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Learning Bayesian networks: approaches and issues

Published online by Cambridge University Press:  12 May 2011

Rónán Daly ,
Qiang Shen  and
Stuart Aitken
Rónán Daly*
Affiliation:
School of Computing Science, University of Glasgow, Glasgow, G12 8QQ, UK; e-mail: ronan.daly@gla.ac.uk
Qiang Shen*
Affiliation:
Department of Computer Science, Aberystwyth University, Aberystwyth, SY23 3DB, UK; e-mail: qqs@aber.ac.uk
Stuart Aitken*
Affiliation:
School of Informatics, University of Edinburgh, Edinburgh, EH8 9LE, UK; e-mail: stuart@aiai.ed.ac.uk
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Abstract

Bayesian networks have become a widely used method in the modelling of uncertain knowledge. Owing to the difficulty domain experts have in specifying them, techniques that learn Bayesian networks from data have become indispensable. Recently, however, there have been many important new developments in this field. This work takes a broad look at the literature on learning Bayesian networks—in particular their structure—from data. Specific topics are not focused on in detail, but it is hoped that all the major fields in the area are covered. This article is not intended to be a tutorial—for this, there are many books on the topic, which will be presented. However, an effort has been made to locate all the relevant publications, so that this paper can be used as a ready reference to find the works on particular sub-topics.

Type
Articles
Information
The Knowledge Engineering Review , Volume 26 , Issue 2 , 12 May 2011 , pp. 99 - 157
Copyright
Copyright © Cambridge University Press 2011

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References

Abramson, B., Finizza, A. 1991. Using belief networks to forecast oil prices. International Journal of Forecasting 7(3), 299–315.CrossRefGoogle Scholar
Abramson, B., Brown, J., Edwards, W., Murphy, A., Winkler, R. L. 1996. Hailfinder: a Bayesian system for forecasting severe weather. International Journal of Forecasting 12(1), 57–71.CrossRefGoogle Scholar
Acid, S., de Campos, L. M. 1995. Approximations of causal networks by polytrees: an empirical study. In Advances in Intelligent Computing – IPMU ’94, Lecture Notes in Computer Science 945, 149–158. Springer.CrossRefGoogle Scholar
Acid, S., de Campos, L. M. 1996a. An algorithm for finding minimum d-separating sets in belief networks. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 3–10.Google Scholar
Acid, S., de Campos, L. M. 1996b. An Algorithm for Finding Minimum d-Separating Sets in Belief Networks. Technical report DECSAI-96-02-14, Departamento de Ciencias de la Computación e Inteligencia Artificial, Universidad de Granada.Google Scholar
Acid, S., de Campos, L. M. 1996c. BENEDICT: an algorithm for learning probabilistic Bayesian networks. In Proceedings of the Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems, Granada, Spain, 979–984.Google Scholar
Acid, S., De Campos, L. M. 2000. Learning right sized belief networks by means of a hybrid methodology. In Principles of Data Mining and Knowledge Discovery: 4th European Conference, PKDD 2000, Zighed, D. Komorowski, J. & Żytkow, J. (eds). Lecture Notes in Artificial Intelligence 1910, 309–315, Springer.Google Scholar
Acid, S., de Campos, L. M. 2001. A hybrid methodology for learning belief networks: BENEDICT. International Journal of Approximate Reasoning 27(3), 235–262.CrossRefGoogle Scholar
Acid, S., de Campos, L. M. 2003. Searching for Bayesian network structures in the space of restricted acyclic partially directed graphs. Journal of Artificial Intelligence Research 18, 445–490.CrossRefGoogle Scholar
Acid, S., de Campos, L. M., Huete, J. F. 2001. The search of causal orderings: a short cut for learning belief networks. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty: Proceedings of the Sixth European Conference, ECSQARU 2001, Lecture Notes in Artificial Intelligence 2143, 216–227. Springer.CrossRefGoogle Scholar
Acid, S., de Campos, L. M., Fernandez-Luna, J. M., Rodriguez, S., Rodriguez, J. M., Salcedo, J. L. 2004. A comparison of learning algorithms for Bayesian networks: a case study based on data from an emergency medical service. Artificial Intelligence in Medicine 30(3), 215–232.CrossRefGoogle ScholarPubMed
Aitken, S., Jirapech-Umpai, T., Daly, R. 2005. Inferring gene regulatory networks from classified microarray data: initial results. BMC Bioinformatics 6(Suppl. 3), S4.CrossRefGoogle Scholar
Aliferis, C. F., Tsamardinos, I. 2002. Algorithms for Large-scale Local Causal Discovery and Feature Selection in the Presence of Limited Sample or Large Causal Neighbourhoods. Technical report DSL-02-08, Department of Biomedical Informatics, Vanderbilt University.Google Scholar
Allen, T. V., Singh, A., Greiner, R., Hoope, P. 2008. Quantifying the uncertainty of a belief net response: Bayesian error-bars for belief net inference. Artficial Intelligence 172(4–5), 483–513.CrossRefGoogle Scholar
Anderson, B., Moore, A. 2005. Active learning for hidden Markov models: objective functions and algorithms. In Proceedings of the Twenty-Second International Conference on Machine Learning (ICML 2005), De Raedt, L. & Wrobel, S. (eds). ACM, 9–16.Google Scholar
Andersson, S. A., Madigan, D., Perlman, M. D. 1997. A characterization of Markov equivalence classes for acyclic digraphs. The Annals of Statistics 25(2), 505–541.Google Scholar
Andreassen, S., Jensen, F. V., Andersen, S. K., Falck, B., Kjrul, U., Woldbye, M., Srensen, A. R., Rosenfalck, A., Jensen, F. 1989. MUNIN–an expert EMG assistant. In Computer-aided Electromyography and Expert Systems, Desmedt, J. (ed.). Elsevier, 255–277.Google Scholar
Bach, F. R., Jordan, M. I. 2003. Learning graphical models with Mercer kernels. In Advances in Neural Information Processing Systems 15 (NIPS*2002), Becker, S., Thrun, S. & Obermayer, K. (eds). The MIT Press, 1009–1016.Google Scholar
Bauer, E., Koller, D., Singer, Y. 1997. Update rules for parameter estimation in Bayesian networks. In Proceedings of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-97), Geiger, D. & Shenoy, P. P. (eds). Morgan Kaufmann, 3–13.Google Scholar
Beal, M. J., Ghahramani, Z. 2003. The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures. In Bayesian Statistics 7: Proceedings of the Seventh Valencia International Meeting, Bernardo, J. M., Bayarri, M. J., Berger, J. O., Dawid, A. P., Heckerman, D., Smith, A. F. M. & West, M. (eds). Oxford University Press, 453–464.CrossRefGoogle Scholar
Becker, A., Geiger, D. 1994. Approximation algorithms for the loop cutset problem. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 60–68.Google Scholar
Becker, A., Geiger, D. 1996a. Optimization of Pearl’s method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem. Artificial Intelligence 83(1), 167–188.CrossRefGoogle Scholar
Becker, A., Geiger, D. 1996b. A sufficiently fast algorithm for finding close to optimal junction trees. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 81–89.Google Scholar
Becker, A., Geiger, D. 2001. A sufficiently fast algorithm for finding close to optimal clique trees. Artificial Intelligence 125(1–2), 3–17.CrossRefGoogle Scholar
Beinlich, I., Suermondt, H., Chavez, R., Cooper, G. 1989. The ALARM monitoring system: a case study with two probabilistic inference techniques for belief networks. In Proceedings of the Second European Conference on Artificial Intelligence in Medicine (AIME 89), Lecture Notes in Medical Informatics 38, 247–256, Springer.CrossRefGoogle Scholar
Binder, J., Koller, D., Russell, S., Kanazawa, K. 1997. Adaptive probabilistic networks with hidden variables. Machine Learning 29(2–3), 213–244.CrossRefGoogle Scholar
Bishop, C., Lawrence, N., Jaakkola, T., Jordan, M. 1998. Approximating posterior distributions in belief networks using mixtures. In Advances in Neural Information Processing Systems 10 (NIPS*1997), Jordan, M. I., Kearns, M, J. & Solla, S. A. (eds). The MIT Press, 416–422.Google Scholar
Blanco, R., Inza, I., Larrañaga, P. 2003. Learning Bayesian networks in the space of structures by estimation of distribution algorithms. International Journal of Intelligent Systems 18(2), 205–220.CrossRefGoogle Scholar
Borchani, H., Amor, N. B., Mellouli, K. 2006. Learning Bayesian network equivalence classes from incomplete data. In Proceedings of the Ninth International Conference on Discovery Science, Lecture Notes in Artificial Intelligence 4265, 291–295, Springer.CrossRefGoogle Scholar
Borchani, H., Chaouachi, M., Amor, N. B. 2007. Learning causal Bayesian networks from incomplete observational data and interventions. In Proceedings of the Ninth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2007), Mellouli, K. (ed.). Lecture Notes in Artificial Intelligence 4724, 17–29, Springer.CrossRefGoogle Scholar
Borchani, H., Amor, N. B., Khalfallah, F. 2008. Learning and evaluating bayesian network equivalence classes from incomplete data. International Journal of Pattern Recognition and Artificial Intelligence 22(2), 253–278.Google Scholar
Bøttcher, S. G. 2004. Learning Bayesian Networks with Mixed Variables. PhD thesis, Department of Mathematical Sciences, Aalborg University.Google Scholar
Bouckaert, R. R. 1993. Probabilistic network construction using the minimum description length principle. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty: European Conference ECSQARU ’93, Lecture Notes in Computer Science 747, 41–48, Springer.CrossRefGoogle Scholar
Bouckaert, R. R. 1994a. Probabilistic Network Construction Using the Minimum Description Length Principle. Technical report RUU-CS-94-27, Department of Computer Science, Utrecht University.Google Scholar
Bouckaert, R. R. 1994b. Properties of Measures for Bayesian Belief Network Learning. Technical report UU-CS-1994-35, Department of Information and Computing Sciences, Utrecht University.CrossRefGoogle Scholar
Bouckaert, R. R. 1994c. A Stratified Simulation Scheme for Inference in Bayesian Belief Networks. Technical report UU-CS-1994-16, Department of Computer Science, Utrecht University.CrossRefGoogle Scholar
Bouckaert, R. R., Castillo, E., Gutiérrez, J. M. 1996. A modified simulation scheme for inference in Bayesian networks. International Journal of Approximate Reasoning 14(1), 55–80.CrossRefGoogle Scholar
Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D. 1996. Context-specific independence in Bayesian networks. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 115–123.Google Scholar
Boyen, X., Koller, D. 1998. Tractable inference for complex stochastic processes. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper, G. F. & Moral, S. (eds). Morgan Kaufmann, 33–42.Google Scholar
Boyen, X., Friedman, N., Koller, D. 1999. Discovering the hidden structure of complex dynamic systems. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 91–100.Google Scholar
Breese, J. S., Horvitz, E. 1991. Ideal reformulation of belief networks. In Uncertainty in Artificial Intelligence 6, Bonissone, P., Henrion, M., Kanal, L. & Lemmer, J. (eds). North-Holland, 129–144.Google Scholar
Bromberg, F., Margaritis, D. 2009. Improving the reliability of causal discovery from small data sets using argumentation. Journal of Machine Learning Research 10, 301–340.Google Scholar
Brown, L. E., Tsamardinos, I., Aliferis, C. F. 2004. A novel algorithm for scalable and accurate Bayesian network learning. In Proceedings of the Eleventh World Congress on Medical Informatics (MEDINFO) Fieschi, M., Coiera, E. & Li, Y. J. (eds). 1, IOS Press, 711–715.Google Scholar
Brown, L. E., Tsamardinos, I., Aliferis, C. F. 2005. A comparison of novel and state-of-the-art polynomial Bayesian network learning algorithms. In Proceedings of the Twentieth National Conference On Artificial Intelligence, Veloso, M. M. & Kambhampati, S. (eds). 2, AAAI Press, 739–745.Google Scholar
Buntine, W. 1991. Theory refinement on Bayesian networks. In Proceedings of the Seventh Annual Conference on Uncertainty in Artificial Intelligence (UAI ’91), Ambrosio, B. D. & Smets, P. (eds). Morgan Kaufmann, 52–60.Google Scholar
Buntine, W. L. 1994. Operations for learning with graphical models. Journal of Artificial Intelligence Research 2, 159–225.CrossRefGoogle Scholar
Buntine, W. 1996. A guide to the literature on learning probabilistic networks from data. IEEE Transactions on Knowledge and Data Engineering 8(2), 195–210.CrossRefGoogle Scholar
Burge, J., Lane, T. 2006. Improving Bayesian network structure search with random variable aggregation hierarchies. In Proceedings of the Seventeenth European Conference on Machine Learning (ECML 2006), Lecture Notes in Artificial Intelligence 4212, 66–77. Springer.CrossRefGoogle Scholar
Burge, J., Lane, T. 2007. Shrinkage estimator for Bayesian network parameters. In Proceedings of the Eighteenth European Conference on Machine Learning (EMCL 2007), Kok, J. N., Koronacki, J., de Mantaras, R. L., Matwin, S., Mladenič, D. & Skowron, A. (eds). Lecture Notes in Artificial Intelligence 4701, 67–78. Springer.Google Scholar
