NDLI: Learning Markov graphs up to edit distance

Content Provider	IEEE Xplore Digital Library
Author	Das, A.K. Netrapalli, P. Sanghavi, S. Vishwanath, S.
Copyright Year	2012
Description	Author affiliation: Department of ECE, The University of Texas at Austin, USA (Das, A.K.; Netrapalli, P.; Sanghavi, S.; Vishwanath, S.)
Abstract	This paper presents a rate distortion approach to Markov graph learning. It provides lower bounds on the number of samples required for any algorithm to learn the Markov graph structure of a probability distribution, up to edit distance. We first prove a general result for any probability distribution, and then specialize it for Ising and Gaussian models. In particular, for both Ising and Gaussian models on p variables with degree at most d, we show that at least Ω((d − s/p)log p) samples are required for any algorithm to learn the graph structure up to edit distance s. Our bounds represent a strong converse; i.e., we show that for a lower number of samples, the probability of error goes to 1 as the problem size increases. These results show that substantial gains in sample complexity may not be possible without paying a significant price in edit distance error.
Starting Page	2731
Ending Page	2735
File Size	151498
Page Count	5
File Format	PDF
ISBN	9781467325806
ISSN	21578117
e-ISBN	9781467325790
e-ISBN	9781467325783
DOI	10.1109/ISIT.2012.6284018
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Markov random fields Graphical models Complexity theory Computational modeling Vectors Covariance matrix Gaussian Markov model Markov networks graphical models strong converse Ising model
Content Type	Text
Resource Type	Article

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