Learning bounded-degree polytrees with known skeleton

Fuente: arXiv
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Main Authors: Choo, Davin, Yang, Joy Qiping, Bhattacharyya, Arnab, Canonne, Clément L.
Format: Preprint
Published: 2023
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author Choo, Davin
Yang, Joy Qiping
Bhattacharyya, Arnab
Canonne, Clément L.
author_facet Choo, Davin
Yang, Joy Qiping
Bhattacharyya, Arnab
Canonne, Clément L.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_06333
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Learning bounded-degree polytrees with known skeleton
Choo, Davin
Yang, Joy Qiping
Bhattacharyya, Arnab
Canonne, Clément L.
Machine Learning
Data Structures and Algorithms
Probability
Statistics Theory
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.
title Learning bounded-degree polytrees with known skeleton
topic Machine Learning
Data Structures and Algorithms
Probability
Statistics Theory
url https://arxiv.org/abs/2310.06333