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arXiv · 1212.2468

Large-Sample Learning of Bayesian Networks is NP-Hard

David Maxwell Chickering·Christopher Meek·David Heckerman
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Abstract

In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to represent the generative distribution exactly. Our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset. We show that identifying high-scoring structures is hard, even when we are given an independence oracle, an inference oracle, and/or an information oracle. Our negative results also apply to the learning of discrete-variable Bayesian networks in which each node has at most k parents, for all k > 3.

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David Maxwell Chickering, Christopher Meek, David Heckerman. 2012-10-19. Large-Sample Learning of Bayesian Networks is NP-Hard. https://arxiv.org/abs/1212.2468

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