 2 & 1 & 0 & 0.0\\
605 * 0 & 0 & 1 & 7.4\\
606 * 1 & 0 & 1 & 2.4\\
607 * 2 & 0 & 1 & 8.9\\
608 * 0 & 1 & 1 & 1.3\\
609 * 1 & 1 & 1 & 1.6\\
610 * 2 & 1 & 1 & 2.6
611 * \end{array}
612 * \f]
613 *
614 * Note that the value of \f$x_4\f$ changes fastest, followed by that of \f$x_8\f$, and \f$x_7\f$
615 * varies the slowest, corresponding to the second line of the block ("4 8 7").
616 * Further, \f$x_4\f$ can take on three values, and \f$x_8\f$ and \f$x_7\f$ each have two possible
617 * values, as described in the third line of the block ("3 2 2"). The table
618 * contains 11 non-zero entries (all except for the fifth entry). Note that the
619 * eleventh and twelveth entries are interchanged.
620 *
621 * A final note: the internal representation in libDAI of the factor above is
622 * different, because the variables are ordered according to their indices
623 * (i.e., the ordering would be \f$x_4 x_7 x_8\f$) and the values of the table are
624 * stored accordingly, with the variable having the smallest index changing
625 * fastest:
626 *
627 * \f[
628 * \begin{array}{ccc|c}
629 * x_4 & x_7 & x_8 & \mbox{value}\\
630 * \hline
631 * 0 & 0 & 0 & 0.1\\
632 * 1 & 0 & 0 & 3.5\\
633 * 2 & 0 & 0 & 2.8\\
634 * 0 & 1 & 0 & 7.4\\
635 * 1 & 1 & 0 & 2.4\\
636 * 2 & 1 & 0 & 8.9\\
637 * 0 & 0 & 1 & 6.3\\
638 * 1 & 0 & 1 & 8.4\\
639 * 2 & 0 & 1 & 0.0\\
640 * 0 & 1 & 1 & 1.3\\
641 * 1 & 1 & 1 & 1.6\\
642 * 2 & 1 & 1 & 2.6
643 * \end{array}
644 * \f]
645 *
646 *
647 * \section fileformats-evidence Evidence (.tab) file format
648 *
649 * This section describes the .tab fileformat used in libDAI to store "evidence",
650 * i.e., a data set consisting of multiple samples, where each sample is the
651 * observed joint state of some variables.
652 *
653 * A .tab file is a tabular data file, consisting of a header line, followed by
654 * an empty line, followed by the data points, with one line for each data point.
655 * Each line (apart from the empty one) should have the same number of columns,
656 * where columns are separated by one tab character. Each column corresponds to
657 * a variable. The header line consists of the variable labels (corresponding to
658 * dai::Var::label()). The other lines are observed joint states of the variables, i.e.,
659 * each line corresponds to a joint observation of the variables, and each column
660 * of a line contains the state of the variable associated with that column.
661 * Missing data is handled simply by having two consecutive tab characters,
662 * without any characters in between.
663 *
664 * \subsection fileformats-evidence-example Example
665 *
666 * <pre>
667 * 1 3 2
668 *
669 * 0 0 1
670 * 1 0 1
671 * 1 1
672 * </pre>
673 *
674 * This would correspond to a data set consisting of three observations concerning
675 * the variables with labels 1, 3 and 2; the first observation being
676 * \f$x_1 = 0, x_3 = 0, x_2 = 1\f$, the second observation being
677 * \f$x_1 = 1, x_3 = 0, x_2 = 1\f$, and the third observation being
678 * \f$x_1 = 1, x_2 = 1\f$ (where the state of \f$x_3\f$ is missing).
679 *
680 * \section fileformats-emalg Expectation Maximization (.em) file format
681 *
682 * This section describes the file format of .em files, which are used
683 * to specify a particular EM algorithm. The .em files are complementary
684 * to .fg files; in other words, an .em file without a corresponding .fg
685 * file is useless. Furthermore, one also needs a corresponding .tab file
686 * containing the data used for parameter learning.
687 *
688 * An .em file starts with a line specifying the number of maximization steps,
689 * followed by an empty line. Then, each maximization step is described in a
690 * block, which should satisfy the format described in the next subsection.
691 *
692 * \subsection fileformats-emalg-maximizationstep Maximization Step block format
693 *
694 * A maximization step block of an .em file starts with a single line
695 * describing the number of shared parameters blocks that will follow.
696 * Then, each shared parameters block follows, in the format described in
697 * the next subsection.
