Poster
Concentration of Multilinear Functions of the Ising Model with Applications to Network Data
Constantinos Daskalakis · Nishanth Dikkala · Gautam Kamath
Pacific Ballroom #178
Keywords: [ Graphical Models ] [ Theory ] [ Large Deviations and Asymptotic Analysis ]
We prove near-tight concentration of measure for polynomial functions of the Ising model, under high temperature, improving the radius of concentration guaranteed by known results by polynomial factors in the dimension (i.e.~the number of nodes in the Ising model). We show that our results are optimal up to logarithmic factors in the dimension. We obtain our results by extending and strengthening the exchangeable-pairs approach used to prove concentration of measure in this setting by Chatterjee. We demonstrate the efficacy of such functions as statistics for testing the strength of interactions in social networks in both synthetic and real world data.
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