Level sets and maximum likelihood estimation for the Ising model
Tomasz Skalski, Tomasz Stroi\'nski
TL;DR
This paper characterizes the conditions for the existence of maximum likelihood estimators in the Ising model using level sets and introduces bounds related to the set of uniqueness in combinatorial problems.
Contribution
It provides a complete characterization of MLE existence in the Ising model and new bounds for the smallest set of uniqueness for Rademacher function products.
Findings
Complete characterization of MLE existence in the Ising model
New bounds for the size of the smallest set of uniqueness
Application of level sets to combinatorial problems
Abstract
Bogdan et al. established a new criterion to determine the existence of a maximum likelihood estimator in discrete exponential families. It uses the notion of the set of uniqueness, which allows to apply the problem to the Ising model from statistical mechanics. We propose a full characterization of the existence of the MLE in the Ising model among the level sets used in related combinatorial problems. Then we establish new bounds for the size of the smallest set of uniqueness for the products of Rademacher functions.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Limits and Structures in Graph Theory · Bayesian Methods and Mixture Models