We investigate the parameterized complexity of Bayesian Network Structure Learn-1 ing (BNSL), a classical problem that has received significant attention in empirical2 but also purely theoretical studies. We follow up on previous works that have3 analyzed the complexity of BNSL w.r.t. the so-called superstructure of the input.4 While known results imply that BNSL is unlikely to be fixed-parameter tractable5 even when parameterized by the size of a vertex cover in the superstructure, here we6 show that a different kind of parameterization--notably by the size of a feedback7 edge set--yields fixed-parameter tractability. We proceed by showing that this8 result can be strengthened to a localized version of the feedback edge set, and9 provide corresponding lower bounds that complement previous results to provide a10 complexity classification of BNSL w.r.t.

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian network greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. Our novel algorithm accomplishes this task, scaling both to large domains and to large treewidths. Our novel approach consistently outperforms the state of the art on experiments with up to thousands of variables.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/