Scalable Bayesian Network Structure Learning Using Tsetlin Machine to Constrain the Search Space
Kunal Dumbre, Lei Jiao, Ole-Christoffer Granmo
TL;DR
The paper tackles the scalability bottleneck of constraint-based Bayesian network structure learning by using a Weighted Tsetlin Machine to preselect a small set of highly informative literals per target variable, thereby reducing the number of conditional independence tests. The method identifies the top-2 important variables via a seven-step WTMs workflow and then conducts CI tests only on these variables to construct a causal graph, achieving linear-time scaling with respect to the number of features. Empirical results on bnlearn datasets show substantial reductions in CI tests and competitive precision, recall, and F1 scores across networks of varying size, compared to established baselines. The approach offers a practical pathway to scalable causal discovery in large, categorical datasets, while acknowledging limitations from restricting to the top-2 variables and outlining avenues for adaptive expansion in future work.
Abstract
The PC algorithm is a widely used method in causal inference for learning the structure of Bayesian networks. Despite its popularity, the PC algorithm suffers from significant time complexity, particularly as the size of the dataset increases, which limits its applicability in large-scale real-world problems. In this study, we propose a novel approach that utilises the Tsetlin Machine (TM) to construct Bayesian structures more efficiently. Our method leverages the most significant literals extracted from the TM and performs conditional independence (CI) tests on these selected literals instead of the full set of variables, resulting in a considerable reduction in computational time. We implemented our approach and compared it with various state-of-the-art methods. Our evaluation includes categorical datasets from the bnlearn repository, such as Munin1, Hepar2. The findings indicate that the proposed TM-based method not only reduces computational complexity but also maintains competitive accuracy in causal discovery, making it a viable alternative to traditional PC algorithm implementations by offering improved efficiency without compromising performance.