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 * - Decimation algorithm.

82 *

83 * These inference methods can be used to calculate partition sums, marginals

84 * over subsets of variables, and MAP states (the joint state of variables that

85 * has maximum probability).

86 *

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

88 * tables by Expectation Maximization.

89 *

90 * \section limitations Limitations

91 * libDAI is not intended to be a complete package for approximate inference.

92 * Instead, it should be considered as an "inference engine", providing

93 * various inference methods. In particular, it contains no GUI, currently

94 * only supports its own file format for input and output (although support

95 * for standard file formats may be added later), and provides very limited

96 * visualization functionalities. The only learning method supported currently

97 * is Expectation Maximization (or Maximum Likelihood if no data is missing)

98 * for learning factor parameters.

99 *

100 * \section rationale Rationale

101 *

102 * In my opinion, the lack of open source "reference" implementations hampers

103 * progress in research on approximate inference. Methods differ widely in terms

104 * of quality and performance characteristics, which also depend in different

105 * ways on various properties of the graphical models. Finding the best

106 * approximate inference method for a particular application therefore often

107 * requires empirical comparisons. However, implementing and debugging these

108 * methods takes a lot of time which could otherwise be spent on research. I hope

109 * that this code will aid researchers to be able to easily compare various

110 * (existing as well as new) approximate inference methods, in this way

111 * accelerating research and stimulating real-world applications of approximate

112 * inference.

113 *

114 * \section language Language

115 * Because libDAI is implemented in C++, it is very fast compared with

116 * implementations in MatLab (a factor 1000 faster is not uncommon).

117 * libDAI does provide a (limited) MatLab interface for easy integration with MatLab.

118 * It also provides a command line interface and experimental python and octave

119 * interfaces (thanks to Patrick Pletscher).

120 *

121 * \section compatibility Compatibility

122 *

123 * The code has been developed under Debian GNU/Linux with the GCC compiler suite.

124 * libDAI compiles successfully with g++ versions 3.4 up to 4.4.

125 *

126 * libDAI has also been successfully compiled with MS Visual Studio 2008 under Windows

127 * (but not all build targets are supported yet) and with Cygwin under Windows.

128 *

129 * Finally, libDAI has been compiled successfully on MacOS X.

130 *

131 * \section download Downloading libDAI

132 * The libDAI sources and documentation can be downloaded from the libDAI website:

133 * http://www.libdai.org.

134 *

135 * \section support Mailing list

136 * The Google group "libDAI" (http://groups.google.com/group/libdai)

137 * can be used for getting support and discussing development issues.

138 */

141 /** \page license License

142 * <hr size="1">

143 * \section license-license License

144 *

145 * libDAI is free software; you can redistribute it and/or modify

146 * it under the terms of the GNU General Public License as published by

147 * the Free Software Foundation; either version 2 of the License, or

148 * (at your option) any later version.

149 *

150 * libDAI is distributed in the hope that it will be useful,

151 * but WITHOUT ANY WARRANTY; without even the implied warranty of

152 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

153 * GNU General Public License for more details.

154 *

155 * <hr size="1">

156 * \section license-gpl GNU General Public License version 2

157 *

158 * \verbinclude COPYING

159 */

162 /** \page citations Citing libDAI

163 * <hr size="1">

164 * \section citations-citations Citing libDAI

165 *

166 * If you write a scientific paper describing research that made substantive use

167 * of this program, please cite the software appropriately, by mentioning the

168 * fashion in which this software was used, including the version number.

169 *

170 * An appropriate citation would be:\n

171 *

172 * Joris M. Mooij et al. (2010) "libDAI 0.2.5: A free/open source C++ library for Discrete

173 * Approximate Inference", http://www.libdai.org

174 *

175 * or in BiBTeX format:

176 *

177 * <pre>

178 * \@misc{mooij2010libdai,

179 * author = "Joris M. Mooij et al.",

180 * title = "lib{DAI} 0.2.5: A free/open source {C}++ library for {D}iscrete {A}pproximate {I}nference",

181 * howpublished = "http://www.libdai.org/",

182 * year = 2010

183 * }

184 * </pre>

185 *

186 * Moreover, as a personal note, I would appreciate it to be informed about any

187 * publications using libDAI at joris dot mooij at libdai dot org.

