Abstract
Message passing algorithms (MPAs) have been traditionally used as an inference method in probabilistic graphical models. Some MPA variants have recently been introduced in the field of estimation of distribution algorithms (EDAs) as a way to improve the efficiency of these algorithms. Multiple developments on MPAs point to an increasing potential of these methods for their application as part of hybrid EDAs. In this paper we review recent work on EDAs that apply MPAs and propose ways to further extend the useful synergies between MPAs and EDAs. Furthermore, we analyze some of the implications that MPA developments can have in their future application to EDAs and other evolutionary algorithms.
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References
Abbeel P, Koller D, Ng AY (2006) Learning factor graphs in polynomial time and sample complexity. J Mach Learn Res 7:1743–1788
Baluja S, Davies S (1997) Using optimal dependency-trees for combinatorial optimization: learning the structure of the search space. In: Fisher DH (ed) Proceedings of the 14th international conference on machine learning. Morgan Kaufmann, San Francisco, pp 30–38
Batra D, Gallagher A, Parikh D, Chen T (2010) Beyond trees: MRF inference via outer-planar decomposition. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR). IEEE, San Francisco, pp 2496–2503
Bickson D (2008) Gaussian belief propagation: theory and application. arXiv preprint arXiv:0811.2518. Accessed 18 Dec 2014
Braunstein A, Mézard M, Zecchina R (2005) Survey propagation: an algorithm for satisfiability. Random Struct Algorithms 27(2):201–226
Braunstein A, Mézard M, Zecchina R (2006) Constraint satisfaction by survey propagation. In: Percus A, Istrate G, Moore C (eds) Computational complexity and statistical physics. Oxford University Press, Oxford, pp 107–124
Brownlee AE, McCall JA, Shakya SK, Zhang Q (2010) Structure learning and optimisation in a Markov network based estimation of distribution algorithm. In: Exploitation of linkage learning in evolutionary algorithms. Springer, Berlin, pp 45–69
Brownlee AEI (2009) Multivariate Markov networks for fitness modelling in an estimation of distribution algorithm. PhD Thesis, The Robert Gordon University, School of Computing, Aberdeen
Brownlee AEI, McCall J, Pelikan M (2012) Influence of selection on structure learning in Markov network EDAs: an empirical study. MEDAL Report No. 2012006. Missouri Estimation of Distribution Algorithms Laboratory (MEDAL)
Brownlee AEI, McCall J, Zhang Q, Brown D (2008) Approaches to selection and their effect on fitness modelling in an estimation of distribution algorithm. In: Proceedings of the 2008 congress on evolutionary computation CEC-2008. IEEE Press, Hong Kong, pp 2621–2628
Ceberio J, Irurozki E, Mendiburu A, Lozano JA (2012) A review on estimation of distribution algorithms in permutation-based combinatorial optimization problems. Prog Artif Intell 1(1):103–117
Ceberio J, Mendiburu A, Lozano JA (2013) The Plackett–Luce ranking model on permutation-based optimization problems. In: 2013 IEEE congress on evolutionary computation (CEC). IEEE, Cancún, pp 494–501
Chen B, Hu J (2010a) An adaptive niching EDA based on clustering analysis. In: 2010 IEEE congress on evolutionary computation (CEC). IEEE, Barcelona, pp 1–7
Chen B, Hu J (2010b) A novel clustering based niching EDA for protein folding. In: Proceedings of the world congress on nature and biologically inspired computing, 2009. NaBIC 2009. IEEE, Coimbatore, pp 748–753
Crick C, Pfeffer A (2003) Loopy belief propagation as a basis for communication in sensor networks. In: Proceedings of the 19th annual conference on uncertainty in artificial intelligence (UAI-2003). Morgan Kaufmann Publishers, San Francisco, pp 159–166
Deming WE, Stephan FF (1940) On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann Math Stat 11(4):427–444
Dolev D, Bickson D, Johnson J (2009) Fixing convergence of Gaussian belief propagation. In: IEEE international symposium on information theory, 2009. ISIT 2009. IEEE, Seoul, pp 1674–1678
Domínguez E, Lage-Castellanos A, Mulet R, Ricci-Tersenghi F, Rizzo T (2011) Characterizing and improving generalized belief propagation algorithms on the 2D Edwards–Anderson model. J Stat Mech Theory Exp 2011(12):P12007
