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Activity Number: 357 - Contemporary Multivariate Methods
Type: Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #314020
Title: Inference in Higher Order Spin Systems
Author(s): Somabha Mukherjee* and Jaesung Son and Bhaswar Bhattarcharya
Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
Keywords: ising model; curie-weiss model; maximum likelihood estimator; maximum pseudolikelihood estimator; central limit theorem; superefficiency

Inference about the inverse temperature parameter in the Ising spin glass model has received a lot of attention during recent years, starting from the monumental works of Talagrand and the seminal work of Sourav Chatterjee (2007). Most of these works focus on the 2-particle interaction system, where the Hamiltonian is a quadratic form of spins. A more realistic model that appears in lattice gas models in Physics, takes into account p-body interactions for some p larger than 2. In this talk, I will present our recent work, where we provide conditions under which the maximum pseudolikelihood estimator (MPLE) of the inverse temperature beta in the p-spin model is $\sqrt{N}$-consistent, and show what happens for the p-spin Curie-Weiss and the Sherrington-Kirkpatrick models. I will also talk about central limit theorems of the MLE and the MPLE of beta in presence of an external magnetic field in the p-spin Curie Weiss model, compare their asymptotic variances, and show a superefficiency phenomenon. Time permitting, I will talk about estimation in Ising models on dense graphs, where I will draw a link with the theory of large deviation of Bernoulli multilinear forms on dense graphs.

Authors who are presenting talks have a * after their name.

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