Learning Bayesian Networks from Big Data with Greedy Search: Computational Complexity and Efficient Implementation
share
Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables, following a general interest in high-dimensional applications ("small n, large p") in systems biology and genetics. More recently, data sets with large numbers of observations (the so-called "big data") have become increasingly common; and many of these data sets are not high-dimensional, having only a few tens of variables. We revisit the computational complexity of Bayesian network structure learning in this setting, showing that the common choice of measuring it with the number of estimated local distributions leads to unrealistic time complexity estimates for the most common class of score-based algorithms, greedy search. We then derive more accurate expressions under common distributional assumptions. These expressions suggest that the speed of Bayesian network learning can be improved by taking advantage of the availability of closed form estimators for local distributions with few parents. Furthermore, we find that using predictive instead of in-sample goodness-of-fit scores improves both speed and accuracy at the same time. We demonstrate these results on large real-world environmental data and on reference data sets available from public repositories.
READ FULL TEXT