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Joint estimation of parameters in Ising Model
November 2, 2018 @ 11:00 am - 12:00 pm
Sumit Mukherjee (Columbia University)
Abstract: Inference in the framework of Ising models has received significant attention in Statistics and Machine Learning in recent years. In this talk we study joint estimation of the inverse temperature parameter β, and the magnetization parameter B, given one realization from the Ising model, under the assumption that the underlying graph of the Ising model is completely specified. We show that if the graph is either irregular or sparse, then both the parameters can be estimated at rate n−1/2 using Besag’s pseudo-likelihood. Conversely, if the underlying graph is dense and regular, we show that no consistent estimates exist for (β, B).
This is joint work with Promit Ghosal from Columbia University.
Biography: Sumit is currently an Assistant Professor in the Statistics Department at Columbia. Prior to this, he received his PhD in Statistics at Stanford, under the guidance of Persi Diaconis.
His research interests lie in the intersection of Theoretical Statistics and Applied Probability. In Statistics, his main focus is developing inferential procedures on probability distributions on combinatorial spaces, such as permutations, graphs, and spin configurations. On the probability side, his main focus is studying persistence of stochastic processes, and graph coloring problems.