Empirical Hardness of Finding Optimal Bayesian Network Structures: Algorithm Selection and Runtime Prediction

Brandon Malone, Kustaa Kangas, Matti Järvisalo, Mikko Koivisto, Petri Myllymäki

Research output: Contribution to journalArticleScientificpeer-review


Various algorithms have been proposed for finding a Bayesian network structure that is guaranteed to maximize a given scoring function. Implementations of state-of-the-art algorithms, solvers, for this Bayesian network structure learning problem rely on adaptive search strategies, such as branch-and-bound and integer linear programming techniques. Thus, the time requirements of the solvers are not well characterized by simple functions of the instance size. Furthermore, no single solver dominates the others in speed. Given a problem instance, it is thus a priori unclear which solver will perform best and how fast it will solve the instance. We show that for a given solver the hardness of a problem instance can be efficiently predicted based on a collection of non-trivial features which go beyond the basic parameters of instance size. Specifically, we train and test statistical models on empirical data, based on the largest evaluation of state-of-the-art exact solvers to date. We demonstrate that we can predict the runtimes to a reasonable degree of accuracy. These predictions enable effective selection of solvers that perform well in terms of runtimes on a particular instance. Thus, this work contributes a highly efficient portfolio solver that makes use of several individual solvers.

Original languageEnglish
JournalMachine Learning
Issue number1
Pages (from-to)247-283
Number of pages37
Publication statusPublished - Jan 2018
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 113 Computer and information sciences
  • Bayesian networks
  • Structure learning
  • Algorithm selection
  • Hyperparameter optimization
  • Empirical hardness
  • Algorithm portfolio
  • Runtime prediction
  • SAT

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