188 */

191 /** \page authors Authors

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

193 *

194 * \verbinclude AUTHORS

195 */

198 /** \page build Building libDAI

199 * <hr size="1">

200 * \section build-unix Building libDAI under UNIX variants (Linux / Cygwin / Mac OS X)

201 *

202 * \subsection build-unix-preparations Preparations

203 *

204 * You need:

205 * - a recent version of gcc (at least version 3.4)

206 * - GNU make

207 * - recent boost C++ libraries (at least version 1.37; however,

208 * version 1.37 shipped with Ubuntu 9.04 is known not to work)

209 * - doxygen (only for building the documentation)

210 * - graphviz (only for using some of the libDAI command line utilities)

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

212 *

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

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

215 * (root permissions needed).

216 *

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

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

219 * Then, a simple

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

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

222 *

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

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

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

226 *

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

228 *

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

230 * - Build the required boost libraries using:

231 * <pre>

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

233 * ./bjam</pre>

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

235 * This can be achieved by a command like:

236 * <pre>

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

238 *

239 *

240 * \subsection build-unix-libdai Building libDAI

241 *

242 * To build the libDAI source, first copy a template Makefile.* to Makefile.conf

243 * (for example, copy Makefile.LINUX to Makefile.conf if you use GNU/Linux).

244 * Then, edit the Makefile.conf template to adapt it to your local setup.

245 * Especially directories may differ from system to system. Platform independent

246 * build options can be set in Makefile.ALL. Finally, run

247 * <pre> make</pre>

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

249 *

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

251 * <pre> examples/example tests/alarm.fg</pre>

252 * or the more extensive test program:

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

254 *

255 *

256 * <hr size="1">

257 * \section build-windows Building libDAI under Windows

258 *

259 * \subsection build-windows-preparations Preparations

260 *

261 * You need:

262 * - A recent version of MicroSoft Visual Studio (2008 is known to work)

263 * - recent boost C++ libraries (version 1.37 or higher)

264 * - GNU make (can be obtained from http://gnuwin32.sourceforge.net)

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

266 *

267 * For the regression test, you need:

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

269 *

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

271 *

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

273 *

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

275 * and unpack it somewhere.

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

277 * and unpack it somewhere else.

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

279 * and unpack it yet somewhere else.

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

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

282 * / instead of Windows \ in pathnames).

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

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

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

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

287 * <pre>

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

289 *

290 * \subsection build-windows-libdai Building libDAI

291 *

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

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

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

295 * <pre> make</pre>

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

297 *

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

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

300 * or the more extensive test program:

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

302 *

303 *

304 * <hr size="1">

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

306 *

307 * You need:

308 * - MatLab

309 * - The platform-dependent requirements described above

310 *

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

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

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

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

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

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

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

318 * 64-bit linux x86_64 system this would be "ME=.mexa64", for a 32-bit linux x86

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

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

321 * The required MEX files are built by issuing

322 * <pre> make</pre>

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

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

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

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

327 * something that MatLab understands.

328 *

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

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

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

332 * <pre> cd path_to_libdai/matlab

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

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

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

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

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

338 * tests/aliases.conf.

339 *

340 * <hr size="1">

341 * \section build-doxygen Building the documentation

342 *

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

344 * <pre> make doc</pre>

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

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

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

348 */

351 /** \page changelog Change Log

352 * \verbinclude ChangeLog

353 */

356 /** \page terminology Terminology and conventions

357 *

358 * \section terminology-graphicalmodels Graphical models

359 *

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

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

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

363 *

364 * An example of a Bayesian network is:

365 * \dot

366 * digraph bayesnet {

367 * size="1,1";

368 * x0 [label="0"];

369 * x1 [label="1"];

370 * x2 [label="2"];

371 * x3 [label="3"];

372 * x4 [label="4"];

373 * x0 -> x1;

374 * x0 -> x2;

375 * x1 -> x3;

376 * x1 -> x4;

377 * x2 -> x4;

378 * }

379 * \enddot

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

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

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

383 *

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

385 * \dot

386 * graph mrf {

387 * size="1.5,1.5";

388 * x0 [label="0"];

389 * x1 [label="1"];

390 * x2 [label="2"];

391 * x3 [label="3"];

392 * x4 [label="4"];

393 * x0 -- x1;

394 * x0 -- x2;

395 * x1 -- x2;

396 * x1 -- x3;

397 * x1 -- x4;

398 * x2 -- x4;

399 * }

400 * \enddot

401 *

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

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

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

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

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

407 * distribution.

