MPE inference in conditional linear gaussian networks

Antonio Salmerón, Rafael Rumí, Helge Langseth, Anders Læsø Madsen, Thomas Dyhre Nielsen

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Abstract

Given evidence on a set of variables in a Bayesian network, the most probable explanation (MPE) is the problem of finding a configuration of the remaining variables with maximum posterior probability. This problem has previously been addressed for discrete Bayesian networks and can be solved using inference methods similar to those used for finding posterior probabilities. However, when dealing with hybrid Bayesian networks, such as conditional linear Gaussian (CLG) networks, the MPE problem has only received little attention. In this paper, we provide insights into the general problem of finding an MPE configuration in a CLG network. For solving this problem, we devise an algorithm based on bucket elimination and with the same computational complexity as that of calculating posterior marginals in a CLG network. We illustrate the workings of the algorithm using a detailed numerical example, and discuss possible extensions of the algorithm for handling the more general problem of finding a maximum a posteriori hypothesis (MAP).
Original languageEnglish
Title of host publicationSymbolic and Quantitative Approaches to Reasoning with Uncertainty : 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings
EditorsSébastien Destercke, Thierry Denoeux
PublisherSpringer
Publication date2015
Pages407-416
ISBN (Print)978-3-319-20806-0
ISBN (Electronic)978-3-319-20807-7
DOIs
Publication statusPublished - 2015
EventThe 13th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty - Compiegne, France
Duration: 15 Jul 201517 Jul 2015

Conference

ConferenceThe 13th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
CountryFrance
CityCompiegne
Period15/07/201517/07/2015
SeriesLecture Notes in Computer Science
Number9161
ISSN0302-9743

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Bayesian networks
Computational complexity

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Salmerón, A., Rumí, R., Langseth, H., Madsen, A. L., & Nielsen, T. D. (2015). MPE inference in conditional linear gaussian networks. In S. Destercke, & T. Denoeux (Eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings (pp. 407-416). Springer. Lecture Notes in Computer Science, No. 9161 https://doi.org/10.1007/978-3-319-20807-7_37
Salmerón, Antonio ; Rumí, Rafael ; Langseth, Helge ; Madsen, Anders Læsø ; Nielsen, Thomas Dyhre. / MPE inference in conditional linear gaussian networks. Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings. editor / Sébastien Destercke ; Thierry Denoeux. Springer, 2015. pp. 407-416 (Lecture Notes in Computer Science; No. 9161).
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abstract = "Given evidence on a set of variables in a Bayesian network, the most probable explanation (MPE) is the problem of finding a configuration of the remaining variables with maximum posterior probability. This problem has previously been addressed for discrete Bayesian networks and can be solved using inference methods similar to those used for finding posterior probabilities. However, when dealing with hybrid Bayesian networks, such as conditional linear Gaussian (CLG) networks, the MPE problem has only received little attention. In this paper, we provide insights into the general problem of finding an MPE configuration in a CLG network. For solving this problem, we devise an algorithm based on bucket elimination and with the same computational complexity as that of calculating posterior marginals in a CLG network. We illustrate the workings of the algorithm using a detailed numerical example, and discuss possible extensions of the algorithm for handling the more general problem of finding a maximum a posteriori hypothesis (MAP).",
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Salmerón, A, Rumí, R, Langseth, H, Madsen, AL & Nielsen, TD 2015, MPE inference in conditional linear gaussian networks. in S Destercke & T Denoeux (eds), Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings. Springer, Lecture Notes in Computer Science, no. 9161, pp. 407-416, Compiegne, France, 15/07/2015. https://doi.org/10.1007/978-3-319-20807-7_37

MPE inference in conditional linear gaussian networks. / Salmerón, Antonio; Rumí, Rafael; Langseth, Helge; Madsen, Anders Læsø; Nielsen, Thomas Dyhre.

Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings. ed. / Sébastien Destercke; Thierry Denoeux. Springer, 2015. p. 407-416.

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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T1 - MPE inference in conditional linear gaussian networks

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AU - Rumí, Rafael

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AU - Madsen, Anders Læsø

AU - Nielsen, Thomas Dyhre

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AB - Given evidence on a set of variables in a Bayesian network, the most probable explanation (MPE) is the problem of finding a configuration of the remaining variables with maximum posterior probability. This problem has previously been addressed for discrete Bayesian networks and can be solved using inference methods similar to those used for finding posterior probabilities. However, when dealing with hybrid Bayesian networks, such as conditional linear Gaussian (CLG) networks, the MPE problem has only received little attention. In this paper, we provide insights into the general problem of finding an MPE configuration in a CLG network. For solving this problem, we devise an algorithm based on bucket elimination and with the same computational complexity as that of calculating posterior marginals in a CLG network. We illustrate the workings of the algorithm using a detailed numerical example, and discuss possible extensions of the algorithm for handling the more general problem of finding a maximum a posteriori hypothesis (MAP).

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Salmerón A, Rumí R, Langseth H, Madsen AL, Nielsen TD. MPE inference in conditional linear gaussian networks. In Destercke S, Denoeux T, editors, Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 13th European Conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. Proceedings. Springer. 2015. p. 407-416. (Lecture Notes in Computer Science; No. 9161). https://doi.org/10.1007/978-3-319-20807-7_37