Parallel Algorithms and Generalized Frameworks for Learning Large-Scale Bayesian Networks

Bayesian networks (BNs) are an important subclass of probabilistic graphical models that employ directed acyclic graphs to compactly represent exponential-sized joint probability distributions over a set of random variables. Since BNs enable probabilistic reasoning about interactions between the variables of interest, they have been successfully applied in a wide range of applications in the fields of medical diagnosis, gene networks, cybersecurity, epidemiology, etc. Furthermore, the recent focus on the need for explainability in human-impact decisions made by machine learning (ML) models has led to a push for replacing the prevalent black-box models with inherently interpretable models like BNs for making high-stakes decisions in hitherto unexplored areas. Learning the exact structure of BNs from observational data is an NP-hard problem and therefore a wide range of heuristic algorithms have been developed for this purpose. However, even the heuristic algorithms are computationally intensive. The existing software packages for BN structure learning with implementations of multiple algorithms are either completely sequential or support limited parallelism and can take days to learn BNs with even a few thousand variables. Previous parallelization efforts have focused on one or two algorithms for specific applications and have not resulted in broadly applicable parallel software. This has prevented BNs from becoming a viable alternative to other ML models. In this dissertation, we develop efficient parallel versions of a variety of BN learning algorithms from two categories: six different constraint-based methods and a score-based method for constructing a specialization of BNs known as module networks. We also propose optimizations for the implementations of these parallel algorithms to achieve maximum performance in practice. Our proposed algorithms are scalable to thousands of cores and outperform the previous state-of-the-art by a large margin. We have made the implementations available as open-source software packages that can be used by ML and application-domain researchers for expeditious learning of large-scale BNs.Ph.D