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arXiv · 2310.06333

Learning bounded-degree polytrees with known skeleton

Davin Choo·Joy Qiping Yang·Arnab Bhattacharyya·Clément L. Canonne
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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 model. Recently, Bhattacharyya et al. (2021) obtained finite-sample guarantees for recovering tree-structured Bayesian networks, i.e., 1-polytrees. We extend their results by providing an efficient algorithm which learns $d$-polytrees in polynomial time and sample complexity for any bounded $d$ when the underlying undirected graph (skeleton) is known. We complement our algorithm with an information-theoretic sample complexity lower bound, showing that the dependence on the dimension and target accuracy parameters are nearly tight.

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Davin Choo, Joy Qiping Yang, Arnab Bhattacharyya, Clément L. Canonne. 2023-10-10. Learning bounded-degree polytrees with known skeleton. https://arxiv.org/abs/2310.06333

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