b08a3371cad4f854d3a8ba071fb38889784c2cdd

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 */

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 **/

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 git HEAD

42 * \date May 12, 2010, or later

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 */

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 */

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 */

190 /** \page authors Authors

191 * \section authors-authors People who contributed to libDAI

192 *

193 * \verbinclude AUTHORS

194 */

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 * - CImg library (only for building the image segmentation example)

211 *

212 * On Debian/Ubuntu, you can easily install the required packages with a single command:

213 * <pre> apt-get install g++ make doxygen graphviz libboost-dev libboost-graph-dev libboost-program-options-dev libboost-test-dev cimg-dev</pre>

214 * (root permissions needed).

215 *

216 * On Mac OS X (10.4 is known to work), these packages can be installed easily via MacPorts.

217 * If MacPorts is not already installed, install it according to the instructions at http://www.macports.org/.

218 * Then, a simple

219 * <pre> sudo port install gmake boost doxygen graphviz</pre>

220 * should be enough to install everything that is needed.

221 *

222 * On Cygwin, the prebuilt Cygwin package boost-1.33.1-x is known not to work.

223 * You can however obtain the latest boost version (you need at least 1.37.0)

224 * from http://www.boost.org/ and build it as described in the next subsection.

225 *

226 * \subsubsection build-unix-boost Building boost under Cygwin

227 *

228 * - Download the latest boost libraries from http://www.boost.org

229 * - Build the required boost libraries using:

230 * <pre>

231 * ./bootstrap.sh --with-libraries=program_options,math,graph,test --prefix=/boost_root/

232 * ./bjam</pre>

233 * - In order to use dynamic linking, the boost .dll's should be somewhere in the path.

234 * This can be achieved by a command like:

235 * <pre>

236 * export PATH=$PATH:/boost_root/stage/lib</pre>

237 *

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 * - CImg library (only for building the image segmentation example)

265 *

266 * For the regression test, you need:

267 * - GNU diff, GNU sed (can be obtained from http://gnuwin32.sourceforge.net)

268 *

269 * \subsubsection build-windows-boost Building boost under Windows

270 *

271 * Because building boost under Windows is tricky, I provide some guidance here.

272 *

273 * - Download the boost zip file from http://www.boost.org/users/download

274 * and unpack it somewhere.

275 * - Download the bjam executable from http://www.boost.org/users/download

276 * and unpack it somewhere else.

277 * - Download Boost.Build (v2) from http://www.boost.org/docs/tools/build/index.html

278 * and unpack it yet somewhere else.

279 * - Edit the file \c boost-build.jam in the main boost directory to change the

280 * \c BOOST_BUILD directory to the place where you put Boost.Build (use UNIX

281 * / instead of Windows \ in pathnames).

282 * - Copy the \c bjam.exe executable into the main boost directory.

283 * Now if you issue <tt>"bjam --version"</tt> you should get a version and no errors.

284 * Issueing <tt>"bjam --show-libraries"</tt> will show the libraries that will be built.

285 * - The following command builds the boost libraries that are relevant for libDAI:

286 * <pre>

287 * bjam --with-graph --with-math --with-program_options --with-test link=static runtime-link=shared</pre>

288 *

289 * \subsection build-windows-libdai Building libDAI

290 *

291 * To build the source, copy Makefile.WINDOWS to Makefile.conf. Then, edit

292 * Makefile.conf to adapt it to your local setup. Platform independent

293 * build options can be set in Makefile.ALL. Finally, run (from the command line)

294 * <pre> make</pre>

295 * The build includes a regression test, which may take a while to complete.

296 *

297 * If the build is successful, you can test the example program:

298 * <pre> examples\\example tests\\alarm.fg</pre>

299 * or the more extensive test program:

300 * <pre> tests\\testdai --aliases tests\\aliases.conf --filename tests\\alarm.fg --methods JTREE_HUGIN BP_SEQMAX</pre>

301 *

302 *

303 * <hr size="1">

304 * \section build-matlab Building the libDAI MatLab interface

305 *

306 * You need:

307 * - MatLab

308 * - The platform-dependent requirements described above

309 *

310 * First, you need to build the libDAI source as described above for your

311 * platform. By default, the MatLab interface is disabled, so before compiling the

312 * source, you have to enable it in Makefile.ALL by setting

313 * <pre> WITH_MATLAB=true</pre>

314 * Also, you have to configure the MatLab-specific parts of

315 * Makefile.conf to match your system (in particular, the Makefile variables ME,

316 * MATLABDIR and MEX). The MEX file extension depends on your platform; for a

317 * 64-bit linux x86_64 system this would be "ME=.mexa64", for a 32-bit linux x86

318 * system "ME=.mexglx". If you are unsure about your MEX file

319 * extension: it needs to be the same as what the MatLab command "mexext" returns.

