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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 27 / No. 1: Twenty-Seventh AAAI Conference on Artificial Intelligence

Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks

March 8, 2023

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Authors

Cassio de Campos

Dalle Molle Institute for Artificial Intelligence


Fabio Cozman

University of Sao Paulo


DOI:

10.1609/aaai.v27i1.8645


Abstract:

Semi-qualitative probabilistic networks (SQPNs) merge two important graphical model formalisms: Bayesian networks and qualitative probabilistic networks. They provide a very general modeling framework by allowing the combination of numeric and qualitative assessments over a discrete domain, and can be compactly encoded by exploiting the same factorization of joint probability distributions that are behind the Bayesian networks.  This paper explores the computational complexity of semi-qualitative probabilistic networks, and takes the polytree-shaped networks as its main target. We show that the inference problem is coNP-Complete for binary polytrees with multiple observed nodes. We also show that inferences can be performed in time linear in the number of nodes if there is a single observed node. Because our proof is constructive, we obtain an efficient linear time algorithm for SQPNs under such assumptions. To the best of our knowledge, this is the first exact polynomial-time algorithm for SQPNs. Together these results provide a clear picture of the inferential complexity in polytree-shaped SQPNs.

Topics: AAAI

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HOW TO CITE:

Cassio de Campos|| Fabio Cozman Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks Proceedings of the AAAI Conference on Artificial Intelligence, 27 (2013) 217.

Cassio de Campos|| Fabio Cozman Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks AAAI 2013, 217.

Cassio de Campos|| Fabio Cozman (2013). Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 27, 217.

Cassio de Campos|| Fabio Cozman. Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 27 2013 p.217.

Cassio de Campos|| Fabio Cozman. 2013. Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks. "Proceedings of the AAAI Conference on Artificial Intelligence, 27". 217.

Cassio de Campos|| Fabio Cozman. (2013) "Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks", Proceedings of the AAAI Conference on Artificial Intelligence, 27, p.217

Cassio de Campos|| Fabio Cozman, "Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks", AAAI, p.217, 2013.

Cassio de Campos|| Fabio Cozman. "Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks". Proceedings of the AAAI Conference on Artificial Intelligence, 27, 2013, p.217.

Cassio de Campos|| Fabio Cozman. "Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks". Proceedings of the AAAI Conference on Artificial Intelligence, 27, (2013): 217.

Cassio de Campos|| Fabio Cozman. Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks. AAAI[Internet]. 2013[cited 2023]; 217.


ISSN: 2374-3468


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