Butz, C., Hua, S., Chen, J., Yao, H. 2009. A simple graphical approach for understanding probabilistic inference in Bayesian networks. Information Sciences 179(6), 699–716.CrossRefGoogle Scholar
Cano, J. E., Hernández, L. D., Moral, S. 1996. Importance sampling algorithms for the propagation of probabilities in belief networks. International Journal of Approximate Reasoning 15(1), 77–92.CrossRefGoogle Scholar
Cartwright, N. 2001. What is wrong with Bayes nets? The Monist 84(2), 242–264.CrossRefGoogle Scholar
Cartwright, N. 2002. Against modularity, the causal Markov condition, and any link between the two: comments on Hausman and Woodward. The British Journal for the Philosophy of Science 53(3), 411–453.CrossRefGoogle Scholar
Cartwright, N. 2006. From metaphysics to method: comments on manipulability and the causal Markov condition. The British Journal for the Philosophy of Science 57(1), 197–218.CrossRefGoogle Scholar
Castelo, R., Kočka, T. 2003. On inclusion-driven learning of Bayesian networks. Journal of Machine Learning Research 4, 527–574.Google Scholar
Castelo, R., Perlman, M. D. 2002. Learning essential graph Markov models from data. In Proceedings of the First European Workshop on Probabilistic Graphical Models (PGM 2002), Gámez, J. A. & Salmerón, A. (eds). Cuenca, Spain, 17–24.Google Scholar
Castelo, R., Siebes, A. 2000. Priors on network structures. Biasing the search for Bayesian networks. International Journal of Approximate Reasoning 24(1), 39–57.CrossRefGoogle Scholar
Castillo, E., Gutiérrez, J. M., Hadi, A. S. 1995. Parametric structure of probabilities in Bayesian networks. In Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU ’95), Lecture Notes in Artificial Intelligence 946, 89–98. Springer.CrossRefGoogle Scholar
Castillo, E., Gutiérrez, J. M., Hadi, A. S. 1996. A new method for efficient symbolic propagation in discrete bayesian networks. Networks 28(1), 31–43.3.0.CO;2-E>CrossRefGoogle Scholar
Castillo, E., Gutiérrez, J. M., Hadi, A. S. 1997a. Expert Systems and Probabilistic Network Models. Monographs in Computer Science, Springer.CrossRefGoogle Scholar
Castillo, E., Hadi, A. S., Solares, C. 1997b. Learning and updating of uncertainty in Dirichlet models. Machine Learning 26(1), 43–63.CrossRefGoogle Scholar
Chang, K.-C., Fung, R. 1995. Symbolic probabilistic inference with both discrete and continuous variables. IEEE Transactions on Systems, Man and Cybernetics 25(6), 910–916.CrossRefGoogle Scholar
Chavez, R. M., Cooper, G. F. 1990. An empirical evaluation of a randomized algorithm for probabilistic inference. In Uncertainty in Artificial Intelligence 5, Henrion, M., Shachter, R., Kanal, L. & Lemmer, J. (eds). North-Holland, 191–208.CrossRefGoogle Scholar
Chavira, M., Darwiche, A. 2007. Compiling Bayesian networks using variable elimination. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence, Veloso, M. M. (ed.). Morgan Kaufmann, 2443–2449.Google Scholar
Cheeseman, P., Stutz, J. 1996. Bayesian classification (AutoClass): theory and results. In Advances in Knowledge Discovery and Data Mining, Fayyad, U. M., Piatetsky-Shapiro, G., Smyth, P. & Uthurusamy, R. (eds). AAAI Press, 153–180.Google Scholar
Chen, X.-W., Anantha, G., Lin, X. 2008. Improving Bayesian network structure learning with mutual information-based node ordering in the K2 algorithm. IEEE Transactions on Knowledge and Data Engineering 20(5), 628–640.CrossRefGoogle Scholar
Cheng, J., Druzdzel, M. J. 2000. AIS-BN: an adaptive importance sampling algorithm for evidential reasoning in large Bayesian networks. Journal of Artificial Intelligence Research 13, 155–188.CrossRefGoogle Scholar
Cheng, J., Druzdzel, M. 2001. Confidence inference in Bayesian networks. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), Breese, J. & Koller, D. (eds). Morgan Kaufmann, 75–82.Google Scholar
Cheng, J., Greiner, R. 1999. Comparing Bayesian network classifiers. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 101–108.Google Scholar
Cheng, J., Bell, D. A., Liu, W. 1997. An algorithm for Bayesian belief network construction from data. In Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics, Smyth, P. & Madigan, D. (eds). Fort Lauderdale, USA, 83–90.Google Scholar
Cheng, J., Greiner, R., Kelly, J., Bell, D., Liu, W. 2002. Learning Bayesian networks from data: an information-theory based approach. Artificial Intelligence 137(1–2), 43–90.CrossRefGoogle Scholar
Chickering, D. M. 1995. A transformational characterization of equivalent Bayesian network structures. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 87–98.Google Scholar
Chickering, D. M. 1996a. Learning Bayesian networks is NP-complete. In Learning from Data: Artificial Intelligence and Statistics V, Fisher, D. & Lenz, H.-J. (eds). Lecture Notes in Statistics 112, 121–130. Springer.CrossRefGoogle Scholar
Chickering, D. M. 1996b. Learning equivalence classes of Bayesian network structures. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 150–157.Google Scholar
Chickering, D. M. 2002a. Learning equivalence classes of Bayesian-network structures. Journal of Machine Learning Research 2, 445–498.Google Scholar
Chickering, D. M. 2002b. Optimal structure identification with greedy search. Journal of Machine Learning Research 3, 507–554.Google Scholar
Chickering, D. M., Heckerman, D. 1997. Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables. Machine Learning 29(2–3), 181–212.CrossRefGoogle Scholar
Chickering, D. M., Heckerman, D. 1999. Fast learning from sparse data. In Proceedings of the Fifteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-99), Morgan Kaufmann, 109–115.Google Scholar
Chickering, D. M., Meek, C. 2002. Finding optimal Bayesian networks. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI-02), Darwiche, A. & Friedman, N. (eds). Morgan Kaufmann, 94–102.Google Scholar
Chickering, D. M., Meek, C. 2006. On the incompatibility of faithfulness and monotone DAG faithfulness. Artificial Intelligence 170(8–9), 653–666.CrossRefGoogle Scholar
Chickering, D. M., Geiger, D., Heckerman, D. 1996. Learning Bayesian networks: search methods and experimental results. In Learning from Data: Artificial Intelligence and Statistics V, Fisher, D. & Lenz, H.-J. (eds). Lecture Notes in Statistics 112, 112–128. Springer.Google Scholar
Chickering, D. M., Heckerman, D., Meek, C. 1997a. A Bayesian approach to learning Bayesian networks with local structure. In Proceedings of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-97). Morgan Kaufmann, 80–89.Google Scholar
Chickering, D. M., Heckerman, D., Meek, C. 1997b. A Bayesian Approach to Learning Bayesian Networks with Local Structure. Technical report MSR-TR-97-07, Microsoft Research.Google Scholar
Chickering, D. M., Heckerman, D., Meek, C. 2004. Large-sample learning of Bayesian networks is NP-hard. Journal of Machine Learning Research 5, 1287–1330.Google Scholar
Chow, C. K., Liu, C. N. 1968. Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory 14(3), 462–467.CrossRefGoogle Scholar
Cooper, G. F. 1990. The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence 42(2–3), 393–405.CrossRefGoogle Scholar
Cooper, G. F. 1995. A Bayesian method for learning belief networks that contain hidden variables. Journal of Intelligent Information Systems 4(1), 71–88.CrossRefGoogle Scholar
Cooper, G. F. 1997. A simple constraint-based algorithm for efficiently mining observational databases for causal relationships. Data Mining and Knowledge Discovery 1(2), 203–224.CrossRefGoogle Scholar
Cooper, G. F., Herskovits, E. 1992. A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9(4), 309–347.CrossRefGoogle Scholar
Cooper, G. F., Yoo, C. 1999. Causal discovery from a mixture of experimental and observational data. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 116–125.Google Scholar
Correa, E. S., Freitas, A. A., Johnson, C. G. 2007. Particle swarm and Bayesian networks applied to attribute selection for protein functional classification. In Proceedings of the Genetic and Evolutionary Computation Conference, Lipson, H. (ed.). ACM, 2651–2658.Google Scholar
Cotta, C., Muruzábal, J. 2002. Towards a more efficient evolutionary induction of Bayesian networks. In Proceedings of the Seventh International Conference on Parallel Problem Solving from Nature (PPSN VII), Lecture Notes in Computer Science 2439, 730–739. Springer.CrossRefGoogle Scholar
Cotta, C., Muruzábal, J. 2004. On the learning of Bayesian network graph structures via evolutionary programming. In Proceedings of the Second European Workshop on Probabilistic Graphical Models, Lucas, P. (ed.). Leiden, Netherlands, 65–72.Google Scholar
Cousins, S. B., Chena, W., Frisse, M. E. 1993. A tutorial introduction to stochastic simulation algorithms for belief networks. Artificial Intelligence in Medicine 5(4), 315–340.CrossRefGoogle ScholarPubMed
Cowell, R. 2001. Conditions under which conditional independence and scoring methods lead to identical selection of Bayesian network models. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), Breese, J. & Koller, D. (eds). Morgan Kaufmann, 91–97.Google Scholar
Cowell, R. G., Dawid, A. P., Lauritzen, S. L., Spiegelhalter, D. J. 1999. Probabilistic Networks and Expert Systems. Statistics for Engineering and Information Science, Springer.Google Scholar
Cruz-Ramírez, N., Acosta-Mesa, H.-G., Barrientos-Martnez, R.-E., Nava-Fernández, L.-A. 2006. How good are the Bayesian information criterion and the minimum description length principle for selection? A Bayesian network analysis. In Proceedings of the Fifth Mexican International Conference on Artificial Intelligence (MICAI 2006), Lecture Notes in Artificial Intelligence 4293, 494–504. Springer.CrossRefGoogle Scholar
Dagum, P., Horvitz, E. 1993. A Bayesian analysis of simulation algorithms for inference in belief networks. Networks 23(5), 499–516.CrossRefGoogle Scholar
Dagum, P., Luby, M. 1993. Approximating probabilistic inference in Bayesian belief networks is NP-hard. Artificial Intelligence 60(1), 141–154.CrossRefGoogle Scholar
Dagum, P., Luby, M. 1997. An optimal approximation algorithm for Bayesian inference. Artificial Intelligence 93(1–2), 1–27.CrossRefGoogle Scholar
Dagum, P., Galper, A., Horvitz, E. 1992. Dynamic network models for forecasting. In Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI-92), Dubois, D., Wellman, M. P., D’Ambrosio, B. & Smets, P. (eds). Morgan Kaufmann, 41–48.Google Scholar
Daly, R., Shen, Q. 2009. Learning Bayesian network equivalence classes with ant colony optimization. Journal of Artificial Intelligence Research 35, 391–447.CrossRefGoogle Scholar
Daly, R., Shen, Q, Aitken, S. 2006. Speeding up the learning of equivalence classes of Bayesian network structures. In Proceedings of the Tenth IASTED International Conference on Artificial Intelligence and Soft Computing, del Pobil, A. P. (ed.). ACTA Press, 34–39.Google Scholar
Darwiche, A. 1995. Conditioning methods for exact and approximate inference in causal networks. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 99–107.Google Scholar
Darwiche, A. 1998. Dynamic jointrees. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper G. F. & Moral S. (eds). Morgan Kaufmann, 97–104.Google Scholar
Darwiche, A. 2001a. Decomposable negation normal form. Journal of the ACM 48(4), 608–647.CrossRefGoogle Scholar
Darwiche, A. 2001b. Recursive conditioning. Artificial Intelligence 126(1–2), 5–41.CrossRefGoogle Scholar
Darwiche, A. 2002. A logical approach to factoring belief networks. In Proceedings of the Eight International Conference on Principles of Knowledge Representation and Reasoning (KR-02), Fensel, D., Giunchiglia, F., McGuinness, D. L. & Williams, M.-A. (eds). Morgan Kaufmann, 409–420.Google Scholar
Darwiche, A. 2003. A differential approach to inference in Bayesian networks. Journal of the ACM 50(3), 280–305.CrossRefGoogle Scholar
Darwiche, A. 2009. Modeling and Reasoning with Bayesian Networks, Cambridge University Press.CrossRefGoogle Scholar
Dasgupta, S. 1997. The sample complexity of learning fixed-structure Bayesian networks. Machine Learning 29(2–3), 165–180.CrossRefGoogle Scholar
Dasgupta, S. 1999. Learning polytrees. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 134–141.Google Scholar
Dash, D., Cooper, G. F. 2004. Model averaging for prediction with discrete Bayesian networks. Journal of Machine Learning Research 5, 1177–1203.Google Scholar
Dash, D., Druzdzel, M. J. 1999. A hybrid anytime algorithm for the construction of causal models from sparse data. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H., Laskey, K. (eds). Morgan Kaufmann, 142–149.Google Scholar
Dash, D., Druzdzel, M. 2003. A robust independence test for constraint-based learning of causal structure. In Proceedings of the Ninteenth Conference on Uncertainty in Artificial Intelligence, Meek, C. & Kjærulff, U. (eds). Morgan Kaufmann, 167–174.Google Scholar
de Campos, L. M. 2006. A scoring function for learning bayesian networks based on mutual information and conditional independence tests. Journal of Machine Learning Research 7, 2149–2187.Google Scholar