320 * The required MEX files are built by issuing

321 * <pre> make</pre>

322 * from the command line. The MatLab interface is much less powerful than using

323 * libDAI from C++. There are two reasons for this: (i) it is boring to write MEX

324 * files; (ii) the large performance penalty paid when large data structures (like

325 * factor graphs) have to be converted between their native C++ data structure to

326 * something that MatLab understands.

327 *

328 * A simple example of how to use the MatLab interface is the following (entered

329 * at the MatLab prompt), which performs exact inference by the junction tree

330 * algorithm and approximate inference by belief propagation on the ALARM network:

331 * <pre> cd path_to_libdai/matlab

332 * [psi] = dai_readfg ('../tests/alarm.fg');

333 * [logZ,q,md,qv,qf] = dai (psi, 'JTREE', '[updates=HUGIN,verbose=0]')

334 * [logZ,q,md,qv,qf] = dai (psi, 'BP', '[updates=SEQMAX,tol=1e-9,maxiter=10000,logdomain=0]')</pre>

335 * where "path_to_libdai" has to be replaced with the directory in which libDAI

336 * was installed. For other algorithms and some default parameters, see the file

337 * tests/aliases.conf.

338 *

339 * <hr size="1">

340 * \section build-doxygen Building the documentation

341 *

342 * Install doxygen, graphviz and a TeX distribution and use

343 * <pre> make doc</pre>

344 * to build the documentation. If the documentation is not clear enough, feel free

345 * to send me an email (or even better, to improve the documentation and send a patch!).

346 * The documentation can also be browsed online at http://www.libdai.org.

347 */

350 /** \page changelog Change Log

351 * \verbinclude ChangeLog

352 */

355 /** \page terminology Terminology and conventions

356 *

357 * \section terminology-graphicalmodels Graphical models

358 *

359 * Commonly used graphical models are Bayesian networks and Markov random fields.

360 * In libDAI, both types of graphical models are represented by a slightly more

361 * general type of graphical model: a factor graph [\ref KFL01].

362 *

363 * An example of a Bayesian network is:

364 * \dot

365 * digraph bayesnet {

366 * size="1,1";

367 * x0 [label="0"];

368 * x1 [label="1"];

369 * x2 [label="2"];

370 * x3 [label="3"];

371 * x4 [label="4"];

372 * x0 -> x1;

373 * x0 -> x2;

374 * x1 -> x3;

375 * x1 -> x4;

376 * x2 -> x4;

377 * }

378 * \enddot

379 * The probability distribution of a Bayesian network factorizes as:

380 * \f[ P(\mathbf{x}) = \prod_{i\in\mathcal{V}} P(x_i \,|\, x_{\mathrm{pa}(i)}) \f]

381 * where \f$\mathrm{pa}(i)\f$ are the parents of node \a i in a DAG.

382 *

383 * The same probability distribution can be represented as a Markov random field:

384 * \dot

385 * graph mrf {

386 * size="1.5,1.5";

387 * x0 [label="0"];

388 * x1 [label="1"];

389 * x2 [label="2"];

390 * x3 [label="3"];

391 * x4 [label="4"];

392 * x0 -- x1;

393 * x0 -- x2;

394 * x1 -- x2;

395 * x1 -- x3;

396 * x1 -- x4;

397 * x2 -- x4;

398 * }

399 * \enddot

400 *

401 * The probability distribution of a Markov random field factorizes as:

402 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{C\in\mathcal{C}} \psi_C(x_C) \f]

403 * where \f$ \mathcal{C} \f$ are the cliques of an undirected graph,

404 * \f$ \psi_C(x_C) \f$ are "potentials" or "compatibility functions", and

405 * \f$ Z \f$ is the partition sum which properly normalizes the probability

406 * distribution.

