Learning bounded-degree polytrees with samples

Qiping Yang, Davin Choo, Arnab Bhattacharyya, Clement Louis Canonne

Keywords: Bayesian networks, finite samples, polytrees, learning

TL;DR: We study learning polytrees with bounded in-degree in the finite sample regime.

Abstract:

We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical models. Very recently, Bhattacharyya et al. [2021] obtained finite-sample guarantees for recovering tree-structured Bayesian networks, i.e., 1-polytrees. We considerably extend their results by providing an efficient algorithm which learns d-polytrees in polynomial time and sample complexity when the in-degree d is constant, provided that the underlying undirected graph (skeleton) is known. We complement our algorithm with an information-theoretic lower bound, showing that the dependence of our sample complexity is nearly tight in both the dimension and target accuracy parameters.

Submission Number: 9845