Abstract
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.
Citation
Luc Devroye. Abbas Mehrabian. Tommy Reddad. "The minimax learning rates of normal and Ising undirected graphical models." Electron. J. Statist. 14 (1) 2338 - 2361, 2020. https://doi.org/10.1214/20-EJS1721
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