407 *

408 * Finally, the same probability distribution can be represented as a factor graph:

409 * \dot

410 * graph factorgraph {

411 * size="1.8,1";

412 * x0 [label="0"];

413 * x1 [label="1"];

414 * x2 [label="2"];

415 * x3 [label="3"];

416 * x4 [label="4"];

417 * f01 [shape="box",label=""];

418 * f02 [shape="box",label=""];

419 * f13 [shape="box",label=""];

420 * f124 [shape="box",label=""];

421 * x0 -- f01;

422 * x1 -- f01;

423 * x0 -- f02;

424 * x2 -- f02;

425 * x1 -- f13;

426 * x3 -- f13;

427 * x1 -- f124;

428 * x2 -- f124;

429 * x4 -- f124;

430 * }

431 * \enddot

432 *

433 * The probability distribution of a factor graph factorizes as:

434 * \f[ P(\mathbf{x}) = \frac{1}{Z} \prod_{I\in \mathcal{F}} f_I(x_I) \f]

435 * where \f$ \mathcal{F} \f$ are the factor nodes of a factor graph (a

436 * bipartite graph consisting of variable nodes and factor nodes),

437 * \f$ f_I(x_I) \f$ are the factors, and \f$ Z \f$ is the partition sum

438 * which properly normalizes the probability distribution.

439 *

440 * Looking at the expressions for the joint probability distributions,

441 * it is obvious that Bayesian networks and Markov random fields can

442 * both be easily represented as factor graphs. Factor graphs most

443 * naturally express the factorization structure of a probability

444 * distribution, and hence are a convenient representation for approximate

445 * inference algorithms, which all try to exploit this factorization.

446 * This is why libDAI uses a factor graph as representation of a

447 * graphical model, implemented in the dai::FactorGraph class.

448 *

449 * \section terminology-inference Inference tasks

450 *

451 * Given a factor graph, specified by the variable nodes \f$\{x_i\}_{i\in\mathcal{V}}\f$

452 * the factor nodes \f$ \mathcal{F} \f$, the graph structure, and the factors

453 * \f$\{f_I(x_I)\}_{I\in\mathcal{F}}\f$, the following tasks are important:

454 *

455 * - Calculating the partition sum:

456 * \f[ Z = \sum_{\mathbf{x}_{\mathcal{V}}} \prod_{I \in \mathcal{F}} f_I(x_I) \f]

457 * - Calculating the marginal distribution of a subset of variables

458 * \f$\{x_i\}_{i\in A}\f$:

459 * \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]

460 * - Calculating the MAP state which has the maximum probability mass:

461 * \f[ \mathrm{argmax}_{\mathbf{x}}\,\prod_{I\in\mathcal{F}} f_I(x_I) \f]

462 *

463 * libDAI offers several inference algorithms, which solve (a subset of) these tasks either

464 * approximately or exactly, for factor graphs with discrete variables. The following

465 * algorithms are implemented:

466 *

467 * Exact inference:

468 * - Brute force enumeration: dai::ExactInf

469 * - Junction-tree method: dai::JTree

470 *

471 * Approximate inference:

472 * - Mean Field: dai::MF

473 * - (Loopy) Belief Propagation: dai::BP [\ref KFL01]

474 * - Fractional Belief Propagation: dai::FBP [\ref WiH03]

475 * - Tree-Reweighted Belief Propagation: dai::TRWBP [\ref WJW03]

476 * - Tree Expectation Propagation: dai::TreeEP [\ref MiQ04]

477 * - Generalized Belief Propagation: dai::HAK [\ref YFW05]

478 * - Double-loop GBP: dai::HAK [\ref HAK03]

479 * - Loop Corrected Belief Propagation: dai::MR [\ref MoR05] and dai::LC [\ref MoK07]

480 * - Gibbs sampling: dai::Gibbs

481 * - Conditioned Belief Propagation: dai::CBP [\ref EaG09]

482 *

483 * Not all inference tasks are implemented by each method: calculating MAP states

484 * is only possible with dai::JTree and dai::BP, calculating partition sums is

485 * not possible with dai::MR, dai::LC and dai::Gibbs.