Dong W, Yao X (2008) NichingEDA: utilizing the diversity inside a population of EDAs for continuous optimization. In: Proceedings of the 2008 congress on evolutionary computation CEC-2008. IEEE Press, Hong Kong, pp 1260–1267
Duchi J, Tarlow D, Elidan G, Koller D (2007) Using combinatorial optimization within max-product belief propagation. In: Advances in neural information processing systems 19: proceedings of the 2006 conference, vol 19. The MIT Press, Cambridge, p 369
Echegoyen C (2012) Contributions to the analysis and understanding of estimation of distribution algorithms. PhD Thesis, Department of Computer Science and Artificial Intelligence, University of the Basque Country
Echegoyen C, Lozano JA, Santana R, Larrañaga P (2007) Exact Bayesian network learning in estimation of distribution algorithms. In: Proceedings of the 2007 congress on evolutionary computation CEC-2007. IEEE Press, Los Alamitos, pp 1051–1058. doi:10.1109/CEC.2007.4424586
Echegoyen C, Santana R, Lozano JA, Larrañaga P (2008) The impact of probabilistic learning algorithms in EDAs based on Bayesian networks. In: Linkage in evolutionary computation, studies in computational intelligence. Springer, Berlin, pp 109–139. doi:10.1007/978-3-540-85068-7_6
Echegoyen C, Mendiburu A, Santana R, Lozano JA (2009) Analyzing the probability of the optimum in EDAs based on Bayesian networks. In: Proceedings of the 2009 congress on evolutionary computation CEC-2009. IEEE Press, Trondheim, pp 1652–1659. doi:10.1109/CEC.2009.4983140
Echegoyen C, Mendiburu A, Santana R, Lozano JA (2010a) Analyzing the k most probable solutions in EDAs based on Bayesian networks. In: Exploitation of linkage learning in evolutionary algorithms, evolutionary learning and optimization. Springer, pp 163–189. doi:10.1007/978-3-642-12834-9_8
Echegoyen C, Mendiburu A, Santana R, Lozano JA (2010b) Estimation of Bayesian networks algorithms in a class of complex networks. In: Proceedings of the 2010 congress on evolutionary computation CEC-2010. IEEE Press, Barcelona. doi:10.1109/CEC.2010.5586511
Echegoyen C, Zhang Q, Mendiburu A, Santana R, Lozano JA (2011) On the limits of effectiveness in estimation of distribution algorithms. In: Proceedings of the 2011 congress on evolutionary computation CEC-2007. IEEE Press, New Orleans, pp 1573–1580. doi:10.1109/CEC.2011.5949803
Echegoyen C, Mendiburu A, Santana R, Lozano JA (2012) Toward understanding EDAs based on Bayesian networks through a quantitative analysis. IEEE Trans Evol Comput 16(2):173–189. doi:10.1109/TEVC.2010.2102037
Etxeberria R, Larrañaga P (1999) Global optimization using Bayesian networks. In: Ochoa A, Soto MR, Santana R (eds) Proceedings of the second symposium on artificial intelligence (CIMAF-99). Editorial Academia, Havana, pp 332–339
Frey BJ, Dueck D (2007) Clustering by passing messages between data points. Science 315:972–976
Furtlehner C, Schoenauer M (2010) Multi-objective 3-SAT with survey-propagation. In: Proceedings of the NIPS 2010 workshop on discrete optimization in machine learning: structures, algorithms and applications (DISCML), Whistler, Canada. http://hal.inria.fr/inria-00533149 Accessed 18 Dec 2014
Gao Y, Culberson JC (2005) Space complexity of estimation of distribution algorithms. Evol Comput 13(1):125–143
Givoni IE, Frey BJ (2009) A binary variable model for affinity propagation. Neural Comput 21(6):1589–1600
Givoni IE, Chung C, Frey BJ (2011) Hierarchical affinity propagation. In: Proceedings of the 27th annual conference on uncertainty in artificial intelligence (UAI-2011). Morgan Kaufmann, Barcelona
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading
González C, Lozano JA, Larrañaga P (2002) Mathematical modeling of UMDAc algorithm with tournament selection. Behaviour on linear and quadratic functions. Int J Approx Reason 31(4):313–340
Grahl J, Minner S, Bosman PA (2008) Learning structure illuminates black boxes—an introduction to estimation of distribution algorithms. In: Advances in metaheuristics for hard optimization. Springer, Berlin, pp 365–395
Harik G (1999) Linkage learning via probabilistic modeling in the ECGA. IlliGAL Report 99010. University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana
Hartmann AK, Weigt M (2005) Phase transitions in combinatorial optimization problems: basics, algorithms and statistical mechanics. Wiley, Weinheim
Helmi BH, Rahmani AT, Pelikan M (2014) A factor graph based genetic algorithm. Int J Appl Math Comput Sci 24(3):621–633
Henrion M (1988) Propagating uncertainty in Bayesian networks by probabilistic logic sampling. In: Lemmer JF, Kanal LN (eds) Proceedings of the second annual conference on uncertainty in artificial intelligence. Elsevier, Amsterdam, pp 149–164
Heskes T (2004) On the uniqueness of belief propagation fixed points. Neural Comput 16:2379–2413
Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann Arbor
Höns R (2006) Estimation of distribution algorithms and minimum relative entropy. PhD Thesis, University of Bonn, Bonn
Höns R (2012) Using maximum entropy and generalized belief propagation in estimation of distribution algorithms. In: Shakya S, Santana R (eds) Markov networks in evolutionary computation. Springer, Berlin, pp 175–190
Höns R, Santana R, Larrañaga P, Lozano JA (2007) Optimization by max-propagation using Kikuchi approximations. Technical Report EHU-KZAA-IK-2/07. Department of Computer Science and Artificial Intelligence, University of the Basque Country
Ihler AT, Fisher J, Willsky AS (2006) Loopy belief propagation: convergence and effects of message errors. J Mach Learn Res 6(1):905
Jiroušek R, Přeučil S (1995) On the effective implementation of the iterative proportional fitting procedure. Comput Stat Data Anal 19:177–189
Johnson A, Shapiro JL (2002) The importance of selection mechanisms in distribution estimation algorithms. In: Collet P (ed) Proceedings of EA 2001, lecture notes in computer science, vol 2310. Springer, pp 91–103
Kaban A, Bootkrajang J, Durrant RJ (2013) Towards large scale continuous EDA: a random matrix theory perspective. In: Proceedings of the genetic and evolutionary computation conference GECCO-2013. ACM, Amsterdam, pp 383–390
Karshenas H, Santana R, Bielza C, Larrañaga P (2011) Multi-objective optimization with joint probabilistic modeling of objectives and variables. In: Evolutionary multi-criterion optimization: sixth international conference, EMO 2011, lecture notes in computer science. Springer, Berlin, pp 298–312. doi:10.1007/978-3-642-19893-9_21
Karshenas H, Santana R, Bielza C, Larrañaga P (2012) Continuous estimation of distribution algorithms based on factorized Gaussian Markov networks. In: Shakya S, Santana R (eds) Markov networks in evolutionary computation. Springer, Berlin, pp 157–173. doi:10.1007/978-3-642-28900-2-10
Kim K, McKay BR, Punithan D (2010) Sampling bias in estimation of distribution algorithms for genetic programming using prototype trees. In: PRICAI 2010: trends in artificial intelligence. Springer, Berlin, pp 100–111
Kroc L, Sabharwal A, Selman B (2009) Message-passing and local heuristics as decimation strategies for satisfiability. In: Proceedings of the 2009 ACM symposium on applied computing. ACM, Honolulu, pp 1408–1414
Kschischang FR, Frey BJ, Loeliger HA (2001) Factor graphs and the sum–product algorithm. IEEE Trans Inf Theory 47(2):498–519
Larrañaga P, Lozano JA (eds) (2002) Estimation of distribution algorithms. A new tool for evolutionary computation. Kluwer Academic Publishers, Boston
Leone M, Weigt S, Weigt M (2007) Clustering by soft-constraint affinity propagation: applications to gene-expression data. Bioinformatics 23(20):2708–2715
Lima CF (2009) Substructural local search in discrete estimation of distribution algorithms. PhD Thesis, University of Algarve
Lima CF, Pelikan M, Goldberg DE, Lobo FG, Sastry K, Hauschild M (2007) Influence of selection and replacement strategies on linkage learning in BOA. In: Proceedings of the 2007 congress on evolutionary computation CEC-2007. IEEE Press, Los Alamitos, pp 1083–1090
Lima CF, Pelikan M, Lobo FG, Goldberg DE (2009) Loopy substructural local search for the Bayesian optimization algorithm. In: Engineering stochastic local search algorithms. Designing, implementing and analyzing effective heuristics. Springer, Berlin, pp 61–75