de Campos, L. M. 1998. Independency relationships and learning algorithms for singly connected networks. Journal of Experimental & Theoretical Artificial Intelligence 10(4), 511–549.CrossRefGoogle Scholar
de Campos, L. M., Castellano, J. G. 2007. Bayesian network learning algorithms using structural restrictions. International Journal of Approximate Reasoning 45(2), 233–254.CrossRefGoogle Scholar
de Campos, L. M., Huete, J. F. 1997. On the use of independence relationships for learning simplified belief networks. International Journal of Intelligent Systems 12(7), 495–522.3.0.CO;2-G>CrossRefGoogle Scholar
de Campos, L. M., Huete, J. F. 2000a. Approximating causal orderings for Bayesian networks using genetic algorithms and simulated annealing. In Proceedings of the Eight Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, Spain, 333–340.Google Scholar
de Campos, L. M., Huete, J. F. 2000b. A new approach for learning belief networks using independence criteria. International Journal of Approximate Reasoning 24(1), 11–37.CrossRefGoogle Scholar
de Campos, L. M., Puerta, J.M. 2001. Stochastic local and distributed search algorithms for learning belief networks. In Proceedings of the Third International Symposium on Adaptive Systems: Evolutionary Computation and Probabilistic Graphical Models, Ochoa, A., Mühlenbein, H., English, T. & Larrañaga, P. (eds). ICIMAF, 109–115.Google Scholar
de Campos, L. M., Fernández-Luna, J. M., Gámez, J. A., Puerta, J. M. 2002a. Ant colony optimization for learning Bayesian networks. International Journal of Approximate Reasoning 31(3), 291–311.CrossRefGoogle Scholar
de Campos, L. M., Fernández-Luna, J. M., Puerta, J. M. 2002b. Local search methods for learning Bayesian networks using a modified neighborhood in the space of DAGs. In Advances in Artificial Intelligence: Proceedings of the Eight Ibero-American Conference on AI (IBERAMIA 2002), Lecture Notes in Artificial Intelligence 2527, 182–192. Springer.CrossRefGoogle Scholar
de Campos, L. M., Gámez, J. A., Puerta, J. M. 2002c. Learning Bayesian networks by ant colony optimisation: searching in two different spaces. Mathware & Soft Computing 9(3), 251–268.Google Scholar
de Campos, L. M., Fernández-Luna, J. M., Puerta, J. M. 2003. An iterated local search algorithm for learning Bayesian networks with restarts based on conditional independence tests. International Journal of Intelligent Systems 18(2), 221–235.CrossRefGoogle Scholar
de Santana, A. L., Frances, C. R., Rocha, C. A., Carvalho, S. V., Vijaykumar, N. L., Rego, L. P., Costa, J. C. 2007a. Strategies for improving the modeling and interpretability of Bayesian networks. Data and Knowledge Engineering 63(1), 91–107.CrossRefGoogle Scholar
de Santana, A. L., Francês, C. R. L., Costa, J. C. W. 2007b. Algorithm for graphical Bayesian modeling based on multiple regressions. In Proceedings of the Sixth Mexican International Conference on Artificial Intelligence (MICAI 2007), Gelbukh, A. & Morales, Á. F. K. (eds). Lecture Notes in Artificial Intelligence 4827, 496–506. Springer.Google Scholar
Dean, T., Kanazawa, K. 1989. A model for reasoning about persistence and causation. Computational Intelligence 5(2), 142–150.CrossRefGoogle Scholar
Delaplace, A., Brouard, T., Cardot, H. 2006. Two evolutionary methods for learning Bayesian network structures. In Proceedings of the International Conference on Computational Intelligence and Security, Wang, Y., Cheung, Y.-M. & Liu, H. (eds). 1, 137–142. IEEE.Google Scholar
Dempster, A. P., Laird, N. M., Rubin, D. B. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Socitety. Series B (Methodological) 39(1), 1–38.Google Scholar
desJardins, M., Rathod, P., Getoor, L. 2008. Learning structured Bayesian networks: combining abstraction hierarchies and tree-structured conditional probability tables. Computational Intelligence 24(1), 1–22.CrossRefGoogle Scholar
Díez, F. J. 1996. Local conditioning in Bayesian networks. Artificial Intelligence 87(1–2), 1–20.CrossRefGoogle Scholar
Díez, F. J., Mira, J. 1994. Distributed inference in Bayesian networks. Cybernetics and Systems 25(1), 39–61.CrossRefGoogle Scholar
Dojer, N. 2006. Learning Bayesian networks does not have to be NP-hard. In Proceedings of the Thirty-First International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 4162, 305–314. Springer.Google Scholar
Dor, D., Tarsi, M. 1992. A Simple Algorithm to Construct a Consistent Extension of a Partially Oriented Graph. Technical report R-185, Cognitive Systems Laboratory, Department of Computer Science, UCLA.Google Scholar
Draper, D., Hanks, S. 1994. Localized partial evaluation of belief networks. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 170–177.Google Scholar
Druzdzel, M. J. 1994. Some properties of joint probability distributions. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 187–194.Google Scholar
Druzdzel, M. J. 1996. Qualitative verbal explanations in Bayesian belief networks. Artificial Intelligence and Simulation of Behaviour Quarterly 94, 43–54.Google Scholar
Druzdzel, M. J., Simon, H. A. 1993. Causality in Bayesian belief networks. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI-93), Heckerman, D. & Mamdani, A. (eds). Morgan Kaufmann, 3–11.CrossRefGoogle Scholar
Eaton, D., Murphy, K. 2007a. Bayesian structure learning using dynamic programming and MCMC. In Proceedings of the Twenty-third Annual Conference on Uncertainty in Artificial Intelligence (UAI-07), Parr, R. & van der Gaag, L. (eds). AUAI Press, 101–108.Google Scholar
Eaton, D., Murphy, K. 2007b. Exact Bayesian structure learning from uncertain interventions. In Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics 2, Journal of Machine Learning Research: Workshop and Conference Proceedings, Meila, M. & Shen, X. (eds). JMLR, 107–114.Google Scholar
Eberhardt, F., Glymour, C., Scheines, R. 2005. On the number of experiments sufficient and in the worst case necessary to identify all causal relations among N variables. In Proceedings of the Twenty-first Conference on Uncertainty in Artificial Intelligence (UAI-05), Bacchus, F. & Jaakkola, T. (eds). AUAI Press, 178–184.Google Scholar
Elidan, G., Friedman, N. 2001. Learning the dimensionality of hidden variables. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), Breese, J. & Koller, D. (eds). Morgan Kaufmann, 144–151.Google Scholar
Elidan, G., Gould, S. 2008. Learning bounded treewidth Bayesian networks. Journal of Machine Learning Research 9, 2699–2731.Google Scholar
Elidan, G., Lotner, N., Friedman, N., Koller, D. 2001. Discovering hidden variables: a structure-based approach. In Advances in Neural Information Processing Systems 13, Leen, T. K., Dietterich, T. G. & Tresp, V. (eds). MIT Press, 479–485.Google Scholar
Elidan, G., Ninio, M., Friedman, N., Schuurmans, D. 2002. Data perturbation for escaping local maxima in learning. In Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI-02), Dechter, R., Kearns, M. & Sutton, R. (eds). AAAI Press, 132–139.Google Scholar
Elidan, G., Nachman, I., Friedman, N. 2007. “Ideal parent” structure learning for continuous variable Bayesian networks. Journal of Machine Learning Research 8, 1799–1833.Google Scholar
Faulkner, E. 2007. K2GA: heuristically guided evolution of Bayesian network structures from data. In Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining (CIDM 2007), IEEE, 18–25. doi: 10.1109/CIDM.2007.368847.CrossRefGoogle Scholar
Feelders, A., van Straalen, R. 2007. Parameter learning for Bayesian networks with strict qualitative influences. In Advances in Intelligent Data Analysis VII: Proceedings of the Seventh International Symposium on Intelligent Data Analysis (IDA 2007), Berthold, M. R., Shawe-Taylor, J. & Lavrač, N. (eds). Lecture Notes in Computer Science 4723, 48–58. Springer.CrossRefGoogle Scholar
Flesch, I., Lucas, P. 2007. Independence decomposition in dynamic Bayesian networks. In Proceedings of the Ninth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2007), Mellouli, K. (ed.). Lecture Notes in Artificial Intelligence 4724560–571. Springer.CrossRefGoogle Scholar
Forbes, J., Huang, T., Kanazawa, K., Russell, S. 1995. The BATmobile: towards a Bayesian automated taxi. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI 95), Mellish, C. S. (ed.). Morgan Kaufmann, 1878–1885.Google Scholar
Friedman, N. 1997. Learning belief networks in the presence of missing values and hidden variables. In Proceedings of the Fourteenth International Conference on Machine Learning (ICML ’97), Fisher, O. H. (ed.). Morgan Kaufmann, 125–133.Google Scholar
Friedman, N. 1998. The Bayesian structural EM algorithm. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper, G. F. & Moral, S. (eds). Morgan Kaufmann, 129–138.Google Scholar
Friedman, N. 2004. Inferring cellular networks using probabilistic graphical models. Science 303(5679), 799–805.CrossRefGoogle ScholarPubMed
Friedman, N., Getoor, L. 1999. Efficient learning using constrained sufficient statistics. In Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, Heckerman, D. & Whittaker, J. (eds). Morgan Kaufmann.Google Scholar
Friedman, N., Goldszmidt, M. 1996a. Discretizing continuous attributes while learning Bayesian networks. In Proceedings of the Thirteenth International Conference on Machine Learning (ICML '96), Saitta, L. (ed.). Morgan Kaufmann, 157–165.Google Scholar
Friedman, N., Goldszmidt, M. 1996b. Learning Bayesian networks with local structure. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 252–262.Google Scholar
Friedman, N., Goldszmidt, M. 1997. Sequential update of Bayesian network structure. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI-97), Geiger, D. & Shenoy, P. P. (eds). Morgan Kaufmann, 165–174.Google Scholar
Friedman, N., Koller, D. 2000. Being Bayesian about network structure. In Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI-00), Boutilier, C. & Goldszmidt, M. (eds). Morgan Kaufmann, 201–210.Google Scholar
Friedman, N., Koller, D. 2003. Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning 50(1–2), 95–125.CrossRefGoogle Scholar
Friedman, N., Yakhini, Z. 1996. On the sample complexity of learning Bayesian networks. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 274–282.Google Scholar
Friedman, N., Geiger, D., Goldszmidt, M. 1997. Bayesian network classifiers. Machine Learning 29(2–3), 131–163.CrossRefGoogle Scholar
Friedman, N., Murphy, K., Russell, S. 1998. Learning the structure of dynamic probabilistic networks. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper, G. F. & Moral, S. (eds). Morgan Kaufmann, 139–148.Google Scholar
Friedman, N., Goldszmidt, M., Wyner, A. 1999a. On the application of the Bootstrap for computing confidence measures on features of induced Bayesian networks. In Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, Heckerman, D. & Whittaker, J. (eds). Morgan Kaufmann, 197–202.Google Scholar
Friedman, N., Goldszmidt, M., Wyner, A. 1999b. Data analysis with Bayesian networks: a bootstrap approach. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 196–205.Google Scholar
Friedman, N., Nachman, I., Pe’er, D. 1999c. Learning Bayesian network structure from massive datasets: the “Sparse Candidate” algorithm. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 206–215.Google Scholar
Friedman, N., Linial, M., Nachman, I., Pe’er, D. 2000. Using Bayesian networks to analyze expression data. Journal of Computational Biology 7(3/4), 601–620.CrossRefGoogle ScholarPubMed
Fu, L. D. 2005. A Comparison of State-of-the-Art Algorithms for Learning Bayesian Network Structure from Continuous Data. Master’s thesis, Vanderbilt University.Google Scholar
Fung, R. M., Chang, K.-C. 1990. Weighing and integrating evidence for stochastic simulation in Bayesian networks. In Uncertainty in Artificial Intelligence 5, Henrion, M., Shachter, R., Kanal, L. & Lemmer, J. (eds). North-Holland, 209–219.CrossRefGoogle Scholar
Fung, R. M., Crawford, S. L. 1990. Constructor: a system for the induction of probabilistic models. In Proceedings of the Eighth National Conference on Artificial Intelligence 2, AAAI Press, 762–769.Google Scholar
Gámez, J. A., Puerta, J. M. 2002. Searching for the best elimination sequence in Bayesian networks by using ant colony optimization. Pattern Recognition Letters 23(1–3), 261–277.CrossRefGoogle Scholar
Gao, S., Xiao, Q., Pan, Q., Li, Q. 2007. Learning dynamic Bayesian networks structure based on Bayesian optimization algorithm. In Advances in Neural Networks: Proceedings of the Fourth International Symposium on Neural Networks (ISNN 2007), Lecture Notes in Computer Science Part II 4492, 424–431. Springer.CrossRefGoogle Scholar
Geiger, D. 1998. Graphical models and exponential families. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper, G. F. & Moral, S. (eds). Morgan Kaufmann, 156–165.Google Scholar
Geiger, D., Heckerman, D. 1994. Learning Gaussian Networks. Technical report MSR-TR-94-10, Microsoft Research.CrossRefGoogle Scholar
Geiger, D., Heckerman, D. 1995. A characterization of the Dirichlet distribution with application to learning Bayesian networks. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 196–207.Google Scholar
