Learning bounded-degree polytrees with known skeleton

• URL: http://arxiv.org/abs/2310.06333v2
• Date: Mon, 22 Jan 2024 02:22:12 GMT
• Title: Learning bounded-degree polytrees with known skeleton
• Authors: Davin Choo, Joy Qiping Yang, Arnab Bhattacharyya, Cl\'ement L. Canonne
• Abstract summary: We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees. We provide an efficient algorithm which learns $d$-polytrees in time and sample complexity for any bounded $d$ when the underlying undirected graph is known.
• Score: 15.137372516678143
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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