Learning Bayesian Networks in the Presence of Structural Side Information
This work addresses computational and statistical challenges in Bayesian network learning for applications where side information is available, offering incremental improvements over existing methods.
The paper tackles the problem of learning Bayesian network structures more efficiently by incorporating structural side information, such as bounds on clique number or diamond-free properties, resulting in polynomial complexity for bounded treewidth networks and outperforming state-of-the-art algorithms in evaluations.
We study the problem of learning a Bayesian network (BN) of a set of variables when structural side information about the system is available. It is well known that learning the structure of a general BN is both computationally and statistically challenging. However, often in many applications, side information about the underlying structure can potentially reduce the learning complexity. In this paper, we develop a recursive constraint-based algorithm that efficiently incorporates such knowledge (i.e., side information) into the learning process. In particular, we study two types of structural side information about the underlying BN: (I) an upper bound on its clique number is known, or (II) it is diamond-free. We provide theoretical guarantees for the learning algorithms, including the worst-case number of tests required in each scenario. As a consequence of our work, we show that bounded treewidth BNs can be learned with polynomial complexity. Furthermore, we evaluate the performance and the scalability of our algorithms in both synthetic and real-world structures and show that they outperform the state-of-the-art structure learning algorithms.