486 *

487 * \section terminology-learning Parameter learning

488 *

489 * In addition, libDAI supports parameter learning of conditional probability

490 * tables by Expectation Maximization (or Maximum Likelihood, if there is no

491 * missing data). This is implemented in dai::EMAlg.

492 *

493 * \section terminology-variables-states Variables and states

494 *

495 * Linear states are a concept that is used often in libDAI, for example for storing

496 * and accessing factors, which are functions mapping from states of a set of variables

497 * to the real numbers. Internally, a factor is stored as an array, and the array index

498 * of an entry corresponds with the linear state of the set of variables. Below we will

499 * define variables, states and linear states of (sets of) variables.

500 *

501 * \subsection terminology-variables Variables

502 *

503 * Each (random) \a variable has a unique identifier, its \a label (which has

504 * a non-negative integer value). If two variables have the same

505 * label, they are considered as identical. A variable can take on a finite

506 * number of different values or \a states.

507 *

508 * We use the following notational conventions. The discrete

509 * random variable with label \f$l\f$ is denoted as \f$x_l\f$, and the number

510 * of possible values of this variable as \f$S_{x_l}\f$ or simply \f$S_l\f$.

511 * The set of possible values of variable \f$x_l\f$ is denoted

512 * \f$X_l := \{0,1,\dots,S_l-1\}\f$ and called its \a state \a space.

513 *

514 * \subsection terminology-variable-sets Sets of variables and the canonical ordering

515 *

516 * Let \f$A := \{x_{l_1},x_{l_2},\dots,x_{l_n}\}\f$ be a set of variables.

517 *

518 * The \a canonical \a ordering of the variables in \a A is induced by their labels.

519 * That is: if \f$l_1 < l_2\f$, then \f$x_{l_1}\f$ occurs before \f$x_{l_2}\f$ in the

520 * canonical ordering. Below, we will assume that \f$(l_i)_{i=1}^n\f$ is

521 * ordered according to the canonical ordering, i.e., \f$l_1 < l_2 < \dots < l_n\f$.

522 *

523 * \subsection terminology-variable-states States and linear states of sets of variables

524 *

525 * A \a state of the variables in \a A refers to a joint assignment of the

526 * variables, or in other words, to an element of the Cartesian product

527 * \f$ \prod_{i=1}^n X_{l_i}\f$ of the state spaces of the variables in \a A.

528 * Note that a state can also be interpreted as a mapping from variables (or

529 * variable labels) to the natural numbers, which assigns to a variable (or its

530 * label) the corresponding state of the variable.

531 *

532 * A state of \a n variables can be represented as an n-tuple of

533 * non-negative integers: \f$(s_1,s_2,\dots,s_n)\f$ corresponds to the

534 * joint assignment \f$x_{l_1} = s_1, \dots, x_{l_n} = s_n\f$.

535 * Alternatively, a state can be represented compactly as one non-negative integer;

536 * this representation is called a \a linear \a state. The linear state

537 * \a s corresponding to the state \f$(s_1,s_2,\dots,s_n)\f$ would be:

538 * \f[

539 * s := \sum_{i=1}^n s_i \prod_{j=1}^{i-1} S_{l_j}

540 * = 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}}.

541 * \f]

542 *

543 * Vice versa, given a linear state \a s for the variables \a A, the

544 * corresponding state \f$s_i\f$ of the \a i 'th variable \f$x_{l_i}\f$ (according to

545 * the canonical ordering of the variables in \a A) is given by

546 * \f[

547 * 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.

548 * \f]

549 *

550 * Finally, the \a number \a of \a states of the set of variables \a A is simply the

551 * number of different joint assignments of the variables, that is, \f$\prod_{i=1}^n S_{l_i}\f$.

552 */

555 /** \page fileformats libDAI file formats

556 *

557 * \section fileformats-factorgraph Factor graph (.fg) file format

558 *

559 * This section describes the .fg file format used in libDAI to store factor graphs.

