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EMNLP '08 Proceedings of the Conference on Empirical Methods in Natural Language Processing
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HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies: short papers - Volume 2
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This paper proposes a framework which unifies graphical model theory and formal language theory through automata theory. Specifically, we propose Bayesian Network Automata (BNAs) as a formal framework for specifying graphical models of arbitrarily large structures, or equivalently, specifying probabilistic grammars in terms of graphical models. BNAs use a formal automaton to specify how to construct an arbitrarily large Bayesian Network by connecting multiple copies of a bounded Bayesian Network. Using a combination of results from graphical models and formal language theory, we show that, for a large class of automata, the complexity of inference with a BNA is bounded by the complexity of inference in the bounded Bayesian Network times the complexity of inference for the equivalent stochastic automaton. This illustrates that BNAs provide a useful framework for developing and analysing models and algorithms for structure prediction.