Large-Sample Learning of Bayesian Networks is NP-Hard

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 structure for which the model is 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 NPhard, even when any combination of one or more of the following hold: the generative distribution is perfect with respect to some DAG containing hidden variables; we are given an independence oracle; we are given an inference oracle; we are given an information oracle; we restrict potential solutions to structures in which each node has at most k parents, for all k ≥ 3. Our proof relies on a new technical result that we establish in the appendices. In particular, we provide a method f...

• Type: Conference
• Year: 2003
• Where: UAI
• Authors: David Maxwell Chickering, Christopher Meek, David Heckerman
• Keywords: Generative Distribution, Learning Algorithm, Scoring Criterion, UAI 2003, UAI 2008