560 * Markov Random Fields are special cases of factor graphs, as are Bayesian

561 * networks. A factor graph can be specified as follows: for each factor, one has

562 * to specify which variables occur in the factor, what their respective

563 * cardinalities (i.e., number of possible values) are, and a table listing all

564 * the values of that factor for all possible configurations of these variables.

565 *

566 * A .fg file is not much more than that. It starts with a line containing the

567 * number of factors in that graph, followed by an empty line. Then all factors

568 * are specified, using one block for each factor, where the blocks are seperated

569 * by empty lines. Each variable occurring in the factor graph has a unique

570 * identifier, its label (which should be a nonnegative integer). Comment lines

571 * which start with # are ignored.

572 *

573 * \subsection fileformats-factorgraph-factor Factor block format

574 *

575 * Each block describing a factor starts with a line containing the number of

576 * variables in that factor. The second line contains the labels of these

577 * variables, seperated by spaces (labels are nonnegative integers and to avoid

578 * confusion, it is suggested to start counting at 0). The third line contains

579 * the number of possible values of each of these variables, also seperated by

580 * spaces. Note that there is some redundancy here, since if a variable appears

581 * in more than one factor, the cardinality of that variable appears several

582 * times in the .fg file; obviously, these cardinalities should be consistent.

583 * The fourth line contains the number of nonzero entries

584 * in the factor table. The rest of the lines contain these nonzero entries;

585 * each line consists of a table index, followed by white-space, followed by the

586 * value corresponding to that table index. The most difficult part is getting

587 * the indexing right. The convention that is used is that the left-most

588 * variables cycle through their values the fastest (similar to MatLab indexing

589 * of multidimensional arrays).

590 *

591 * \subsubsection fileformats-factorgraph-factor-example Example

592 *

593 * An example block describing one factor is:

594 *

595 * <pre>

596 * 3

597 * 4 8 7

598 * 3 2 2

599 * 11

600 * 0 0.1

601 * 1 3.5

602 * 2 2.8

603 * 3 6.3

604 * 4 8.4

605 * 6 7.4

606 * 7 2.4

607 * 8 8.9

608 * 9 1.3

609 * 10 1.6

610 * 11 2.6

611 * </pre>

612 *

613 * which corresponds to the following factor:

614 *

615 * \f[

616 * \begin{array}{ccc|c}

617 * x_4 & x_8 & x_7 & \mbox{value}\\

618 * \hline

619 * 0 & 0 & 0 & 0.1\\

620 * 1 & 0 & 0 & 3.5\\

621 * 2 & 0 & 0 & 2.8\\

622 * 0 & 1 & 0 & 6.3\\

623 * 1 & 1 & 0 & 8.4\\

624 * 2 & 1 & 0 & 0.0\\

625 * 0 & 0 & 1 & 7.4\\

626 * 1 & 0 & 1 & 2.4\\

627 * 2 & 0 & 1 & 8.9\\

628 * 0 & 1 & 1 & 1.3\\

629 * 1 & 1 & 1 & 1.6\\

630 * 2 & 1 & 1 & 2.6

631 * \end{array}

632 * \f]

633 *

634 * Note that the value of \f$x_4\f$ changes fastest, followed by that of \f$x_8\f$, and \f$x_7\f$

635 * varies the slowest, corresponding to the second line of the block ("4 8 7").

636 * Further, \f$x_4\f$ can take on three values, and \f$x_8\f$ and \f$x_7\f$ each have two possible

637 * values, as described in the third line of the block ("3 2 2"). The table

638 * contains 11 non-zero entries (all except for the fifth entry). Note that the

639 * eleventh and twelveth entries are interchanged.

640 *

641 * A final note: the internal representation in libDAI of the factor above is

642 * different, because the variables are ordered according to their indices

643 * (i.e., the ordering would be \f$x_4 x_7 x_8\f$) and the values of the table are

644 * stored accordingly, with the variable having the smallest index changing

645 * fastest:

