文章基本信息

标题：The minimax learning rates of normal and Ising undirected graphical models
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作者：Luc Devroye ; Abbas Mehrabian ; Tommy Reddad 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：1
页码：2338-2361
DOI：10.1214/20-EJS1721
语种：English
出版社：Institute of Mathematical Statistics
摘要：Let $G$ be an undirected graph with $m$ edges and $d$ vertices. We show that $d$-dimensional Ising models on $G$ can be learned from $n$ i.i.d. samples within expected total variation distance some constant factor of $\min \{1,\sqrt{(m+d)/n}\}$, and that this rate is optimal. We show that the same rate holds for the class of $d$-dimensional multivariate normal undirected graphical models with respect to $G$. We also identify the optimal rate of $\min \{1,\sqrt{m/n}\}$ for Ising models with no external magnetic field.
关键词：Density estimation; distribution learning; graphical model; Markov random field; Ising model; multivariate normal; Fano’s lemma