Learning Large-Scale Bayesian Networks with the sparsebn Package

The widespread growth of high-dimensional biological data in particular has spurred a renewed interest in the use of graphical models to aid in the discovery of novel biological mechanisms (Bühlmann, Kalisch, and Meier 2014). While the past decade has witnessed tremendous developments towards understanding undirected graphical models (Meinshausen and Bühlmann 2006; Ravikumar, Wainwright, and Lafferty 2010; Yang, Ravikumar, Allen, and Liu 2015), there has been less progress towards understanding directed graphical models--also known as Bayesian networks (BNs) or structural equation models (SEM)--for high-dimensional data with p n. A BN is represented by a directed acyclic graph (DAG), whose structure contains a richer and different set of conditional independence relations than an undirected graph. Moreover, DAGs are commonly used 2 Learning Large-Scale Bayesian Networks with the sparsebn Package in causal inference where the direction of an edge encodes causality. Consequently, there have been continuing efforts in structure learning of directed graphs from data.