646 *

647 * \f[

648 * \begin{array}{ccc|c}

649 * x_4 & x_7 & x_8 & \mbox{value}\\

650 * \hline

651 * 0 & 0 & 0 & 0.1\\

652 * 1 & 0 & 0 & 3.5\\

653 * 2 & 0 & 0 & 2.8\\

654 * 0 & 1 & 0 & 7.4\\

655 * 1 & 1 & 0 & 2.4\\

656 * 2 & 1 & 0 & 8.9\\

657 * 0 & 0 & 1 & 6.3\\

658 * 1 & 0 & 1 & 8.4\\

659 * 2 & 0 & 1 & 0.0\\

660 * 0 & 1 & 1 & 1.3\\

661 * 1 & 1 & 1 & 1.6\\

662 * 2 & 1 & 1 & 2.6

663 * \end{array}

664 * \f]

665 *

666 *

667 * \section fileformats-evidence Evidence (.tab) file format

668 *

669 * This section describes the .tab fileformat used in libDAI to store "evidence",

670 * i.e., a data set consisting of multiple samples, where each sample is the

671 * observed joint state of some variables.

672 *

673 * A .tab file is a tabular data file, consisting of a header line, followed by

674 * an empty line, followed by the data points, with one line for each data point.

675 * Each line (apart from the empty one) should have the same number of columns,

676 * where columns are separated by one tab character. Each column corresponds to

677 * a variable. The header line consists of the variable labels (corresponding to

678 * dai::Var::label()). The other lines are observed joint states of the variables, i.e.,

679 * each line corresponds to a joint observation of the variables, and each column

680 * of a line contains the state of the variable associated with that column.

681 * Missing data is handled simply by having two consecutive tab characters,

682 * without any characters in between.

683 *

684 * \subsection fileformats-evidence-example Example

685 *

686 * <pre>

687 * 1 3 2

688 *

689 * 0 0 1

690 * 1 0 1

691 * 1 1

692 * </pre>

693 *

694 * This would correspond to a data set consisting of three observations concerning

695 * the variables with labels 1, 3 and 2; the first observation being

696 * \f$x_1 = 0, x_3 = 0, x_2 = 1\f$, the second observation being

697 * \f$x_1 = 1, x_3 = 0, x_2 = 1\f$, and the third observation being

698 * \f$x_1 = 1, x_2 = 1\f$ (where the state of \f$x_3\f$ is missing).

699 *

700 * \section fileformats-emalg Expectation Maximization (.em) file format

701 *

702 * This section describes the file format of .em files, which are used

703 * to specify a particular EM algorithm. The .em files are complementary

704 * to .fg files; in other words, an .em file without a corresponding .fg

705 * file is useless. Furthermore, one also needs a corresponding .tab file

706 * containing the data used for parameter learning.

707 *

708 * An .em file starts with a line specifying the number of maximization steps,

709 * followed by an empty line. Then, each maximization step is described in a

710 * block, which should satisfy the format described in the next subsection.

711 *

712 * \subsection fileformats-emalg-maximizationstep Maximization Step block format

713 *

714 * A maximization step block of an .em file starts with a single line

715 * describing the number of shared parameters blocks that will follow.

716 * Then, each shared parameters block follows, in the format described in

717 * the next subsection.

718 *

719 * \subsection fileformats-emalg-sharedparameters Shared parameters block format

720 *

721 * A shared parameters block of an .em file starts with a single line

722 * consisting of the name of a ParameterEstimation subclass

723 * and its parameters in the format of a PropertySet. For example:

724 * <pre> CondProbEstimation [target_dim=2,total_dim=4,pseudo_count=1]</pre>

725 * The next line contains the number of factors that share their parameters.

726 * Then, each of these factors is specified on separate lines (possibly

727 * seperated by empty lines), where each line consists of several fields

728 * seperated by a space or a tab character. The first field contains

729 * the index of the factor in the factor graph. The following fields should

730 * contain the variable labels of the variables on which that factor depends,

731 * in a specific ordering. This ordering can be different from the canonical

732 * ordering of the variables used internally in libDAI (which would be sorted

733 * ascendingly according to the variable labels). The ordering of the variables

734 * specifies the implicit ordering of the shared parameters: when iterating

735 * over all shared parameters, the corresponding index of the first variable

736 * changes fastest (in the inner loop), and the corresponding index of the

737 * last variable changes slowest (in the outer loop). By choosing the right

738 * ordering, it is possible to let different factors (depending on different

739 * variables) share parameters in parameter learning using EM. This convention

740 * is similar to the convention used in factor blocks in a factor graph .fg

741 * file (see \ref fileformats-factorgraph-factor).