Geiger, D., Heckerman, D. 1997. A characterization of the Dirichlet distribution through global and local parameter independence. The Annals of Statistics 25(3), 1344–1369.CrossRefGoogle Scholar
Geiger, D., Paz, A., Pearl, J. 1990. Learning causal trees from dependence information. In Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI 1990), AAAI Press, 770–776.Google Scholar
Geiger, D., Heckerman, D., Meek, C. 1996. Asymptotic model selection for directed networks with hidden variables. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 283–290.Google Scholar
Geiger, D., Heckerman, D., King, H., Meek, C. 2001. Stratified exponential families: graphical models and model selection. The Annals of Statistics 29(2), 505–529.CrossRefGoogle Scholar
Ghahramani, Z. 1998. Learning dynamic Bayesian networks. In Adaptive Processing of Sequences and Data Structures, Giles, C. L. & Gori, M. (eds). Lecture Notes in Artificial Intelligence 1387, 168–197. Springer.CrossRefGoogle Scholar
Ghahramani, Z., Jordan, M. I. 1997. Factorial hidden Markov models. Machine Learning 29(2–3), 245–273.CrossRefGoogle Scholar
Gillispie, S., Perlman, M. D. 2001. Enumerating Markov equivalence classes of acyclic digraph models. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), Breese, J. & Koller, D. (eds). Morgan Kaufmann, 171–177.Google Scholar
Gillispie, S. B., Perlman, M. D. 2002. The size distribution for Markov equivalence classes of acyclic digraph models. Artificial Intelligence 141(1–2), 137–155.CrossRefGoogle Scholar
Giudici, P., Castelo, R. 2003. Improving Markov chain Monte Carlo model search for data mining. Machine Learning 50(1–2), 127–158.CrossRefGoogle Scholar
Giudici, P., Green, P. J. 1999. Decomposable graphical Gaussian model determination. Biometrika 86(4), 785–801.CrossRefGoogle Scholar
Giudici, P., Green, P., Tarantola, C. 1999. Efficient model determination for discrete graphical models. Discussion paper 99-93, Department of Statistics, Athens University of Economics and Business.Google Scholar
Glymour, C., Cooper, G. F., (eds). 1999. Computation, Causation, & Discovery. The MIT Press.Google Scholar
Glymour, C., Scheines, R., Spirtes, P., Kelly, K. 1986. Discovering Causal Structure: Artifical Intelligence, Philosophy of Science and Statistical Modeling. Report CMU-PHIL-1, Department of Philosophy, Carnegie Mellon University.Google Scholar
Glymour, C., Scheines, R., Spirtes, P., Kelly, K. 1987. Discovering Causal Structure: Artificial Intelligence, Philosophy of Science, and Statistical Modeling. Academic Press.Google Scholar
Gold, E. M. 1967. Language identification in the limit. Information and Control 10(5), 447–474.CrossRefGoogle Scholar
Goldenberg, A., Moore, A. 2004. Tractable learning of large Bayes net structures from sparse data. In Proceedings of the Twenty-first International Conference on Machine Learning (ICML 2004), Carla E. Brodley (ed.). ACM, 44–51.Google Scholar
Gou, K. X., Jun, G. X., Zhao, Z. 2007. Learning Bayesian network structure from distributed homogeneous data. In Proceedings of the Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007) 3, Wenying Feng & Feng Gao (eds). IEEE, 250–254.Google Scholar
Greiner, R., Grove, A., Schuurmans, D. 1997. Learning Bayesian nets that perform well. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI-97), Geiger, D. & Shenoy, P. P. (eds). Morgan Kaufmann, 198–207.Google Scholar
Grzegorczyk, M., Husmeier, D. 2008. Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move. Machine Learning 71(2–3), 265–305.CrossRefGoogle Scholar
Guo, H., Hsu, W. 2002. A survey of algorithms for real-time Bayesian network inference. In Papers from the AAAI Workshop on Real-Time Decision Support and Diagnosis Systems, Guo, H., Horvitz, E., Hsu, W. H. & Santos, E. Jr (eds). AAAI Press, 1–12.Google Scholar
Guo, Y.-Y., Wong, M.-L., Cai, Z.-H. 2006. A novel hybrid evolutionary algorithm for learning Bayesian networks from incomplete data. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2006), 916–923.Google Scholar
Guyon, I., Aliferis, C., Cooper, G., Elisseeff, A., Pellet, J.-P., Spirtes, P., Statnikov, A. 2008. Design and analysis of the causation and prediction challenge. In Causation and Prediction Challenge (WCCI 2008), Lawrence, N. (ed.). 3, JMLR Workshop and Conference Proceedings, Journal of Machine Learning Research, 1–33.Google Scholar
Gyftodimos, E., Flach, P. A. 2004. Hierarchical Bayesian networks: an approach to classification and learning for structured data. In Methods and Applications of Artificial Intelligence: Proceedings of the Third Hellenic Conference on AI (SETN 2004), Lecture Notes in Artificial Intelligence 3025, 291–300. Springer.CrossRefGoogle Scholar
Hausman, D. M., Woodward, J. 1999. Independence, invariance and the causal markov condition. The British Journal for the Philosophy of Science 50(4), 521–583.CrossRefGoogle Scholar
Hausman, D. M., Woodward, J. 2004. Modularity and the causal Markov condition: a restatement. The British Journal for the Philosophy of Science 55(1), 147–161.CrossRefGoogle Scholar
He, Y.-B., Geng, Z. 2008. Active learning of causal networks with intervention experiments and optimal designs. Journal of Machine Learning Research 9, 2523–2547.Google Scholar
Heckerman, D. 1995a. A Bayesian Approach to Learning Causal Networks. Technical report MSR-TR-95-04, Microsoft Research.Google Scholar
Heckerman, D. 1995b. A Tutorial on Learning with Bayesian Networks. Technical report MSR-TR-95-06, Microsoft Research.Google Scholar
Heckerman, D. 2007. A Bayesian approach to learning causal networks. In Advances in Decision Analysis: from Foundations to Applications, Edwards, W. & Miles R. F. Jr (eds). Chapter 11, Cambridge University Press, 202–220.CrossRefGoogle Scholar
Heckerman, D., Breese, J. S. 1996. Causal independence for probability assessment and inference using Bayesian networks. IEEE Transactions on Systems, Man, and Cybernetics–Part A 26(6), 826–831.CrossRefGoogle Scholar
Heckerman, D., Geiger, D. 1995 . Likelihoods and Parameter Priors for Bayesian Networks. Technical report MSR-TR-95-54, Microsoft Research.Google Scholar
Heckerman, D. E., Horvitz, E. J., Nathwani, B. N. 1992. Toward normative expert systems: part I. The Pathfinder project. Methods of Information in Medicine 31(2), 90–105.Google ScholarPubMed
Heckerman, D., Geiger, D., Chickering, D. M. 1995. Learning Bayesian networks: the combination of knowledge and statistical data. Machine Learning 20(3), 197–243.CrossRefGoogle Scholar
Heng, X.-C., Qin, Z., Wang, X.-H., Shao, L.-P. 2006. Research on learning Bayesian networks by particle swarm optimization. Information Technology Journal 5(3), 540–545.CrossRefGoogle Scholar
Henrion, M. 1988. Propagating uncertainty in Bayesian networks by probabilistic logic sampling. In Uncertainty in Artificial Intelligence 2, Lemmer, J. F, & Kanal, L. N. (eds). North-Holland, 149–163.CrossRefGoogle Scholar
Hernández, L. D., Moral, S., Salmerón, A. 1998. A Monte Carlo algorithm for probabilistic propagation in belief networks based on importance sampling and stratified simulation techniques. International Journal of Approximate Reasoning 18(1–2), 53–91.CrossRefGoogle Scholar
Herskovits, E., Cooper, G. 1991. Kutató: an entropy-driven system for construction of probabilistic expert systems from data. In Uncertainty in Artificial Intelligence 6, Bonissone, P., Henrion, M., Kanal, L. & Lemmer, J. (eds). North-Holland, 54–62.Google Scholar
Hewawasam, R., Premaratne, K. 2007. Learning Bayesian network parameters from imperfect data: Enhancements to the EM algorithm. In: Intelligent Computing: Theory and Applications V, Proceedings of SPIE, Priddy, K. E. & Ertin, E. (eds). 6560, SPIE, 65600E-1–65600E-10. doi: 10.1117/12.719290.CrossRefGoogle Scholar
Hoeting, J. A., Madigan, D., Raftery, A. E., Volinsky, C. T. 1999. Bayesian model averaging: a tutorial. Statistical Science 14(4), 382–417.Google Scholar
Hofmann, R., Tresp, V. 1996. Discovering structure in continuous variables using Bayesian networks. In Advances in Neural Information Processing Systems 8 (NIPS*1995), Touretzky, D. S., Mozer, M. C. & Hasselmo, M. E. (eds). The MIT Press, 500–506.Google Scholar
Holness, G. F. 2007. A direct measure for the efficacy of Bayesian network structures learned from data. In Proceedings of the Fifth International Conference on Machine Learning and Data Mining in Pattern Recognition (MLDM 2007), Lecture Notes in Artificial Intelligence 4571, 601–615. Springer.CrossRefGoogle Scholar
Hsu, W. H., Guo, H., Perry, B. B., Stilson, J. A. 2002. A permutation genetic algorithm for variable ordering in learning Bayesian networks from data. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2002), Langdon, W. B. et al. (eds). Morgan Kaufmann, 383–390.Google Scholar
Huang, C., Darwiche, A. 1996. Inference in belief networks: a procedural guide. International Journal of Approximate Reasoning 15(3), 225–263.CrossRefGoogle Scholar
Huang, K., Henrion, M. 1996. Efficient search-based inference for noisy-OR belief networks: TopEpsilon. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 325–331.Google Scholar
Huang, Y., Valtorta, M. 2006. Identifiability in causal Bayesian networks: a sound and complete algorithm. In Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI-06) 2, AAAI Press, 1149–1154.Google Scholar
Huang, J., Pan, H., Wan, Y. 2005. An algorithm for cooperative learning of Bayesian network structure from data. In Proceedings of the Eight International Conference on Computer Supported Cooperative Work in Design (CSCWD 2004), Lecture Notes in Computer Science 3168, 86–94. Springer.Google Scholar
Huete, J. F., de Campos, L. M. 1993. Learning causal polytrees. In Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU ’93), Clarke, M., Kruse, R. & Moral, S. (eds). Lecture Notes in Computer Science 747, 180–185. Springer.CrossRefGoogle Scholar
Husmeier, D. 2003. Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks. Bioinformatics 19(17), 2271–2282.CrossRefGoogle ScholarPubMed
Hwang, K.-B., Lee, J. W., Chung, S.-W., Zhang, B.-T. 2002. Construction of large-scale bayesian networks by local to global search. In Trends in Artificial Intelligence: Proceedings of the Seventh Pacific Rim International Conference on Artificial Intelligence (PRICAI 2002), Lecture Notes in Artificial Intelligence 2417, 375–384. Springer.Google Scholar
Hwang, K.-B., Kim, B.-H., Zhang, B.-T. 2006. Learning hierarchical Bayesian networks for large-scale data analysis. In Proceedings of the Thirteenth International Conference on Neural Information Processing (ICONIP 2006), Lecture Notes in Computer Science 4232, 670–679. Springer.CrossRefGoogle Scholar
Imoto, S., Goto, T., Miyano, S. 2002. Estimation of genetic networks and functional structures between genes by using Bayesian networks and nonparametric regression. In Proceedings of the Seventh Pacific Symposium on Biocomputing, Altman, R. B., Dunker, A. K., Hunter, L. & Klein, T. E. (eds). World Scientific, 175–186.Google Scholar
Jaakkola, T. S., Jordan, M. I. 1996. Computing upper and lower bounds on likelihoods in intractable networks. A.I. Memo 1571, Artficial Intelligence Lab, Massachusetts Institute of Technology.Google Scholar
Jaakkola, T. S., Jordan, M. I. 1997. Recursive algorithms for approximating probabilities in graphical models. In Advances in Neural Information Processing Systems 9 (NIPS*1996), Mozer, M., Jordan, M. I. & Petsche, T. (eds). The MIT Press, 487–493.Google Scholar
Jaakkola, T. S., Jordan, M. I. 1999a. Improving the mean field approximation via the use of mixture distributions. In Learning in Graphical Models, Jordan, M. I. (ed.). MIT Press, 163–174.Google Scholar
Jaakkola, T. S., Jordan, M. I. 1999b. Variational probabilistic inference and the QMR-DT network. Journal of Artificial Intelligence Research 10, 291–322.CrossRefGoogle Scholar
Jensen, F. V., Jensen, F. 1994. Optimal junction trees. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 360–366.Google Scholar
Jensen, F. V., Nielsen, T. D. 2007. Bayesian networks and decision graphs. Information Science and Statistics, 2nd edn.Springer.Google Scholar
Jensen, F. V., Lauritzen, S. L., Olesen, K. G. 1990a. Bayesian updating in causal probabilistic networks by local computations. Computational Statistics Quarterly 4, 269–282.Google Scholar
Jensen, F. V., Olesen, K. G., Andersen, S. K. 1990b. An algebra of Bayesian belief universes for knowledge-based systems. Networks 20(5), 637–659.CrossRefGoogle Scholar
Jia, H., Liu, D., Chen, J., Liu, X. 2007. A hybrid approach for learning Markov equivalence classes of Bayesian network. In Proceedings of the Second International Conference on Knowledge Science, Engineering and Management (KSEM 2007), Lecture Notes in Artificial Intelligence 4798, 611–616. Springer.Google Scholar
Jitnah, N., Nicholson, A. E. 1999. Arc weights for approximate evaluation of dynamic belief networks. In Proceedings of the Twelfth Australian Joint Conference on Artificial Intelligence (AI’99), Foo, N. (ed.). Lecture Notes in Artificial Intelligence 1747, 393–404. Springer.Google Scholar
