On Pruning for Score-Based Bayesian Network Structure Learning

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Abstract

Many algorithms for score-based Bayesian network structure learning (BNSL), in particular exact ones, take as input a collection of potentially optimal parent sets for each variable in the data. Constructing such collections naively is computationally intensive since the number of parent sets grows exponentially with the number of variables. Thus, pruning techniques are not only desirable but essential. While good pruning rules exist for the Bayesian Information Criterion (BIC), current results for the Bayesian Dirichlet equivalent uniform (BDeu) score reduce the search space very modestly, hampering the use of the (often preferred) BDeu. We derive new non-trivial theoretical upper bounds for the BDeu score that considerably improve on the state-of-the-art. Since the new bounds are mathematically proven to be tighter than previous ones and at little extra computational cost, they are a promising addition to BNSL methods.
Original languageEnglish
Pages (from-to)2709-2718
JournalProceedings of Machine Learning Research
Volume108
Publication statusPublished - 2020
Event23rd International Conference on Artificial Intelligence and Statistics - Palermo, Italy
Duration: 3 Jun 20205 Jun 2020

Keywords

  • Statistics - Machine Learning
  • Computer Science - Machine Learning

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