698 *
699 * \subsection fileformats-emalg-sharedparameters Shared parameters block format
700 *
701 * A shared parameters block of an .em file starts with a single line
702 * consisting of the name of a ParameterEstimation subclass
703 * and its parameters in the format of a PropertySet. For example:
704 * <pre> CondProbEstimation [target_dim=2,total_dim=4,pseudo_count=1]</pre>
705 * The next line contains the number of factors that share their parameters.
706 * Then, each of these factors is specified on separate lines (possibly
707 * seperated by empty lines), where each line consists of several fields
708 * seperated by a space or a tab character. The first field contains
709 * the index of the factor in the factor graph. The following fields should
710 * contain the variable labels of the variables on which that factor depends,
711 * in a specific ordering. This ordering can be different from the canonical
712 * ordering of the variables used internally in libDAI (which would be sorted
713 * ascendingly according to the variable labels). The ordering of the variables
714 * specifies the implicit ordering of the shared parameters: when iterating
715 * over all shared parameters, the corresponding index of the first variable
716 * changes fastest (in the inner loop), and the corresponding index of the
717 * last variable changes slowest (in the outer loop). By choosing the right
718 * ordering, it is possible to let different factors (depending on different
719 * variables) share parameters in parameter learning using EM. This convention
720 * is similar to the convention used in factor blocks in a factor graph .fg
721 * file (see \ref fileformats-factorgraph-factor).
722 *
723 * \section fileformats-aliases Aliases file format
724 *
725 * An aliases file is basically a list of "macros" and the strings that they
726 * should be substituted with.
727 *
728 * Each line of the aliases file can be either empty, contain a comment
729 * (if the first character is a '#') or contain an alias. In the latter case,
730 * the line should contain a colon; the part before the colon contains the
731 * name of the alias, the part after the colon the string that it should be
732 * substituted with. Any whitespace before and after the colon is ignored.
733 *
734 * For example, the following line would define the alias \c BP_SEQFIX
735 * as a shorthand for "BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]":
736 * <pre>
737 * BP_SEQFIX: BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]
738 * </pre>
739 *
740 * Aliases files can be used to store default options for algorithms.
741 */
742
743 /** \page bibliography Bibliography
744 * \anchor EaG09 \ref EaG09
745 * F. Eaton and Z. Ghahramani (2009):
746 * "Choosing a Variable to Clamp",
747 * <em>Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS 2009)</em> 5:145-152,
748 * http://jmlr.csail.mit.edu/proceedings/papers/v5/eaton09a/eaton09a.pdf
749 *
750 * \anchor EMK06 \ref EMK06
751 * G. Elidan and I. McGraw and D. Koller (2006):
752 * "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing",
753 * <em>Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)</em>,
754 * http://uai.sis.pitt.edu/papers/06/UAI2006_0091.pdf
755 *
756 * \anchor HAK03 \ref HAK03
757 * T. Heskes and C. A. Albers and H. J. Kappen (2003):
758 * "Approximate Inference and Constrained Optimization",
759 * <em>Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03)</em> pp. 313-320,
760 * http://www.snn.ru.nl/reports/Heskes.uai2003.ps.gz
761 *
762 * \anchor KFL01 \ref KFL01
763 * F. R. Kschischang and B. J. Frey and H.-A. Loeliger (2001):
764 * "Factor Graphs and the Sum-Product Algorithm",
765 * <em>IEEE Transactions on Information Theory</em> 47(2):498-519,
766 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=910572
767 *
768 * \anchor KoF09 \ref KoF09
769 * D. Koller and N. Friedman (2009):
770 * <em>Probabilistic Graphical Models - Principles and Techniques</em>,
771 * The MIT Press, Cambridge, Massachusetts, London, England.