John, G., Langley, P. 1995. Estimating continuous distributions in Bayesian classifiers. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 338–345.Google Scholar
Jonsson, A., Barto, A. 2007. Active learning of dynamic Bayesian networks in Markov decision processes. In Proceedings of the Seventh International Symposium on Abstraction, Reformulation, and Approximation (SARA 2007), Lecture Notes in Artificial Intelligence 4612, 273–284. Springer.CrossRefGoogle Scholar
Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., Saul, L. K. 1999. An introduction to variational methods for graphical models. Machine Learning 37(2), 183–233.CrossRefGoogle Scholar
Jurgelenaite, R., Heskes, T. 2008. Learning symmetric causal independence models. Machine Learning 71(2–3), 133–153.CrossRefGoogle Scholar
Kalisch, M., Bühlmann, P. 2007. Estimating high-dimensional directed acyclic graphs with the PC-algorithm. Journal of Machine Learning Research 8, 613–636.Google Scholar
Kanazawa, K., Koller, D., Russell, S. 1995. Stochastic simulation algorithms for dynamic probabilistic networks. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 346–351.Google Scholar
Kayaalp, M., Cooper, G. F. 2002. A Bayesian network scoring metric that is based on globally uniform parameter priors. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI-02), Darwiche, A. & Friedman, N. (eds). Morgan Kaufmann, 251–258.Google Scholar
Kennedy, J., Eberhart, R. 1995. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks 4, IEEE, 1942–1948. doi: 10.1109/ICNN.1995.488968.CrossRefGoogle Scholar
Kennedy, J., Eberhart, R. C. 1997. A discrete binary version of the particle swarm optimization algorithm. In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 5, IEEE, 4104–4108. doi: 10.1109/ICSMC.1997.637339.CrossRefGoogle Scholar
Kennett, R. J., Korb, K. B., Nicholson, A. E. 2001. Seabreeze prediction using Bayesian networks. In Proceedings of the Fifth Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining (PAKDD 2001), Lecture Notes in Artificial Intelligence 2035, 148–153. Springer.CrossRefGoogle Scholar
Kim, J. H., Pearl, J. 1983. A computational model for causal and diagnostic reasoning in inference systems. In Proceedings of the Eighth International Joint Conference on Artificial Intelligence (IJCAI 83), Bundy, A. (ed.). William Kaufmann, 190–193.Google Scholar
Kim, K.-J., Cho, S.-B. 2006. Evolutionary aggregation and refinement of Bayesian networks. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2006), IEEE, 1513–1520. doi: 10.1109/CEC.2006.1688488.CrossRefGoogle Scholar
Kirkpatrick, S., Gelatt, C. D. Jr, Vecchi, M. P. 1983. Optimization by simulated annealing. Science 220(4598), 671–680.CrossRefGoogle ScholarPubMed
Kjærulff, U. 1992a. A computational scheme for reasoning in dynamic probabilistic networks. In Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI-92), Dubois, D., Wellman, M. P., D’Ambrosio, B. & Smets, P. (eds). Morgan Kaufmann, 121–129.Google Scholar
Kjærulff, U. 1992b. Optimal decomposition of probabilistic networks by simulated annealing. Statistics and Computing 2(1), 7–17.CrossRefGoogle Scholar
Kjærulff, U. 1993. Approximation of Bayesian Networks Through Edge Removals. Technical report IR-93-2007, Department of Mathematics and Computer Science, Aalborg University.Google Scholar
Kjærulff, U. 1994. Reduction of computational complexity in Bayesian networks through removal of weak dependences. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 374–382.Google Scholar
Kjærulff, U. 1997. Nested junction trees. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI-97), Geiger, D. & Shenoy, P. P. (eds). Morgan Kaufmann, 294–301.Google Scholar
Kjaerulff, U. B., Madsen, A. L. 2008. Bayesian networks and influence diagrams: a guide to construction and analysis. Information Science and Statistics, Jordan, M., Kleinberg, J. & Schölkopf, B. (eds). Springer.Google Scholar
Kočka, T., Castelo, R. 2001. Improved learning of Bayesian networks. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), Breese, J. & Koller, D. (eds). Morgan Kaufmann, 269–276.Google Scholar
Kočka, T., Bouckaert, R.R., Studený, M. 2001. On the Inclusion Problem. Research report 2010, Institute of Information Theory and Automation, Prague.Google Scholar
Koivisto, M. 2006. Advances in exact Bayesian structure discovery in Bayesian networks. In Proceedings of the Twenty-second Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), Dechter, R. & Richardson, T. (eds). AUAI Press, 241–248.Google Scholar
Koivisto, M., Sood, K. 2004. Exact Bayesian structure discovery in Bayesian networks. Journal of Machine Learning Research 5, 549–573.Google Scholar
Korb, K. B., Nicholson, A. E. 2004. Bayesian Artificial Intelligence. Series in Computer Science and Data Analysis, Chapman & Hall/CRC.Google Scholar
Korb, K. B., Nyberg, E. 2006. The power of intervention. Minds and Machines 16(3), 289–302.CrossRefGoogle Scholar
Ku, H. H., Kullback, S. 1969. Approximating discrete probability distributions. IEEE Transactions on Information Theory 15(4), 444–447.CrossRefGoogle Scholar
Kullback, S., Leibler, R. A. 1951. On information and sufficiency. The Annals of Mathematical Statistics 22(1), 79–86.CrossRefGoogle Scholar
Kwoh, C. K., Gillies, D. F. 1996. Using hidden nodes in Bayesian networks. Artificial Intelligence 88(1–2), 1–38.CrossRefGoogle Scholar
Lähdesmäki, H., Shmulevich, I. 2008. Learning the structure of dynamic Bayesian networks from time series and steady state measurements. Machine Learning 71(2–3), 185–217.CrossRefGoogle Scholar
Lam, W. 1998. Bayesian network refinement via machine learning approach. Transactions on Pattern Analysis and Machine Intelligence 20(3), 240–251.CrossRefGoogle Scholar
Lam, W., Bacchus, F. 1993. Using causal information and local measures to learn Bayesian networks. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI-93), Heckerman, D. & Mamdani, A. (eds). Morgan Kaufmann, 243–250.CrossRefGoogle Scholar
Lam, W., Bacchus, F. 1994a. Learning Bayesian belief networks: an approach based on the MDL principle. Computational Intelligence 10(3), 269–293.CrossRefGoogle Scholar
Lam, W., Bacchus, F. 1994b. Using new data to refine a Bayesian network. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 383–390.Google Scholar
Larrañaga, P., Kuijpers, C. M. H., Murga, R. H., Yurramendi, Y. 1996a. Learning Bayesian network structures by searching for the best ordering with genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics—Part A 26(4), 487–493.CrossRefGoogle Scholar
Larrañaga, P., Poza, M., Yurramendi, Y., Murga, R. H., Kuijpers, C. M. H. 1996b. Structure learning of Bayesian networks by genetic algorithms: a performance analysis of control parameters. Transactions on Pattern Analysis and Machine Intelligence 18(9), 912–926.CrossRefGoogle Scholar
Lauritzen, S. L. 1995. The EM algorithm for graphical association models with missing data. Computational Statistics & Data Analysis 19(2), 191–201.CrossRefGoogle Scholar
Lauritzen, S. L., Spiegelhalter, D. J. 1988. Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society. Series B (Methodological) 50(2), 157–224.CrossRefGoogle Scholar
Lauritzen, S. L., Wermuth, N. 1989. Graphical models for associations between variables, some of which are qualitative and some quantitative. The Annals of Statistics 17(1), 31–57.Google Scholar
Leray, P., François, O. 2005. Bayesian network structural learning and incomplete data. In Proceedings of the International and Interdisciplinary Conference on Adaptive Knowledge Representation and Reasoning (AKRR 2005), Honkela, T., Könöner, V., Pöllä, M. & Simula, O. (eds). Espoo, Finland, 33–40.Google Scholar
Li, Z., D’Ambrosio, B. 1994. Efficient inference in Bayes networks as a combinatorial optimization problem. International Journal of Approximate Reasoning 11(1), 55–81.CrossRefGoogle Scholar
Li, J., Wang, Z. J. 2009. Controlling the false discovery rate of the association/causality structure learned with the PC algorithm. Journal of Machine Learning Research 10, 475–514.Google Scholar
Li, X.-L., Wang, S.-C., He, X.-D. 2006. Learning Bayesian networks structures based on memory binary particle swarm optimization. In Proceedings of the Sixth International Conference on Simulated Evolution and Learning (SEAL 2006), Lecture Notes in Computer Science 4247, 568–574. Springer.CrossRefGoogle Scholar
Li, G., Dai, H., Tu, Y. 2002. Linear causal model discovery using the MML criterion. In Proceedings of the IEEE International Conference on Data Mining (ICDM 2002), Kumar, V., Tsumoto, S., Zhong, N., Yu, P. S. & Wu, X. (eds). IEEE, 274–281. doi: 10.1109/ICDM.2002.1183913.CrossRefGoogle Scholar
Liang, F., Zhang, J. 2009. Learning Bayesian networks for discrete data. Computational Statistics & Data Analysis 53(4), 865–876.CrossRefGoogle Scholar
Lin, Y., Druzdzel, M. J. 1999. Stochastic sampling and search in belief updating algorithms for very large Bayesian networks. In Working Notes of the AAAI Spring Symposium on Search Techniques for Problem Solving under Uncertainty and Incomplete Information, Zhang, W. & Koenig, S. (eds). AAAI Press, 77–82.Google Scholar
Liu, F., Zhu, Q. 2007a. The max-relevance and min-redundancy greedy Bayesian network learning algorithm. In Bio-inspired Modeling of Cognitive Tasks: Proceedings of the Second International Work-Conference on the Interplay between Natural and Artificial Computation (IWINAC 2007), Lecture Notes in Computer Science 4527, 346–356. Springer, Part I.CrossRefGoogle Scholar
Liu, F., Zhu, Q. 2007b. Max-relevance and min-redundancy greedy Bayesian network learning on high dimensional data. In Proceedings of the Third International Conference on Natural Computation (ICNC 2007), Lei, J., Yoo, J. & Zhang, Q. (eds). 1, IEEE, 217–221.CrossRefGoogle Scholar
Liu, F., Tian, F., Zhu, Q. 2007a. Bayesian network structure ensemble learning. In Proceedings of the Third International Conference on Advanced Data Mining and Applications (ADMA 2007), Lecture Notes in Artificial Intelligence 4632, 454–465. Springer.CrossRefGoogle Scholar
Liu, F., Tian, F., Zhu, Q. 2007b. An improved greedy Bayesian network learning algorithm on limited data. In Proceedings of the Seventeenth International Conference on Artificial Neural Networks (ICANN 2007), Lecture Notes in Computer Science 4668, 49–57. Springer, Part I.CrossRefGoogle Scholar
Lucas, P. 2002. Restricted Bayesian network structure learning. In Proceedings of the First European Workshop on Probabilistic Graphical Models (PGM 2002), Gámez J. A. & Salmeron A. (eds). 117–126.Google Scholar
Lucas, P. J. F., van der Gaag, L. C., Abu-Hanna, A. 2004. Bayesian networks in biomedicine and health-care. Artificial Intelligence in Medicine 30(3), 201–214.CrossRefGoogle ScholarPubMed
Madigan, D., Raftery, A. E. 1994. Model selection and accounting for model uncertainty in graphical models using Occam’s window. Journal of the American Statistical Association 89(428), 1535–1546.CrossRefGoogle Scholar
Madigan, D., Raftery, A. E., York, J. C., Bradshaw, J. M., Almond, R. G. 1993. Strategies for graphical model selection. In Proceedings of the Fourth International Workshop on Artificial Intelligence and Statistics, Cheeseman, P. & Oldford, R. W. (eds). Fort Lauderdale, USA, 331–336.Google Scholar
Madigan, D., Gavrin, J., Raftery, A. E. 1994. Enhancing the Predictive Performance of Bayesian Graphical Models. Technical report 270, Department of Statistics, University of Washington.Google Scholar
Madigan, D., York, J., Allard, D. 1995. Bayesian graphical models for discrete data. International Statistical Review 63(2), 215–232.CrossRefGoogle Scholar
Madigan, D., Andersson, S. A., Perlman, M. D., Volinsky, C. T. 1996. Bayesian model averaging and model selection for Markov equivalence classes of acyclic digraphs. Communications in Statistics—Theory and Methods 25(11), 2493–2519.CrossRefGoogle Scholar
Madigan, D., Mosurski, K., Almond, R. G. 1997. Graphical explanation in belief networks. Journal of Computational and Graphical Statistics 6(2), 160–181.Google Scholar
Malvestuto, F. 1991. Approximating discrete probability distributions with decomposable models. Systems, Man and Cybernetics, IEEE Transactions on 21(5), 1287–1294.CrossRefGoogle Scholar
Mansinghka, V., Kemp, C., Griffiths, T., Tenenbaum, J. 2006. Structured priors for structure learning. In Proceedings of the Twenty-Second Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), Dechter, R. & Richardson, T. (eds). AUAI Press, 324–331.Google Scholar
Margaritis, D. 2004. Distribution-free Learning of Graphical Model Structure in Continuous Domains. Technical report TR-ISU-CS-04-06, Department of Computer Science, Iowa State University.Google Scholar
Margaritis, D., Thrun, V. 2000. Bayesian network induction via local neighborhoods. In Advances in Neural Information Processing Systems 12 (NIPS*1999), Solla, S. A., Leen, T. K. & Müller, K.-R. (eds). The MIT Press, 505–511.Google Scholar