742 *

743 * \section fileformats-aliases Aliases file format

744 *

745 * An aliases file is basically a list of "macros" and the strings that they

746 * should be substituted with.

747 *

748 * Each line of the aliases file can be either empty, contain a comment

749 * (if the first character is a '#') or contain an alias. In the latter case,

750 * the line should contain a colon; the part before the colon contains the

751 * name of the alias, the part after the colon the string that it should be

752 * substituted with. Any whitespace before and after the colon is ignored.

753 *

754 * For example, the following line would define the alias \c BP_SEQFIX

755 * as a shorthand for "BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]":

756 * <pre>

757 * BP_SEQFIX: BP[updates=SEQFIX,tol=1e-9,maxiter=10000,logdomain=0]

758 * </pre>

759 *

760 * Aliases files can be used to store default options for algorithms.

761 */

763 /** \page bibliography Bibliography

764 * \anchor EaG09 \ref EaG09

765 * F. Eaton and Z. Ghahramani (2009):

766 * "Choosing a Variable to Clamp",

767 * <em>Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS 2009)</em> 5:145-152,

768 * http://jmlr.csail.mit.edu/proceedings/papers/v5/eaton09a/eaton09a.pdf

769 *

770 * \anchor EMK06 \ref EMK06

771 * G. Elidan and I. McGraw and D. Koller (2006):

772 * "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing",

773 * <em>Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)</em>,

774 * http://uai.sis.pitt.edu/papers/06/UAI2006_0091.pdf

775 *

776 * \anchor HAK03 \ref HAK03

777 * T. Heskes and C. A. Albers and H. J. Kappen (2003):

778 * "Approximate Inference and Constrained Optimization",

779 * <em>Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03)</em> pp. 313-320,

780 * http://www.snn.ru.nl/reports/Heskes.uai2003.ps.gz

781 *

782 * \anchor KFL01 \ref KFL01

783 * F. R. Kschischang and B. J. Frey and H.-A. Loeliger (2001):

784 * "Factor Graphs and the Sum-Product Algorithm",

785 * <em>IEEE Transactions on Information Theory</em> 47(2):498-519,

786 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=910572

787 *

788 * \anchor KoF09 \ref KoF09

789 * D. Koller and N. Friedman (2009):

790 * <em>Probabilistic Graphical Models - Principles and Techniques</em>,

791 * The MIT Press, Cambridge, Massachusetts, London, England.

793 * \anchor Min05 \ref Min05

794 * T. Minka (2005):

795 * "Divergence measures and message passing",

796 * <em>MicroSoft Research Technical Report</em> MSR-TR-2005-173,

797 * http://research.microsoft.com/en-us/um/people/minka/papers/message-passing/minka-divergence.pdf

798 *

799 * \anchor MiQ04 \ref MiQ04

800 * T. Minka and Y. Qi (2004):

801 * "Tree-structured Approximations by Expectation Propagation",

802 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 16,

803 * http://books.nips.cc/papers/files/nips16/NIPS2003_AA25.pdf

804 *

805 * \anchor MoK07 \ref MoK07

806 * J. M. Mooij and H. J. Kappen (2007):

807 * "Loop Corrections for Approximate Inference on Factor Graphs",

808 * <em>Journal of Machine Learning Research</em> 8:1113-1143,

809 * http://www.jmlr.org/papers/volume8/mooij07a/mooij07a.pdf

810 *

811 * \anchor MoK07b \ref MoK07b

812 * J. M. Mooij and H. J. Kappen (2007):

813 * "Sufficient Conditions for Convergence of the Sum-Product Algorithm",

814 * <em>IEEE Transactions on Information Theory</em> 53(12):4422-4437,

815 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4385778

816 *

817 * \anchor Moo08 \ref Moo08

818 * J. M. Mooij (2008):

819 * "Understanding and Improving Belief Propagation",

820 * <em>Ph.D. Thesis</em> Radboud University Nijmegen

821 * http://webdoc.ubn.ru.nl/mono/m/mooij_j/undeanimb.pdf

822 *

823 * \anchor MoR05 \ref MoR05

824 * A. Montanari and T. Rizzo (2005):