408 *

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

410 * \dot

411 * graph factorgraph {

412 * size="1.8,1";

413 * x0 [label="0"];

414 * x1 [label="1"];

415 * x2 [label="2"];

416 * x3 [label="3"];

417 * x4 [label="4"];

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

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

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

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

422 * x0 -- f01;

423 * x1 -- f01;

424 * x0 -- f02;

425 * x2 -- f02;

426 * x1 -- f13;

427 * x3 -- f13;

428 * x1 -- f124;

429 * x2 -- f124;

430 * x4 -- f124;

431 * }

432 * \enddot

433 *

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

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

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

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

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

439 * which properly normalizes the probability distribution.

440 *

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

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

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

444 * naturally express the factorization structure of a probability

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

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

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

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

449 *

450 * \section terminology-inference Inference tasks

451 *

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

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

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

455 *

456 * - Calculating the partition sum:

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

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

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

460 * \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]

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

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

463 *

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

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

466 * algorithms are implemented:

467 *

468 * Exact inference:

469 * - Brute force enumeration: dai::ExactInf

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

471 *

472 * Approximate inference:

473 * - Mean Field: dai::MF

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

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

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

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

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

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

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

481 * - Gibbs sampling: dai::Gibbs

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

483 * - Decimation algorithm: dai::DECMAP

484 *

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

486 * is only possible with dai::JTree, dai::BP and dai::DECMAP; calculating partition sums is

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

488 *

489 * \section terminology-learning Parameter learning

490 *

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

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

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

494 *

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

496 *

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

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

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

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

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

502 *

503 * \subsection terminology-variables Variables

504 *

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

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

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

508 * number of different values or \a states.

509 *

510 * We use the following notational conventions. The discrete

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

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

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

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

515 *

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

517 *

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

519 *

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

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

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

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

524 *

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

526 *

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

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

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

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

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

532 * label) the corresponding state of the variable.

533 *

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

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

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

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

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

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

540 * \f[

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

542 * = 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}}.

543 * \f]

544 *

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

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

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

548 * \f[

549 * 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.

550 * \f]

551 *

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

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

554 */

557 /** \page fileformats libDAI file formats

558 *

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

560 *

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

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

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

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

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

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

567 *

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

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

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

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

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

573 * which start with # are ignored.

574 *

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

576 *

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

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

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

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

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

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

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

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

585 * The fourth line contains the number of nonzero entries

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

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

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

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

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

591 * of multidimensional arrays).

592 *

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

594 *

595 * An example block describing one factor is:

596 *

597 * <pre>

598 * 3

599 * 4 8 7

600 * 3 2 2

601 * 11

602 * 0 0.1

603 * 1 3.5

604 * 2 2.8

605 * 3 6.3

606 * 4 8.4

607 * 6 7.4

608 * 7 2.4

609 * 8 8.9

610 * 9 1.3

611 * 10 1.6

612 * 11 2.6

613 * </pre>

614 *

615 * which corresponds to the following factor:

616 *

617 * \f[

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

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

620 * \hline

621 * 0 & 0 & 0 & 0.1\\

622 * 1 & 0 & 0 & 3.5\\

623 * 2 & 0 & 0 & 2.8\\

624 * 0 & 1 & 0 & 6.3\\

625 * 1 & 1 & 0 & 8.4\\

626 * 2 & 1 & 0 & 0.0\\

627 * 0 & 0 & 1 & 7.4\\

628 * 1 & 0 & 1 & 2.4\\

629 * 2 & 0 & 1 & 8.9\\

630 * 0 & 1 & 1 & 1.3\\

631 * 1 & 1 & 1 & 1.6\\

632 * 2 & 1 & 1 & 2.6

633 * \end{array}

634 * \f]

635 *

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

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

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

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

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

641 * eleventh and twelveth entries are interchanged.