Mascherini, M., Stefanini, F. M. 2007. Using weak prior information on structures to learn bayesian networks. In Proceedings of the Eleventh International Conference on Knowledge-based Intelligent Information and Engineering Systems (KES 2007), Lecture Notes in Artificial Intelligence 4692, 413–420. Springer, Part I.Google Scholar
Meek, C. 1995. Causal inference and causal explanation with background knowledge. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 403–410.Google Scholar
Meek, C. 1997. Graphical Models: Selecting Causal and Statistical Models. PhD thesis, Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
Meek, C., Heckerman, D. 1997. Structure and parameter learning for causal independence and causal interaction models. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI-97), Geiger, D. & Shenoy, P. P. (eds). Morgan Kaufmann, 366–375.Google Scholar
Meganck, S., Leray, P., Manderick, B. 2006. Learning causal Bayesian networks from observations and experiments: a decision theoretic approach. In Proceedings of the Third International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2006), Lecture Notes in Computer Science 3885, 58–69. Springer.Google Scholar
Meilaˇ, M., Jaakkola, T. 2006. Tractable Bayesian learning of tree belief networks. Statistics and Computing 16(1), 77–92.CrossRefGoogle Scholar
Middleton, B., Shwe, M., Heckerman, D., Henrion, M., Horvitz, E., Lehmann, H., Cooper, G. 1991. Probabilistic diagnosis using a reformulation of the INTERNIST-1/QMR knowledge base: II. Evaluation of diagnostic performance. Methods of Information in Medicine 30(4), 256–267.Google ScholarPubMed
Miguel, I., Shen, Q. 2001. Solution techniques for constraint satisfaction problems: advanced approaches. Artificial Intelligence Review 15(4), 269–293.CrossRefGoogle Scholar
Mondragón-Becerra, R., Cruz-Ramírez, N., Garcia-López, D.A., Gutiérrez-Fragoso, K., Luna-Ramrez, W.A., Ortiz-Hernández, G., Piña-Garca, C.A. 2006. Automatic construction of bayesian network structures by means of a concurrent search mechanism. In Proceedings of the Fifth Mexican International Conference on Artificial Intelligence (MICAI 2006), Lecture Notes in Artificial Intelligence 4293, 652–662. Springer.Google Scholar
Monti, S., Cooper, G. F. 1996. Bounded recursive decomposition: a search-based method for belief-network inference under limited resources. International Journal of Approximate Reasoning 15(1), 49–75.CrossRefGoogle Scholar
Monti, S., Cooper, G.F. 1997a. Learning Bayesian belief networks with neural network estimators. In Advances in Neural Information Processing Systems 9 (NIPS*1996), Mozer, M., Jordan, M. I. & Petsche, T. (eds). The MIT Press, 578–584.Google Scholar
Monti, S., Cooper, G. F. 1997b. Learning Hybrid Bayesian Networks from Data. Technical report ISSP-97-01, Intelligent Systems Program, University of Pittsburgh.Google Scholar
Monti, S., Cooper, G. F. 1998. A multivariate discretization method for learning Bayesian networks from mixed data. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper, G. F. & Moral, S. (eds). Morgan Kaufmann, 404–413.Google Scholar
Moore, A., Lee, M. S. 1998. Cached sufficient statistics for efficient machine learning with large datasets. Journal of Artificial Intelligence Research 8, 67–91.CrossRefGoogle Scholar
Moore, A., Wong, W.-K. 2003. Optimal reinsertion: a new search operator for accelerated and more accurate Bayesian network structure learning. In Proceedings of the Twentieth International Conference on Machine Learning, Fawcett, T. & Mishra, N. (eds). AAAI Press, 552–559.Google Scholar
Morales, M. M., Domínguez, R. G., Ramírez, N. C., Hernández, A. G., Andrade, J. L. J. 2004. A method based on genetic algorithms and fuzzy logic to induce Bayesian networks. In Proceedings of the Fifth Mexican International Conference in Computer Science (ENC ’04), Baeza-Yates, R., Marroquin, J. L. & Chávez, E. (eds). IEEE Computer Society, 176–180.Google Scholar
Munteanu, P., Bendou, M. 2001. The EQ framework for learning equivalence classes of Bayesian networks. In Proceedings of the 2001 IEEE International Conference on Data Mining, Cercone, N., Lin, T. Y. & Wu, X. (eds). IEEE Computer Society, 417–424.CrossRefGoogle Scholar
Munteanu, P., Cau, D. 2000. Efficient score-based learning of equivalence classes of Bayesian networks. In Proceedings of the Fourth European Conference on the Principles of Data Mining and Knowledge Discovery (PKDD 2000), Zighed, D. A., Komorowski, H. J. & Zytkow, J. M. (eds). Lecture Notes in Computer Science 1910, 96–105. Springer.CrossRefGoogle Scholar
Murphy, K. P. 2001. Active Learning of Causal Bayes Net Structure. Technical report, Department of Computer Science, University of California, Berkeley.Google Scholar
Murphy, K. P., Mian, S. 1999. Modelling Gene Expression Data Using Dynamic Bayesian Networks. Technical report, Computer Science Division, University of California, Berkeley.Google Scholar
Murphy, K. P., Weiss, Y., Jordan, M. I. 1999. Loopy belief propagation for approximate inference: an empirical study. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 467–475.Google Scholar
Muruzábal, J., Cotta, C. 2004. A primer on the evolution of equivalence classes of Bayesian-network structures. In Proceedings of the 8th International Conference on Parallel Problem Solving from Nature—PPSN VIII, Yao, X., Burke, E., Lozano, J. A., Smith, J., Merelo-Guervós, J. J., Bullinaria, J. A., Rowe, J., Tiňo, P., Kabán, A. & Schwefel, H.-P. (eds). Lecture Notes in Computer Science 3242, 612–621. Springer.Google Scholar
Myers, J. W., Laskey, K. B., DeJong, K. A. 1999a. Learning Bayesian networks from incomplete data using evolutionary algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference, Banzhaf, W., Daida, J., Eiben, A. E., Garzon, M. H., Honavar, V., Jakiela, M. & Smith, R. E. (eds). 1, Morgan Kaufmann, 458–465.Google Scholar
Myers, J. W., Laskey, K. B., Levitt, T. S. 1999b. Learning Bayesian networks from incomplete data with stochastic search algorithms. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 476–484.Google Scholar
Nägele, A., Dejori, M., Stetter, M. 2007. Bayesian substructure learning—approximate learning of very large network structures. In Proceedings of the Eighteenth European Conference on Machine Learning (ECML 2007), Lecture Notes in Artificial Intelligence 4701, 238–249. Springer.Google Scholar
Neal, R. M. 1992. Connectionist learning of belief networks. Artificial Intelligence 56(1), 71–113.CrossRefGoogle Scholar
Neal, R. M., Hinton, G. E. 1999. A view of the EM algorithm that justifies incremental, sparse, and other variants. In Learning in Graphical Models, Jordan, M. I. (ed.). MIT Press.Google Scholar
Neapolitan, R. E. 2004. Learning Bayesian Networks. Series in Artificial Intelligence. Prentice Hall.Google Scholar
Neil, J. R., Korb, K. B. 1999. The evolution of causal models: a comparison of Bayesian metrics and structure priors. In Proceedings of the Third Pacific-Asia Conference on Methodologies for Knowledge Discovery and Data Mining (PAKDD ’99), Lecture Notes in Artificial Intelligence 1574, 432–437. Springer.Google Scholar
Neil, J., Wallace, C., Korb, K. 1999. Learning Bayesian networks with restricted causal interactions. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI-99), Prade, H. & Laskey, K. (eds). Morgan Kaufmann, 486–493.Google Scholar
Nielsen, S. H., Nielsen, T. D. 2008. Adapting Bayes network structures to non-stationary domains. International Journal of Approximate Reasoning 49(2), 379–397.CrossRefGoogle Scholar
Nielsen, J. D., Kočka, T., Peña, J. 2003. On local optima in learning Bayesian networks. In Proceedings of the Ninteenth Conference on Uncertainty in Artificial Intelligence, Meek, C. & Kjærulff, U. (eds). Morgan Kaufmann, 435–444.Google Scholar
Novobilski, A. J. 2003. The random selection and manipulation of legally encoded Bayesian networks in genetic algorithms. In Proceedings of the First International Conference on Artificial Intelligence (IC-AI ’03), Arabnia, H. R., Joshua, R. & Mun, Y. (eds). 1, CSREA Press, 438–443.Google Scholar
O’Donnell, R. T., Allison, L., Korb, K. B. 2006a. Learning hybrid Bayesian networks by MML. In Advances in Artificial Intelligence: Proceedings of the Ninteenth Australian Joint Conference on Artificial Intelligence (AI 2006), Lecture Notes in Artificial Intelligence 4304, 192–203. Springer.Google Scholar
O’Donnell, R. T., Nicholson, A. E., Han, B., Korb, K. B., Alam, M. J., Hope, L. R. 2006b. Causal discovery with prior information. In Proceedings of the Ninteenth Australian Joint Conference on Artificial Intelligence (AI 2006), Lecture Notes in Artificial Intelligence 4304, 1162–1167. Springer.Google Scholar
Ott, S., Miyano, S. 2003. Finding optimal gene networks using biological constraints. Genome Informatics 14, 124–133.Google ScholarPubMed
Ott, S., Imoto, S., Miyano, S. 2004. Finding optimal models for small gene networks. In Proceedings of the Ninth Pacific Symposium on Biocomputing, Altman, R. B., Dunker, A. K., Hunter, L., Jung, T. A. & Klein, T. E. (eds). World Scientific, 557–567.Google Scholar
Pakzad, P., Anantharam, V. 2002. Belief propagation and statistical physics. In Proceedings of the 2002 Conference on Information Sciences and Systems, Princeton University, USA.Google Scholar
Park, J. D., Darwiche, A. 2004. A differential semantics for jointree algorithms. Artificial Intelligence 156(2), 197–216.CrossRefGoogle Scholar
Pearl, J. 1982. Reverend Bayes on inference engines: a distributed hierarchical approach. In Proceedings of the Second National Conference on Artificial Intelligence, Waltz, D. L. (ed.). The AAAI Press, 133–136.Google Scholar
Pearl, J. 1986a. A constraint—propagation approach to probabilistic reasoning. In Uncertainty in Artificial Intelligence, Kanal, L. N. & Lemmer, J. F. (eds). North-Holland, 357–369.CrossRefGoogle Scholar
Pearl, J. 1986b. Fusion, propagation, and structuring in belief networks. Artificial Intelligence 29(3), 241–288.CrossRefGoogle Scholar
Pearl, J. 1987. Evidential reasoning using stochastic simulation of causal models. Artificial Intelligence 32(2), 245–257.CrossRefGoogle Scholar
Pearl, J 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Series in Representation and Reasoning, Morgan Kaufmann.Google Scholar
Pearl, J. 2000. Causality. Cambridge University Press.Google Scholar
Pearl, J., Verma, T. S. 1991. A theory of inferred causation. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, Allen, J. F., Fikes, R. & Sandewall, E. (eds). San Mateo, California: Morgan Kaufmann, 441–452.Google Scholar
Peng, H., Ding, C. 2003. Structure search and stability enhancement of Bayesian networks. In Proceedings of the Third IEEE International Conference on Data Mining (ICDM 2003), Wu, X., Tuzhilin, A. & Shavlik, J. (eds). IEEE Computer Society, 621–624. doi: 10.1109/ICDM.2003.1250992.CrossRefGoogle Scholar
Peot, M. A., Shachter, R. D. 1991. Fusion and propagation with multiple observations in belief networks. Artificial Intelligence 48(3), 299–318.CrossRefGoogle Scholar
Perlman, M. D. 2001. Graphical Model Search Via Essential Graphs. Technical report 367, Department of Statistics, University of Washington.CrossRefGoogle Scholar
Perrier, E., Imoto, S., Miyano, S. 2008. Finding optimal Bayesian network given a super-structure. Journal of Machine Learning Research 9, 2251–2286.Google Scholar
Poole, D. 1993a. Average-case analysis of a search algorithm for estimating prior and posterior probabilities in Bayesian networks with extreme probabilities. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (IJCAI 93), Bajcsy, R. (ed.). Morgan Kaufmann, 606–612.Google Scholar
Poole, D. 1993b. The use of conflicts in searching Bayesian networks. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI-93), Heckerman, D. & Mamdani, A. (eds). Morgan Kaufmann, 359–367.CrossRefGoogle Scholar
Poole, D. 1996. Probabilistic conflicts in a search algorithm for estimating posterior probabilities in Bayesian networks. Artificial Intelligence 88(1–2), 69–100.CrossRefGoogle Scholar
Poole, D. 1997. Probabilistic partial evaluation: exploiting rule structure in probabilistic inference. In Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence (IJCAI 97), Pollack, M. E. (ed.). Morgan Kaufmann, 1284–1291.Google Scholar
Poole, D. 1998. Context-specific approximation in probabilistic inference. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), Cooper, G. F. & Moral, S. (eds). Morgan Kaufmann, 447–454.Google Scholar
Poole, D., Zhang, N. L. 2003. Exploiting contextual independence in probabilistic inference. Journal of Artificial Intelligence Research 18, 263–313.CrossRefGoogle Scholar
Pourret, O., Naïm, P., Marcot, B. (eds). 2008. Bayesian Networks: A Practical Guide to Applications. Statistics in Practice, Wiley.CrossRefGoogle Scholar
Pradhan, M., Dagum, P. 1996. Optimal Monte-Carlo estimation of belief network inference. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 446–453.Google Scholar
Provan, G. M., Singh, M. 1996. Learning Bayesian networks using feature selection. In Learning from Data: Artificial Intelligence and Statistics V, Fisher, D. & Lenz, H.-J. (eds). Lecture Notes in Statistics 112, 450–456. Springer.Google Scholar