Lozano JA, Larrañaga P, Inza I, Bengoetxea E (eds) (2006) Towards a new evolutionary computation: advances on estimation of distribution algorithms. Springer, Heidelberg
Mahfoud SW (1995) Niching methods for genetic algorithms. PhD Thesis, University of Illinois at Urbana-Champaign, Urbana. Also IlliGAL Report No. 95001
Malioutov DM, Johnson JK, Willsky AS (2006) Walk-sums and belief propagation in Gaussian graphical models. J Mach Learn Res 7:2031–2064
Meltzer T, Yanover C, Weiss Y (2005) Globally optimal solutions for energy minimization in stereo vision using reweighted belief propagation. In: Tenth IEEE international conference on computer vision, pp 428–435
Mendiburu A, Lozano J, Miguel-Alonso J (2005) Parallel implementation of EDAs based on probabilistic graphical models. IEEE Trans Evol Comput 9(4):406–423
Mendiburu A, Santana R, Bengoetxea E, Lozano, J (2007a) A parallel framework for loopy belief propagation. In: Thierens D et al (eds) Proceedings of the genetic and evolutionary computation conference GECCO-2007, vol II. Companion material. ACM Press, London, pp 2843–2850. http://dl.acm.org/citation.cfm?id=1274084 Accessed 18 Dec 2014
Mendiburu A, Santana R, Lozano JA (2007b) Introducing belief propagation in estimation of distribution algorithms: a parallel framework. Technical Report EHU-KAT-IK-11/07. Department of Computer Science and Artificial Intelligence, University of the Basque Country
Mendiburu A, Santana R, Lozano JA (2012) Fast fitness improvements in estimation of distribution algorithms using belief propagation. In: Santana R, Shakya S (eds) Markov networks in evolutionary computation. Springer, Berlin, pp 141–155. doi:10.1007/978-3-642-28900-2-9
Mézard M, Parisi G, Zechina R (2002) Analytic and algorithmic solution of random satisfiability problems. Science 297:812–812. doi:10.1126/science.1073287
Minka T (2001) A family of algorithms for approximate bayesian inference. PhD Thesis, Massachusetts Institute of Technology
Minka T (2005) Divergence measures and message passing. Technical Report TR-2005-173. Mitsubishi Electric Research Laboratories
Mooij JM (2005) Validity estimates for loopy belief propagation on binary real-world networks. In: Advances in neural information processing systems 17. MIT Press, Cambridge, pp 945–952
Mooij J (2010) libDAI: a free and open source C++ library for discrete approximate inference in graphical models. J Mach Learn Res 11:2169–2173
Mühlenbein H (2012) Convergence theorems of estimation of distribution algorithms. In: Shakya S, Santana R (eds) Markov networks in evolutionary computation. Springer, Berlin, pp 91–108
Mühlenbein H, Höns R (2006) The factorized distributions and the minimum relative entropy principle. In: Pelikan M, Sastry K, Cantú-Paz E (eds) Scalable optimization via probabilistic modeling: from algorithms to applications, studies in computational intelligence. Springer, Berlin, pp 11–38
Mühlenbein H, Mahnig T (2002) Evolutionary optimization and the estimation of search distributions with applications to graph bipartitioning. Int J Approx Reason 31(3):157–192
Mühlenbein H, Paaß G (1996) From recombination of genes to the estimation of distributions I. Binary parameters. In: Voigt HM, Ebeling W, Rechenberg I, Schwefel HP (eds) Parallel problem solving from nature—PPSN IV, lectures notes in computer science, vol 1141. Springer, Berlin, pp 178–187
Mühlenbein H, Mahnig T, Ochoa A (1999) Schemata, distributions and graphical models in evolutionary optimization. J Heuristics 5(2):213–247
Munetomo M, Murao N, Akama K (2008) Introducing assignment functions to Bayesian optimization algorithms. Inf Sci 178(1):152–163
Murphy KP, Weiss Y, Jordan MI (1999) Loopy belief propagation for approximate inference: an empirical study. In: Proceedings of the fifteenth conference on Uncertainty in artificial intelligence. Morgan Kaufmann Publishers, Inc., San Francisco, pp 467–475
Nilsson D (1998) An efficient algorithm for finding the M most probable configurations in probabilistic expert systems. Stat Comput 2:159–173
Ocenasek J, Schwarz J (2002) Estimation of distribution algorithm for mixed continuous–discrete optimization problems. In: Proceedings of the 2nd Euro-international symposium on computational intelligence. IOS Press, Kosice, pp 227–232
