Learning a tree-structured ising model in order to make predictions
Name
1604.06749.pdf
Description
Accepted version
Size
1.2 MB
Format
Adobe PDF
Checksum (MD5)
7c489fb105e2aec0f95514ad77b66438
Author(s)
Bresler, Guy
Karzand, Mina
Date Issued
April 2020
Journal
Annals of Statistics
Publisher
Institute of Mathematical Statistics
Citation
Bresler, Guy and Mina Karzand. “Learning a tree-structured ising model in order to make predictions.” Annals of Statistics, 48, 2 (April 2020): 713-737 © 2020 The Author(s)
Version
Author's final manuscript
Abstract
We study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables given values of some other subset of variables. Virtually all previous work on graphical model learning has focused on recovering the true underlying graph. We define a distance (“small set TV” or ssTV) between distributions P and Q by taking the maximum, over all subsets S of a given size, of the total variation between the marginals of P and Q on S; this distance captures the accuracy of the prediction task of interest. We derive nonasymptotic bounds on the number of samples needed to get a distribution (from the same class) with small ssTV relative to the one generating the samples. One of the main messages of this paper is that far fewer samples are needed than for recovering the underlying tree, which means that accurate predictions are possible using the wrong tree.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/19-AOS1808