Ramoni, M., Sebastiani, P. 1997a. Learning Bayesian Networks from Incomplete Databases. Technical report KMI-TR-43, Knowledge Media Institute, The Open University.Google Scholar
Ramoni, M., Sebastiani, P. 1997b. The use of exogenous knowledge to learn Bayesian networks from incomplete databases. In Proceedings of the Second International Symposium on Advances in Intelligent Data Analysis, Reasoning about Data (IDA ’97), Lecture Notes in Computer Science 1280, 537–548. Springer.CrossRefGoogle Scholar
Ramoni, M., Sebastiani, P. 1999. Learning conditional probabilities from incomplete databases: an experimental comparison. In Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, Heckerman, D. & Whittaker, J. (eds). Morgan Kaufmann.Google Scholar
Ramoni, M., Sebastiani, P. 2001. Robust learning with missing data. Machine Learning 45(2), 147–170.CrossRefGoogle Scholar
Rebane, G., Pearl, J. 1987. The recovery of causal poly-trees from statistical data. In Uncertainty in Artificial Intelligence 3, Kanal, L. N., Levitt, T. S. & Lemmer, J. F. (eds). North-Holland, 175–182.Google Scholar
Richardson, T., Spirtes, P. 2002. Ancestral graph Markov models. The Annals of Statistics 30(4), 962–1030.CrossRefGoogle Scholar
Riggelsen, C. 2008. Learning Bayesian networks: a MAP criterion for joint selection of model structure and parameter. In Proceedings of the Eighth IEEE International Conference on Data Mining (ICDM ’08), Giannotti, F., Gunopulos, D., Turini, F., Zaniolo, C., Ramakrishnan, N. & Wu, X. (eds). IEEE, 522–529.CrossRefGoogle Scholar
Riggelsen, C., Feelders, A. 2005. Learning Bayesian network models from incomplete data using importance sampling. In Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, Cowell, R. G. & Ghahramani, Z. (eds). Society for Artificial Intelligence and Statistics, 301–308.Google Scholar
Rissanen, J. 1978. Modeling by shortest data description. Automatica 14(5), 465–471.CrossRefGoogle Scholar
Robinson, J. W., Hartemink, A. J. 2009. Non-stationary dynamic Bayesian networks. In Advances in Neural Information Processing Systems 21 (NIPS*2008), Koller, D., Schuurmans, D., Bengio, Y. & Bottou, L. (eds). The MIT Press, 1369–1376.Google Scholar
Russell, S. J., Binder, J., Koller, D., Kanazawa, K. 1995. Local learning in probabilistic networks with hidden variables. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI 95), Mellish, C. S. (ed.). 2, Morgan Kaufmann, 1146–1152.Google Scholar
Sahin, F., Devasia, A. 2007. Distributed particle swarm optimization for structural Bayesian network learning. In Swarm Intelligence: Focus on Ant and Particle Swarm Optimization, Chan, F. T. S. & Tiwari, M. K. (eds). chapter 27, I-Tech Education and Publishing, Vienna, Austria, 505–532.Google Scholar
Sanscartier, M. J., Neufeld, E. 2007. Identifying hidden variables from context-specific independencies. In Proceedings of the Twentieth International Florida Artificial Intelligence Research Society Conference (FLAIRS 2007), Wilson, D. C. & Sutcliffe, G. C. J. (eds). AAAI Press, 472–477.Google Scholar
Santos, E. Jr, Shimony, S. E. 1998. Deterministic approximation of marginal probabilities in Bayes nets. IEEE Transactions on Systems, Man, and Cybernetics–Part A 28(4), 377–393.CrossRefGoogle Scholar
Santos, E. Jr, Shimony, S. E., Williams, E. 1996. Sample-and-accumulate algorithms for belief updating in Bayes networks. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 477–484.Google Scholar
Santos, E. Jr, Shimony, S. E., Williams, E. 1997. Hybrid algorithms for approximate belief updating in Bayes nets. International Journal of Approximate Reasoning 17(2–3), 191–216.CrossRefGoogle Scholar
Sarkar, S., Murthy, I. 1996. Constructing efficient belief network structures with expert provided information. IEEE Transactions on Knowledge and Data Engineering 8(1), 134–143.CrossRefGoogle Scholar
Scheines, R., Spries, P., Glymour, C. 1991. Building Latent Variable Models. Technical report CMU-PHIL-19, Department of Philosophy, Carnegie Mellon University.Google Scholar
Schmidt, T., Shenoy, P. P. 1998. Some improvements to the Shenoy-Shafer and Hugin architectures for computing marginals. Artificial Intelligence 102(2), 323–333.CrossRefGoogle Scholar
Schulte, O., Luo, W., Greiner, R. 2007. Mind change optimal learning of Bayes net structure. In Learning Theory: Proceedings of the Twentieth Annual Conference on Learning Theory (COLT 2007), Lecture Notes in Artificial Intelligence 4539, 187–202. Springer.CrossRefGoogle Scholar
Shachter, R. D. 1986a. Evaluating influence diagrams. Operations Research 34(6), 871–882.CrossRefGoogle Scholar
Shachter, R. D. 1986b. Intelligent probabilistic inference. In Uncertainty in Artificial Intelligence, Kanal, L. N. & Lemmer, J. F. (eds). North-Holland, 371–382.CrossRefGoogle Scholar
Shachter, R. D. 1988. Probabilistic inference and influence diagrams. Operations Research 36(4), 589–604.CrossRefGoogle Scholar
Shachter, R., Peot, M. 1990. Simulation approaches to general probabilistic inference on belief networks. In Uncertainty in Artificial Intelligence 5, Henrion, M., Shachter, R., Kanal, L. & Lemmer, J. (eds). North-Holland, 221–234.CrossRefGoogle Scholar
Shachter, R., Andersen, S., Szolovits, P. 1994. Global conditioning for probabilistic inference in belief networks. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 514–522.Google Scholar
Shafer, G. R., Shenoy, P. P. 1990. Probability propagation. Annals of Mathematics and Artificial Intelligence 2(1–4), 327–351.CrossRefGoogle Scholar
Shaughnessy, P., Livingston, G. 2005. Evaluating the Causal Explanatory Value of Bayesian Network Structure Learning Algorithms. Research paper 2005-013, Department of Computer Science, University of Massachusetts Lowell.Google Scholar
Shenoy, P. P. 1997. Binary join trees for computing marginals in the Shenoy-Shafer architecture. International Journal of Approximate Reasoning 17(2–3), 239–263.CrossRefGoogle Scholar
Shenoy, P. P., Shafer, G. 1990. Axioms for probability and belief-function propagation. In Readings in Uncertain Reasoning, Shafer, G. & Pearl, J. (eds). chapter 7, Morgan Kaufmann, 575–610.Google Scholar
Shimony, S. E., Santos, E. Jr 1996. Exploiting case-based independence for approximating marginal probabilities. International Journal of Approximate Reasoning 14(1), 25–54.CrossRefGoogle Scholar
Shwe, M., Cooper, G. 1991. An empirical analysis of likelihood-weighting simulation on a large, multiply connected medical belief network. Computers and Biomedical Research 24(5), 453–475.CrossRefGoogle ScholarPubMed
Shwe, M., Middleton, B., Heckerman, D., Henrion, M., Horvitz, E., Lehmann, H., Cooper, G. 1991. Probabilistic diagnosis using a reformulation of the INTERNIST-1/QMR knowledge base: I. The probabilistic model and inference algorithms. Methods of Information in Medicine 30(4), 241–255.CrossRefGoogle ScholarPubMed
Silander, T., Myllymäki, P. 2006. A simple approach for finding the globally optimal Bayesian network structure. In Proceedings of the Twenty-second Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), Dechter, R. & Richardson, T. (eds). AUAI Press, 445–452.Google Scholar
Silander, T., Kontkanen, P., Myllymaki, P. 2007. On sensitivity of the MAP Bayesian network structure to the equivalent sample size parameter. In Proceedings of the Twenty-third Conference on Uncertainty in Artificial Intelligence (UAI-07), AUAI Press, 360–367.Google Scholar
Singh, A. P., Moore, A. W. 2005. Finding Optimal Bayesian Networks by Dynamic Programming. Technical report CMU-CALD-05-106, School of Computer Science, Carnegie Mellon University.Google Scholar
Singh, M., Valtorta, M. 1993. An algorithm for the construction of Bayesian network structures from data. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI-93), Heckerman, D. & Mamdani, A. (eds). Morgan Kaufmann, 259–265.CrossRefGoogle Scholar
Singh, M., Valtorta, M. 1995. Construction of Bayesian network structures from data: a brief survey and an efficient algorithm. International Journal of Approximate Reasoning 12(2), 111–131.CrossRefGoogle Scholar
Smyth, P. 1997. Belief networks, hidden Markov models, and Markov random fields: a unifying view. Pattern Recognition Letters 18(11–13), 1261–1268.CrossRefGoogle Scholar
Spiegelhalter, D. J. 1986. Probabilistic reasoning in predictive expert systems. In Uncertainty in Artificial Intelligence, Kanal, L. N. & Lemmer, J. F. (eds). North-Holland, 47–67.CrossRefGoogle Scholar
Spiegelhalter, D. J., Lauritzen, S. L. 1990. Sequential updating of conditional probabilities on directed graphical structures. Networks 20(5), 579–605.CrossRefGoogle Scholar
Spirtes, P. 1991. Detecting causal relations in the presence of unmeasured variables. In Proceedings of the Seventh Annual Conference on Uncertainty in Artificial Intelligence (UAI-91), Morgan Kaufmann, San Mateo, CA, 392–397.Google Scholar
Spirtes, P., Glymour, C. 1990a. An Algorithm for Fast Recovery of Sparse Causal Graphs. Report CMU-PHIL-15, Department of Philosophy, Carnegie Mellon University.Google Scholar
Spirtes, P., Glymour, C. 1990b. Casual Structure among Measured Variables Preserved with Unmeasured Variables. Report CMU-PHIL-14, Department of Philosophy, Carnegie Mellon University.Google Scholar
Spirtes, P., Glymour, C. 1991. An algorithm for fast recovery of sparse causal graphs. Social Science Computer Review 90(1), 62–72.CrossRefGoogle Scholar
Spirtes, P., Meek, C. 1995. Learning Bayesian networks with discrete variables from data. In Proceedings of First International Conference on Knowledge Discovery and Data Mining, Fayyad, U. M. & Uthurusamy, R. (eds). AAAI Press, 294–299.Google Scholar
Spirtes, P., Glymour, C., Scheines, R. 1989. Causality from Probability. Report CMU-PHIL-12, Department of Philosophy, Carnegie Mellon University.Google Scholar
Spirtes, P., Glymour, C., Scheines, R. 1990. From probability to causality. Philosophical Studies 64(1), 1–36.CrossRefGoogle Scholar
Spirtes, P., Glymour, C., Scheines, R. 1993. Causation, Prediction and Search, Lecture Notes in Statistics, 1st edn. 81, Springer.CrossRefGoogle Scholar
Spirtes, P., Meek, C., Richardson, T. 1995. Causal inference in the presence of latent variables and selection bias. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95), Besnard, P. & Hanks, S. (eds). Morgan Kaufmann, 499–506.Google Scholar
Spirtes, P., Glymour, C., Scheines, R. 2000. Causation, Prediction, and Search. Adaptive Computation and Machine Learning, 2nd edn.The MIT Press.Google Scholar
Srinivas, S. 1993. A generalization of the noisy-or model. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI-93), Heckerman, D. & Mamdani, A. (eds). Morgan Kaufmann, 208–218.CrossRefGoogle Scholar
Steck, H. 2000. On the use of skeletons when learning in Bayesian networks. In Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI-00), Boutilier, C. & Goldszmidt, M. (eds). Morgan Kaufmann, 558–565.Google Scholar
Steck, H. 2008. Learning the Bayesian network structure: Dirichlet prior vs data. In Proceedings of the Twenty-fourth Conference on Uncertainty in Artificial Intelligence (UAI-08), McAllester, D. A. & Myllymäki, P. (eds). AUAI Press, 511–518.Google Scholar
Steck, H., Jaakkola, T. S. 2002. Unsupervised active learning in large domains. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI-02), Darwiche, A. & Friedman, N. (eds). Morgan Kaufmann, 469–476.Google Scholar
Steck, H., Jaakkola, T. S. 2003a. On the Dirichlet prior and Bayesian regularization. In Advances in Neural Information Processing Systems 15 (NIPS*2002), Becker, S., Thrun, S. & Obermayer, K. (eds). The MIT Press, 697–704.Google Scholar
Steck, H., Jaakkola, T. S. 2003b. (Semi-)predictive discretization during model selection. AI Memo 2003-002, Artificial Intelligence Laboratory, Massachusetts Institute of Technology.Google Scholar
Steel, D. 2005. Indeterminism and the causal Markov condition. The British Journal for the Philosophy of Science 56(1), 3–26.CrossRefGoogle Scholar
Steel, D. 2006. Comment on Hausman & Woodward on the causal Markov condition. The British Journal for the Philosophy of Science 57(1), 219–231.CrossRefGoogle Scholar
Steinsky, B. 2003. Efficient coding of labeled directed acyclic graphs. Soft Computing 7(5), 350–356.CrossRefGoogle Scholar
Suermondt, H. J., Cooper, G. F. 1988. Updating Probabilities in Multiply-Connected Belief Networks. Technical report SMI-88-0207, Medical Computer Science Group, Stanford University.Google Scholar
Suermondt, H. J., Cooper, G. F. 1990. Probabilistic inference in multiply connected belief networks using loop cutsets. International Journal of Approximate Reasoning 4(4), 283–306.CrossRefGoogle Scholar
Suermondt, H. J., Cooper, G. F. 1991. Initialization for the method of conditioning in Bayesian belief networks. Artificial Intelligence 50(1), 83–94.CrossRefGoogle Scholar
Suzuki, J. 1993. A construction of Bayesian networks from databases based on an MDL principle. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI-93), Heckerman, D. & Mamdani, A. (eds). Morgan Kaufmann, 266–273.CrossRefGoogle Scholar