825 * "How to Compute Loop Corrections to the Bethe Approximation",

826 * <em>Journal of Statistical Mechanics: Theory and Experiment</em> 2005(10)-P10011,

827 * http://stacks.iop.org/1742-5468/2005/P10011

828 *

829 * \anchor StW99 \ref StW99

830 * A. Steger and N. C. Wormald (1999):

831 * "Generating Random Regular Graphs Quickly",

832 * <em>Combinatorics, Probability and Computing</em> Vol 8, Issue 4, pp. 377-396,

833 * http://www.math.uwaterloo.ca/~nwormald/papers/randgen.pdf

834 *

835 * \anchor WiH03 \ref WiH03

836 * W. Wiegerinck and T. Heskes (2003):

837 * "Fractional Belief Propagation",

838 * <em>Advances in Neural Information Processing Systems</em> (NIPS) 15, pp. 438-445,

839 * http://books.nips.cc/papers/files/nips15/LT16.pdf

840 *

841 * \anchor WJW03 \ref WJW03

842 * M. J. Wainwright, T. S. Jaakkola and A. S. Willsky (2003):

843 * "Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching",

844 * <em>9th Workshop on Artificial Intelligence and Statistics</em>,

845 * http://www.eecs.berkeley.edu/~wainwrig/Papers/WJW_AIStat03.pdf

846 *

847 * \anchor YFW05 \ref YFW05

848 * J. S. Yedidia and W. T. Freeman and Y. Weiss (2005):

849 * "Constructing Free-Energy Approximations and Generalized Belief Propagation Algorithms",

850 * <em>IEEE Transactions on Information Theory</em> 51(7):2282-2312,

851 * http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1459044

852 */

855 /** \page discussion Ideas not worth exploring

856 * \section discuss_extendedgraphs Extended factorgraphs/regiongraphs

857 *

858 * A FactorGraph and a RegionGraph are often equipped with

859 * additional properties for nodes and edges. The code to initialize those

860 * is often quite similar. Maybe one could abstract this, e.g.:

861 * \code

862 * template <typename Node1Properties, typename Node2Properties, typename EdgeProperties>

863 * class ExtFactorGraph : public FactorGraph {

864 * public:

865 * std::vector<Node1Properties> node1Props;

866 * std::vector<Node2Properties> node2Props;

867 * std::vector<std::vector<EdgeProperties> > edgeProps;

868 * // ...

869 * }

870 * \endcode

871 *

872 * Advantages:

873 * - Less code duplication.

874 * - Easier maintainability.

875 * - Easier to write new inference algorithms.

876 *

877 * Disadvantages:

878 * - Cachability may be worse.

879 * - A problem is the case where there are no properties for either type of nodes or for edges.

880 * Maybe this can be solved using specializations, or using variadac template arguments?

881 * Another possible solution would be to define a "class Empty {}", and add some code

882 * that checks for the typeid, comparing it with Empty, and doing something special in that case

883 * (e.g., not allocating memory).

884 * - The main disadvantage of this approach seems to be that it leads to even more entanglement.

885 * Therefore this is probably a bad idea.

886 *

887 * \section discuss_templates Polymorphism by template parameterization

888 *

889 * Instead of polymorphism by inheritance, use polymorphism by template parameterization.

890 * For example, the real reason for introducing the complicated inheritance scheme of dai::InfAlg

891 * was for functions like dai::calcMarginal. Instead, one could use a template function:

892 * \code

893 * template<typename InfAlg>

894 * Factor calcMarginal( const InfAlg &obj, const VarSet &ns, bool reInit );

895 * \endcode

896 * This would assume that the type InfAlg supports certain methods. Ideally, one would use

897 * concepts to define different classes of inference algorithms with different capabilities,

898 * for example the ability to calculate logZ, the ability to calculate marginals, the ability to

899 * calculate bounds, the ability to calculate MAP states, etc. Then, one would use traits

900 * classes in order to be able to query the capabilities of the model. For example, one would be

901 * able to query whether the inference algorithm supports calculation of logZ. Unfortunately,

902 * this is compile-time polymorphism, whereas tests/testdai needs runtime polymorphism.

903 * Therefore this is probably a bad idea.

904 */