Learning Bayesian Networks with Low Rank Conditional Probability Tables
This work addresses the challenge of efficient structure learning in Bayesian networks for applications in probabilistic modeling and inference, representing an incremental improvement through the introduction of low rankness.
The paper tackles the problem of learning the directed structure of a Bayesian network from data, using a black-box model accessed via conditional probability queries, and introduces a 'low rankness' notion for conditional probability tables to enable exact recovery with very few queries, proving correctness, polynomial time, and sample efficiency.
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation of conditional probability tables for the nodes in the Bayesian network, that we call "low rankness". We connect this notion to the Fourier transformation of real valued set functions and propose a method which learns the exact directed structure of a `low rank` Bayesian network using very few queries. We formally prove that our method correctly recovers the true directed structure, runs in polynomial time and only needs polynomial samples with respect to the number of nodes. We also provide further improvements in efficiency if we have access to some observational data.