Suzuki, J. 1999. Learning Bayesian belief networks based on the MDL principle: an efficient algorithm using the branch and bound technique. IEICE Transactions on Information and Systems E82-D(2), 356–367.Google Scholar
Teyssier, M., Koller, D. 2005. Ordering-based search: a simple and effective algorithm for learning Bayesian networks. In Proceedings of the Twenty-first Conference on Uncertainty in Artificial Intelligence (UAI-05), Bacchus, F. & Jaakkola, T. (eds). AUAI Press, 584–590.Google Scholar
Thiesson, B. 1995. Accelerated quantification of Bayesian networks with incomplete data. In Proceedings of the First International Conference on Knowledge Discovery and Data Mining (KDD-95), Fayyad, U. M. & Uthurusamy, R. (eds). AAAI Press, 306–311.Google Scholar
Thiesson, B. 1997. Score and information for recursive exponential models with incomplete data. In Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI-97), Geiger, D. & Shenoy, P. P. (eds). Morgan Kaufmann, 453–463.Google Scholar
Thiesson, B., Meek, C., Chickering, D. M., Heckerman, D. 1998a. Learning Mixtures of Bayesian Networks. Technical report MSR-TR-97-30, Microsoft Research.Google Scholar
Thiesson, B., Meek, C., Chickering, D. M., Heckerman, D. 1998b. Learning Mixtures of DAG Models. Technical report MSR-TR-97-30, Microsoft Research.Google Scholar
Tian, F., Zhang, H., Lu, Y., Shi, C. 2001. Incremental learning of Bayesian networks with hidden variables. In Proceedings of the 2001 IEEE International Conference on Data Mining (ICDM 2001), Cercone, C., Lin, T. Y. & Wu, X. (eds). IEEE Computer Society, 651–652. doi: 10.1109/ICDM.2001.989594.CrossRefGoogle Scholar
Tian, F., Zhang, H., Lu, Y. 2003. Learning Bayesian networks from incomplete data based on EMI method. In Proceedings of the Third IEEE Conference on Data Mining (ICDM 2003), Wu, X., Tuzhilin, A. & Shavlik, J. (eds). IEEE Computer Society, 323–330. doi: 10.1109/ICDM.2003.1250936.CrossRefGoogle Scholar
Tian, F., Li, H., Wang, Z., Yu, J. 2007. Learning Bayesian networks based on a mutual information scoring function and EMI method. In Advances in Neural Networks: Proceedings of the Fourth International Symposium on Neural Networks (ISNN 2007), Lecture Notes in Computer Science 4492, 414–423. Springer, Part II.CrossRefGoogle Scholar
Tong, S., Koller, D. 2001a. Active learning for parameter estimation in Bayesian networks. In Advances in Neural Information Processing Systems 13 (NIPS*2000), Leen, T. K., Dietterich, T. G. & Tresp, V. (eds). MIT Press, 647–653.Google Scholar
Tong, S., Koller, D. 2001b. Active learning for structure in Bayesian networks. In Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence (IJCAI 01), Nebel, B. (ed.). Morgan Kaufmann, 863–869.Google Scholar
Tsamardinos, I., Aliferis, C. F., Statnikov, A. 2003a. Algorithms for large scale Markov blanket discovery. In Proceedings of the Sixteenth International FLAIRS Conference, Russell, I. & Haller, S. M. (eds). AAAI Press, 376–381.Google Scholar
Tsamardinos, I., Aliferis, C. F., Statnikov, A. 2003b. Time and sample efficient discovery of Markov blankets and direct causal relations. In Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’03), Getoor, L., Senator, T. E., Domingos, P. & Faloutsos, C. (eds). ACM, 673–678.CrossRefGoogle Scholar
Tsamardinos, I., Aliferis, C. F., Statnikov, A., Brown, L. E. 2003c. Scaling-up Bayesian Network Learning to Thousands of Variables Using Local Learning Techniques. Technical report DSL-03-02, Department of Biomedical Informatics, Vanderbilt University, Nashville, Tennessee.Google Scholar
Tsamardinos, I., Brown, L. E., Aliferis, C. F. 2006. The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning 65(1), 31–78.CrossRefGoogle Scholar
Tucker, A., Liu, X. 2004. Learning dynamic Bayesian networks from multivariate time series with changing dependencies. In Advances in Intelligent Data Analysis V: Proceedings of the Fifth International Symposium on Intelligent Data Analysis (IDA 2003), Lecture Notes in Computer Science 2810, 100–110. Springer.Google Scholar
Tucker, A., Liu, X. 1999. Extending evolutionary programming methods to the learning of dynamic Bayesian networks. In Proceedings of the Genetic and Evolutionary Computation Conference, Banzhaf, W., Daida, J., Eiben, A. E., Garzon, M. H., Honavar, V., Jakiela, M. & Smith, R. E. (eds). 1, Morgan Kaufmann, 923–929.Google Scholar
Tucker, A., Liu, X., Ogden-Swift, A. 2001. Evolutionary learning of dynamic probabilistic models with large time lags. International Journal of Intelligent Systems 16(5), 621–646.CrossRefGoogle Scholar
Valtorta, M., Huang, Y. 2008. Identifiability in causal Bayesian networks: a gentle introduction. Cybernetics and Systems 39(4), 425–442.CrossRefGoogle Scholar
van Dijk, S., Thierens, D. 2004. On the use of a non-redundant encoding for learning Bayesian networks from data with a GA. In Proceedings of the Eight International Conference on Parallel Problem Solving from Nature (PPSN VIII), Yao, X. et al., (eds). Lecture Notes in Computer Science 3242, 141–150. Springer.CrossRefGoogle Scholar
van Dijk, S., Thierens, D., van der Gaag, L. C. 2003a. Building a GA from design principles for learning Bayesian networks. In Proceedings of the Genetic and Evolutionary Computation Conference, Lecture Notes in Computer Science 2723, 886–897. Springer, Part I.Google Scholar
van Dijk, S., van der Gaag, L. C., Thierens, D. 2003b. A skeleton-based approach to learning Bayesian networks from data. In Proceedings of the Seventh European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD 2003), Lavrač, N., Gamberger, D., Todorovski, L. & Blockeel, H. (eds). Lecture Notes in Artificial Intelligence 2838, 132–143. Springer.Google Scholar
van Engelen, R. A. 1997. Approximating Bayesian belief networks by arc removal. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(8), 916–920.CrossRefGoogle Scholar
Verma, T., Pearl, J. 1991. Equivalence and synthesis of causal models. In Uncertainty in Artificial Intelligence 6, Bonissone, P., Henrion, M., Kanal, L. & Lemmer, J. (eds). North-Holland, 255–268.Google Scholar
Verma, T., Pearl, J. 1992. An algorithm for deciding if a set of observed independencies has a causal explanation. In Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI-92), Dubois, D., Wellman, M. P., D’Ambrosio, B. & Smets, P. (eds). Morgan Kaufmann, 323–330.Google Scholar
Wallace, C. S., Boulton, D. M. 1968. An information measure for classification. The Computer Journal 11(2), 185–194.CrossRefGoogle Scholar
Wallace, C. S., Korb, K. B. 1999. Learning linear causal models by MML sampling. In Causal Models and Intelligent Data Management, Gammerman, A. (ed.). Springer, 89–111.CrossRefGoogle Scholar
Wallace, C. S., Korb, K. B., Dai, H. 1996. Causal discovery via MML. In Proceedings of the Thirteenth International Conference on Machine Learning (ICML ’96), Saitta, L. (ed.). Morgan Kaufmann, 516–524.Google Scholar
Wang, H., Yu, K., Yao, H. 2006. Learning dynamic Bayesian networks using evolutionary MCMC. In Proceedings of the International Conference on Computational Intelligence and Security, Wang, Y., Cheang, Y. & Liu, H. (eds). 1, IEEE, 45–50.Google Scholar
Wang, M., Chen, Z., Cloutier, S. 2007. A hybrid Bayesian network learning method for constructing gene networks. Computational Biology and Chemistry 31(5–6), 361–372.CrossRefGoogle ScholarPubMed
Watanabe, K., Shiga, M., Watanabe, S. 2009. Upper bound for variational free energy of Bayesian networks. Machine Learning 75(2), 199–215.CrossRefGoogle Scholar
Weiss, Y. 2000. Correctness of local probability propagation in graphical models with loops. Neural Computation 12(1), 1–41.CrossRefGoogle ScholarPubMed
Wellman, M. P., Liu, C.-L. 1994. State-space abstraction for anytime evaluation of probabilistic networks. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 567–574.Google Scholar
Whittaker, J. 1990. Graphical Models in Applied Multivariate Statistics. Wiley.Google Scholar
Williamson, J. 2005. Bayesian Nets and Causality. Oxford University Press.Google Scholar
Wong, M. L., Guo, Y. Y. 2006. Discover Bayesian networks from incomplete data using a hybrid evolutionary algorithm. In Proceedings of the Sixth International Conference on Data Mining (ICDM ’06), Clifton, C. W., Zhong, N., Liu, J., Wah, B. W. & Wu, X. (eds). IEEE, 1146–1150.CrossRefGoogle Scholar
Wong, M. L., Guo, Y. Y. 2008. Learning Bayesian networks from incomplete databases using a novel evolutionary algorithm. Decision Support Systems 45(2), 368–383.CrossRefGoogle Scholar
Wong, M. L., Leung, K. S. 2004. An efficient data mining method for learning Bayesian networks using an evolutionary algorithm-based hybrid approach. IEEE Transactions on Evolutionary Computation 8(4), 378–404.CrossRefGoogle Scholar
Wong, M. L., Lam, W., Leung, K. S. 1999. Using evolutionary programming and minimum description length principle for data mining of Bayesian networks. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(2), 174–178.CrossRefGoogle Scholar
Wong, M. L., Lee, S. Y., Leung, K. S. 2002. A hybrid approach to discover Bayesian networks from databases using evolutionary programming. In Proceedings of the 2002 IEEE International Conference on Data Mining (ICDM 2002), Kumar, V., Tsumoto, S., Zhong, N., Yu, P. S. & Wu, X. (eds). IEEE Computer Society, 498–505. doi: 10.1109/ICDM.2002.1183994.CrossRefGoogle Scholar
Xiang, Y., Chu, T. 1999. Parallel learning of belief networks in large and difficult domains. Data Mining and Knowledge Discovery 3(3), 315–339.CrossRefGoogle Scholar
Xiang, Y., Wong, S. K. M., Cercone, N. 1996. Critical remarks on single link search in learning belief networks. In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI-96), Horvitz, E. & Jensen, F. (eds). Morgan Kaufmann, 564–571.Google Scholar
Xie, X., Geng, Z. 2008. A recursive method for structural learning of directed acyclic graphs. Journal of Machine Learning Research 9, 459–483.Google Scholar
Xing-Chen, H., Lei, Q. Z. T., Li-Ping, S. 2007a. Learning Bayesian network structures with discrete particle swarm optimization algorithm. In Proceedings of the IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), Mendel, J. M., Omori, T. & Yao, X. (eds). IEEE, 47–52. doi: 10.1109/FOCI.2007.372146.CrossRefGoogle Scholar
Xing-Chen, H., Zheng, Q., Lei, T., Li-Ping, S. 2007b. Research on structure learning of dynamic Bayesian networks by particle swarm optimization. In Proceedings of the IEEE Symposium on Artificial Life (ALIFE ’07), IEEE, 85–91.CrossRefGoogle Scholar
Yedidia, J. S., Freeman, W. T., Weiss, Y. 2001. Generalized belief propagation. In Advances in Neural Information Processing Systems 13 (NIPS*2000), Leen, T. K., Dietterich, T. G. & Tresp, V. (eds). MIT Press, 689–695.Google Scholar
Yehezkel, R., Lerner, B. 2006. Bayesian network structure learning by recursive autonomy identification. In Proceedings of the Joint IAPR International Workshops on Structural, Syntactic, and Statistical Pattern Recognition (SSPR 2006 and SPR 2006), Lecture Notes in Computer Science 4109, 154–162. Springer.Google Scholar
Yu, K., Wang, H., Wu, X. 2007. A parallel algorithm for learning Bayesian networks. In Proceedings of the Eleventh Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining (PAKDD 2007), Lecture Notes in Artificial Intelligence 4426, 1055–1063. Springer.CrossRefGoogle Scholar
Zhang, J. 2008. Causal reasoning with ancestral graphs. Journal of Machine Learning Research 9, 1437–1474.Google Scholar
Zhang, J., Spirtes, P. 2008. Detection of unfaithfulness and robust causal inference. Minds and Machines 18(2), 239–271.CrossRefGoogle Scholar
Zhang, N. L. 1996. Irrelevance and parameter learning in Bayesian networks. Artificial Intelligence 88(1–2), 359–373.CrossRefGoogle Scholar
Zhang, N. L., Poole, D. 1994a. Intercausal independence and heterogeneous factorization. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI-94), de Mantaras, R. L. & Poole, D. (eds). Morgan Kaufmann, 606–614.Google Scholar
Zhang, N. L., Poole, D. 1994b. A simple approach to Bayesian network computations. In Proceedings of the Tenth Biennial Conference of the Canadian Society for Computational Studies of Intelligence, Banff, Canada, 171–178.Google Scholar
Zhang, N. L., Poole, D. 1996. Exploiting causal independence in Bayesian network inference. Journal of Artificial Intelligence Research 5, 301–328.CrossRefGoogle Scholar
Zhang, N. L., Yan, L. 1998. Independence of causal influence and clique tree propagation. International Journal of Approximate Reasoning 19(3–4), 335–349.CrossRefGoogle Scholar
Ziegler, V. 2008. Approximation algorithms for restricted Bayesian network structures. Information Processing Letters 108(2), 60–63.CrossRefGoogle Scholar
Zuk, O., Margel, S., Domany, E. 2006. On the number of samples needed to learn the correct structure of a Bayesian network. In Proceedings of the Twenty-second Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), Dechter, R. & Richardson, T. (eds). AUAI Press, 560–567.Google Scholar