The inferential complexity of Bayesian and credal networks

Authors:
Cassio Polpo De Campos;Fabio Gagliardi Cozman
Affiliations:
Universidade de São Paulo, Escola Politécica and Pontifica Universidade Católica de São Paulo;Universidade de São, Escola Politécica
Venue:
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Year:
2005

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Abstract

This paper presents new results on the complexity of graph-theoretical models that represent probabilities (Bayesian networks) and that represent interval and set valued probabilities (credal networks). We define a new class of networks with bounded width, and introduce a new decision problem for Bayesian networks, the maximin a posteriori. We present new links between the Bayesian and credal networks, and present new results both for Bayesian networks (most probable explanation with observations, maximin a posteriori) and for credal networks (bounds on probabilities a posteriori, most probable explanation with and without observations, maximum a posteriori).