Concentration of multilinear functions of the ising model with applications to network data
Name
NIPS-2017-concentration-of-multilinear-functions-of-the-ising-model-with-applications-to-network-data-Paper.pdf
Description
Published version
Size
336.33 KB
Format
Adobe PDF
Checksum (MD5)
fa9b6bcb5e61a2dd28d657d2cce91b25
Author(s)
Daskalakis, C
Dikkala, N
Kamath, G
Date Issued
January 1, 2017
Journal
Advances in Neural Information Processing Systems
Citation
Daskalakis, C, Dikkala, N and Kamath, G. 2017. "Concentration of multilinear functions of the ising model with applications to network data." Advances in Neural Information Processing Systems, 2017-December.
Version
Final published version
Abstract
© 2017 Neural information processing systems foundation. All rights reserved. We prove near-tight concentration of measure for polynomial functions of the Ising model under high temperature. For any degree d, we show that a degree-d polynomial of a n-spin Ising model exhibits exponential tails that scale as exp(-r2/d) at radius r = Ω(nd/2) Our concentration radius is optimal up to logarithmic factors for constant d, improving known results by polynomial factors in the number of spins. We demonstrate the efficacy of polynomial functions as statistics for testing the strength of interactions in social networks in both synthetic and real world data.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://papers.nips.cc/paper/2017/hash/4e732ced3463d06de0ca9a15b6153677-Abstract.html