Ochoa A, Höns R, Soto MR, Mühlenbein H (2003) A maximum entropy approach to sampling in EDA—the single connected case. In: Progress in pattern recognition, speech and image analysis, lectures notes in computer science, vol 2905. Springer, Berlin, pp 683–690
Pearl J (1988) Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann, San Mateo
Pelikan M, Goldberg DE, Lobo F (2002) A survey of optimization by building and using probabilistic models. Comput Optim Appl 21(1):5–20
Peña J, Lozano JA, Larrañaga P (2005) Globally multimodal problem optimization via an estimation of distribution algorithm based on unsupervised learning of Bayesian networks. Evol Comput 13(1):43–66
Ponce de León E, Díaz E (2012) Adaptive evolutionary algorithm based on a cliqued gibbs sampling over graphical Markov model structure. In: Shakya S, Santana R (eds) Markov networks in evolutionary computation. Springer, Berlin, pp 109–123
Regnier-Coudert O (2013) Bayesian network structure learning using characteristic properties of permutation representations with applications to prostate cancer treatment. PhD Thesis, Robert Gordon University
Rivera JP, Santana R (2000) Design of an algorithm based on the estimation of distributions to generate new rules in the XCS classifier system. Technical Report ICIMAF 2000-100, CEMAFIT 2000-78. Institute of Cybernetics, Mathematics and Physics, Havana
Santana R (2003) Factorized Distribution Algorithms: selection without selected population. Technical Report ICIMAF 2003-240. Institute of Cybernetics, Mathematics and Physics, Havana
Santana R (2006) Advances in probabilistic graphical models for optimization and learning. Applications in protein modelling. PhD Thesis, University of the Basque Country
Santana R, Larrañaga P, Lozano JA (2005) Interactions and dependencies in estimation of distribution algorithms. In: Proceedings of the 2005 congress on evolutionary computation CEC-2005. IEEE Press, Edinburgh, pp 1418–1425. doi:10.1109/CEC.2005.1554856
Santana R, Mendiburu A, Lozano JA (2008) An empirical analysis of loopy belief propagation in three topologies: grids, small-world networks and random graphs. In: Jaeger M, Nielsen TD (eds) Proceedings of the fourth European workshop on probabilistic graphical models (PGM-2008), pp 249–256
Santana R, Larrañaga P, Lozano JA (2010) Learning factorizations in estimation of distribution algorithms using affinity propagation. Evol Comput 18(4):515–546. http://www.mitpressjournals.org/doi/abs/10.1162/EVCO_a_00002. Accessed 18 Dec 2014
Santana R, Mendiburu A, Lozano JA (2012a) Evolving NK-complexity for evolutionary solvers. In: Companion proceedings of the 2012 genetic and evolutionary computation conference GECCO-2012. ACM Press, Philadelphia, pp 1473–1474. http://dl.acm.org/citation.cfm?id=2330997. Accessed 18 Dec 2014
Santana R, Mendiburu A, Lozano JA (2012b) New methods for generating populations in Markov network based EDAs: decimation strategies and model-based template recombination. Technical Report EHU-KZAA-TR:2012-05. Department of Computer Science and Artificial Intelligence, University of the Basque Country. http://hdl.handle.net/10810/9180. Accessed 18 Dec 2014
Santana R, Mendiburu A, Lozano JA (2013) Message passing methods for estimation of distribution algorithms based on Markov networks. In: Proceedings of the 4th conference on swarm, evolutionary, and memetic computing (SEMCCO-2013), lectures notes in computer science. Springer, Chennai, pp 419–430 (in press)
Sastry K, Abbass HA, Goldberg DE, Johnson D (2005) Sub-structural niching in estimation of distribution algorithms. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM, Washington, DC, pp 671–678
Sastry K, Lima CF, Goldberg DE (2006) Evaluation relaxation using substructural information and linear estimation. In: Proceedings of the 8th annual conference on genetic and evolutionary computation. ACM, New York, pp 419–426
Sastry K, Goldberg DE, Llorá X (2007) Towards billion-bit optimization via a parallel estimation of distribution algorithm. In: Thierens D et al (eds) Proceedings of the genetic and evolutionary computation conference GECCO-2007, vol I. ACM Press, London, pp 577–584