642 *

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

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

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

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

647 * fastest:

648 *

649 * \f[

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

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

652 * \hline

653 * 0 & 0 & 0 & 0.1\\

654 * 1 & 0 & 0 & 3.5\\

655 * 2 & 0 & 0 & 2.8\\

656 * 0 & 1 & 0 & 7.4\\

657 * 1 & 1 & 0 & 2.4\\

658 * 2 & 1 & 0 & 8.9\\

659 * 0 & 0 & 1 & 6.3\\

660 * 1 & 0 & 1 & 8.4\\

661 * 2 & 0 & 1 & 0.0\\

662 * 0 & 1 & 1 & 1.3\\

663 * 1 & 1 & 1 & 1.6\\

664 * 2 & 1 & 1 & 2.6

665 * \end{array}

666 * \f]

667 *

668 *

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

670 *

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

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

673 * observed joint state of some variables.

674 *

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

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

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

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

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

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

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

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

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

684 * without any characters in between.

685 *

686 * \subsection fileformats-evidence-example Example

687 *

688 * <pre>

689 * 1 3 2

690 *

691 * 0 0 1

692 * 1 0 1

693 * 1 1

694 * </pre>

695 *

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

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

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

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

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

701 *

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

703 *

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

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

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

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

708 * containing the data used for parameter learning.

709 *

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

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

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

713 *

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

715 *

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

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

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

719 * the next subsection.

720 *

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

722 *

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

724 * consisting of the name of a ParameterEstimation subclass

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

744 *

745 * \section fileformats-aliases Aliases file format

746 *

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

748 * should be substituted with.

749 *

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

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

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

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

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

755 *

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

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

758 * <pre>

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

760 * </pre>

761 *

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

763 */

765 /** \page bibliography Bibliography

766 * \anchor EaG09 \ref EaG09

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

768 * "Choosing a Variable to Clamp",

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

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

771 *

772 * \anchor EMK06 \ref EMK06

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

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

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

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

777 *

778 * \anchor HAK03 \ref HAK03

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

780 * "Approximate Inference and Constrained Optimization",

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

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

783 *

784 * \anchor KFL01 \ref KFL01

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

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

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

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

789 *

790 * \anchor KoF09 \ref KoF09

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

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

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

795 * \anchor Min05 \ref Min05

796 * T. Minka (2005):

797 * "Divergence measures and message passing",

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

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

800 *

801 * \anchor MiQ04 \ref MiQ04

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

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

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

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

806 *

807 * \anchor MoK07 \ref MoK07

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

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

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

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

812 *

813 * \anchor MoK07b \ref MoK07b

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

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

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

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

818 *

819 * \anchor Moo08 \ref Moo08

820 * J. M. Mooij (2008):

821 * "Understanding and Improving Belief Propagation",

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

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

824 *

825 * \anchor MoR05 \ref MoR05

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

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

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

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

830 *

831 * \anchor StW99 \ref StW99

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

833 * "Generating Random Regular Graphs Quickly",

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

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

836 *

837 * \anchor WiH03 \ref WiH03

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

839 * "Fractional Belief Propagation",

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

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

842 *

843 * \anchor WJW03 \ref WJW03

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

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

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

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

848 *

849 * \anchor YFW05 \ref YFW05

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

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

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

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

854 */

857 /** \page discussion Ideas not worth exploring

858 * \section discuss_extendedgraphs Extended factorgraphs/regiongraphs

859 *

860 * A FactorGraph and a RegionGraph are often equipped with

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

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

863 * \code

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

865 * class ExtFactorGraph : public FactorGraph {

866 * public:

867 * std::vector<Node1Properties> node1Props;

868 * std::vector<Node2Properties> node2Props;

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

870 * // ...

871 * }

872 * \endcode

873 *

874 * Advantages:

875 * - Less code duplication.

876 * - Easier maintainability.

877 * - Easier to write new inference algorithms.

878 *

879 * Disadvantages:

880 * - Cachability may be worse.

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

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

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

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

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

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

887 * Therefore this is probably a bad idea.

888 *

889 * \section discuss_templates Polymorphism by template parameterization

890 *

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

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

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

894 * \code

895 * template<typename InfAlg>

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

897 * \endcode

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

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

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

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

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

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

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

905 * Therefore this is probably a bad idea.

906 */