772
773 * \anchor Min05 \ref Min05
774 * T. Minka (2005):
775 * "Divergence measures and message passing",
776 * <em>MicroSoft Research Technical Report</em> MSR-TR-2005-173,
777 * http://research.microsoft.com/en-us/um/people/minka/papers/message-passing/minka-divergence.pdf
778 *
779 * \anchor MiQ04 \ref MiQ04
780 * T. Minka and Y. Qi (2004):
781 * "Tree-structured Approximations by Expectation Propagation",
782 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 16,
783 * http://books.nips.cc/papers/files/nips16/NIPS2003_AA25.pdf
784 *
785 * \anchor MoK07 \ref MoK07
786 * J. M. Mooij and H. J. Kappen (2007):
787 * "Loop Corrections for Approximate Inference on Factor Graphs",
788 * <em>Journal of Machine Learning Research</em> 8:1113-1143,
789 * http://www.jmlr.org/papers/volume8/mooij07a/mooij07a.pdf
790 *
791 * \anchor MoK07b \ref MoK07b
792 * J. M. Mooij and H. J. Kappen (2007):
793 * "Sufficient Conditions for Convergence of the Sum-Product Algorithm",
794 * <em>IEEE Transactions on Information Theory</em> 53(12):4422-4437,
795 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4385778
796 *
797 * \anchor MoR05 \ref MoR05
798 * A. Montanari and T. Rizzo (2005):
799 * "How to Compute Loop Corrections to the Bethe Approximation",
800 * <em>Journal of Statistical Mechanics: Theory and Experiment</em> 2005(10)-P10011,
801 * http://stacks.iop.org/1742-5468/2005/P10011
802 *
803 * \anchor StW99 \ref StW99
804 * A. Steger and N. C. Wormald (1999):
805 * "Generating Random Regular Graphs Quickly",
806 * <em>Combinatorics, Probability and Computing</em> Vol 8, Issue 4, pp. 377-396,
807 * http://www.math.uwaterloo.ca/~nwormald/papers/randgen.pdf
808 *
809 * \anchor WiH03 \ref WiH03
810 * W. Wiegerinck and T. Heskes (2003):
811 * "Fractional Belief Propagation",
812 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 15, pp. 438-445,
813 * http://books.nips.cc/papers/files/nips15/LT16.pdf
814 *
815 * \anchor WJW03 \ref WJW03
816 * M. J. Wainwright, T. S. Jaakkola and A. S. Willsky (2003):
817 * "Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching",
818 * <em>9th Workshop on Artificial Intelligence and Statistics</em>,
819 * http://www.eecs.berkeley.edu/~wainwrig/Papers/WJW_AIStat03.pdf
820 *
821 * \anchor YFW05 \ref YFW05
822 * J. S. Yedidia and W. T. Freeman and Y. Weiss (2005):
823 * "Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms",
824 * <em>IEEE Transactions on Information Theory</em> 51(7):2282-2312,
825 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1459044
826 */
827
828
829 /** \page discussion Ideas not worth exploring
830 * \section discuss_extendedgraphs Extended factorgraphs/regiongraphs
831 *
832 * A FactorGraph and a RegionGraph are often equipped with
833 * additional properties for nodes and edges. The code to initialize those
834 * is often quite similar. Maybe one could abstract this, e.g.:
835 * \code
836 * template <typename Node1Properties, typename Node2Properties, typename EdgeProperties>
837 * class ExtFactorGraph : public FactorGraph {
838 * public:
839 * std::vector<Node1Properties> node1Props;
840 * std::vector<Node2Properties> node2Props;
841 * std::vector<std::vector<EdgeProperties> > edgeProps;
842 * // ...
843 * }
844 * \endcode
845 *
846 * Advantages:
847 * - Less code duplication.
848 * - Easier maintainability.
849 * - Easier to write new inference algorithms.
850 *
851 * Disadvantages:
852 * - Cachability may be worse.
853 * - A problem is the case where there are no properties for either type of nodes or for edges.
854 * Maybe this can be solved using specializations, or using variadac template arguments?
855 * Another possible solution would be to define a "class Empty {}", and add some code
856 * that checks for the typeid, comparing it with Empty, and doing something special in that case
857 * (e.g., not allocating memory).
858 * - The main disadvantage of this approach seems to be that it leads to even more entanglement.
859 * Therefore this is probably a bad idea.
860 *
861 * \section discuss_templates Polymorphism by template parameterization
862 *
863 * Instead of polymorphism by inheritance, use polymorphism by template parameterization.
864 * For example, the real reason for introducing the complicated inheritance scheme of dai::InfAlg
865 * was for functions like dai::calcMarginal. Instead, one could use a template function:
866 * \code
867 * template<typename InfAlg>
868 * Factor calcMarginal( const InfAlg &obj, const VarSet &ns, bool reInit );
869 * \endcode
870 * This would assume that the type InfAlg supports certain methods. Ideally, one would use
871 * concepts to define different classes of inference algorithms with different capabilities,
872 * for example the ability to calculate logZ, the ability to calculate marginals, the ability to
873 * calculate bounds, the ability to calculate MAP states, etc. Then, one would use traits
874 * classes in order to be able to query the capabilities of the model. For example, one would be
875 * able to query whether the inference algorithm supports calculation of logZ. Unfortunately,
876 * this is compile-time polymorphism, whereas tests/testdai needs runtime polymorphism.
877 * Therefore this is probably a bad idea.
878 */