Testing Bayesian Networks
This work addresses the challenge of efficiently testing complex probabilistic models for researchers in statistics and machine learning, representing a foundational advancement in distribution testing.
The paper tackled the problem of testing high-dimensional structured distributions, specifically identity and closeness testing of Bayesian networks, by developing the first non-trivial efficient testing algorithms with sample complexity sublinear in the dimension, achieving sample-optimal results up to constant factors for a wide range of parameters.
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a directed acyclic graph, where we associate a random variable with each node. The value at any particular node is conditionally independent of all the other non-descendant nodes once its parents are fixed. Specifically, we study the properties of identity testing and closeness testing of Bayesian networks. Our main contribution is the first non-trivial efficient testing algorithms for these problems and corresponding information-theoretic lower bounds. For a wide range of parameter settings, our testing algorithms have sample complexity sublinear in the dimension and are sample-optimal, up to constant factors.