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Learning the structure of Bayesian networks from data is known to be acomputationally challenging, NP-hard problem. The literature has longinvestigated how to perform structure learning from data containing largenumbers of variables, following a general interest in high-dimensionalapplications ("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 these data sets are notnecessarily high-dimensional, sometimes having only a few tens of variablesdepending on the application. We revisit the computational complexity ofBayesian network structure learning in this setting, showing that the commonchoice of measuring it with the number of estimated local distributions leadsto unrealistic time complexity estimates for the most common class ofscore-based algorithms, greedy search. We then derive more accurate expressionsunder common distributional assumptions. These expressions suggest that thespeed of Bayesian network learning can be improved by taking advantage of theavailability of closed form estimators for local distributions with fewparents. Furthermore, we find that using predictive instead of in-samplegoodness-of-fit scores improves speed; and we confirm that is improves theaccuracy of network reconstruction as well, as previously observed byChickering and Heckerman (2000). We demonstrate these results on largereal-world environmental and epidemiological data; and on reference data setsavailable from public repositories.

Learning Bayesian Networks from Big Data with Greedy Search: Computational Complexity and Efficient Implementation