Sato H, Hasegawa Y, Bollegala D, Iba H (2012) Probabilistic model building GP with belief propagation. In: 2012 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–8
Shakya S, Santana R, Lozano JA (2012) A Markovianity based optimisation algorithm. Genet Program Evol Mach 13(2):159–195. doi:10.1007/s10710-011-9149-y
Soto MR (2003) A single connected factorized distribution algorithm and its cost of evaluation. PhD Thesis, University of Havana, Havana (in Spanish)
Suwannik W, Chongstitvatana P (2008) Solving one-billion-bit noisy OneMax problem using estimation distribution algorithm with arithmetic coding. In: Proceedings of the 2008 congress on evolutionary computation CEC-2008. IEEE Press, Hong Kong, pp 1203–1206
Tanaka K, Shouno H, Okada M, Titterington D (2004) Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing. J Phys A 37(36):8675
Valdez-Peña IS, Hernández-Aguirre A, Botello-Rionda S (2009) Approximating the search distribution to the selection distribution in EDAs. In: Proceedings of the genetic and evolutionary computation conference GECCO-2009. ACM, New York, pp 461–468
Van Hoyweghen C, Goldberg D, Naudts B (2002a) From twomax to the Ising model: easy and hard symmetrical problems. In: Proceedings of the genetic and evolutionary computation conference GECCO-2002. Morgan Kaufmann Publishers, Inc., San Francisco, pp 626–633
Van Hoyweghen C, Naudts B, Goldberg D (2002b) Spin-flip symmetry and synchronization. Evol Comput 10(4):317–344
Wainwright MJ, Jordan MI (2003) Graphical models, exponential families, and variational inference. Technical Report 649. Department of Statistics, University of California, Berkeley
Wainwright M, Jaakkola T, Willsky A (2002) Exact MAP estimates by (hyper) tree agreement. Adv Neural Inf Process Syst 15:809–816
Wainwright M, Jaakkola T, Willsky A (2004) Tree consistency and bounds on the performance of the max-product algorithm and its generalizations. Stat Comput 14:143–166
Wang Z, Zoghi M, Hutter F, Matheson D, De Freitas N (2013) Bayesian optimization in high dimensions via random embeddings. In: Proceedings of the Twenty-Third international joint conference on Artificial Intelligence. AAAI Press, Chicago, pp 1778–1784
Weiss Y (2000) Correctness of local probability propagation in graphical models with loops. Neural Comput 12:1–41
Weiss Y, Freeman WT (2001) On the optimality of solutions of the max-product belief propagation algorithm in arbitrary graphs. IEEE Trans Inf Theory 47(2):723–735
Welling M (2004) On the choice of regions for generalized belief propagation. In: Proceedings of the 20th conference on uncertainty in artificial intelligence (UAI-2004). Morgan Kaufmann Publishers, Banff, pp 585–592
Wiegerinck W, Heskes T (2003) Fractional belief propagation. In: Advances in neural information processing systems. MIT, Vancouver, pp 455–462
Xing EP, Jordan MI (2003) Graph partition strategies for generalized mean field inference. Technical Report CSD-03-1274. Division of Computer Science, University of California, Berkeley
Yanover C, Weiss Y (2003) Approximate inference and protein-folding. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems 15. MIT Press, Cambridge, pp 1457–1464
Yedidia JS, Freeman WT, Weiss Y (2005) Constructing free energy approximations and generalized belief propagation algorithms. IEEE Trans Inf Theory 51(7):2282–2312
Yuille A (2001) A double-loop algorithm to minimize the Bethe and Kikuchi free energies. Neural Comput 14(6):1691–1722
Zilberstein S (1996) Using anytime algorithms in intelligent systems. AI Mag 17(3):73
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This work has been partially supported by the Saiotek and Research Groups 2013–2018 (IT-609-13) programs (Basque Government), TIN2013-41272P (Ministry of Science and Technology of Spain), COMBIOMED network in computational bio-medicine (Carlos III Health Institute), and by the NICaiA Project PIRSES-GA-2009-247619 (European Commission).
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Santana, R., Mendiburu, A. & Lozano, J.A. A review of message passing algorithms in estimation of distribution algorithms. Nat Comput 15, 165–180 (2016). https://doi.org/10.1007/s11047-014-9473-2
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DOI: https://doi.org/10.1007/s11047-014-9473-2