Global Testing Against Sparse Alternatives under Ising Models

Seminar | April 18 | 4-5 p.m. | 1011 Evans Hall

 Rajarshi Mukherjee, UC Berkeley

 Department of Statistics

We study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the magnetizations of an Ising model and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence (i.e. the coupling constant of the Ising model). The impact of dependence can be illustrated under the Curie-Weiss model where one observes the effect of a "thermodynamic" phase transition. In particular, the critical state exhibits a subtle "blessing of dependence" phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop a testing procedure that is broadly applicable to account for dependence and show that it is asymptotically minimax-separation optimal under some regularity conditions.

This talk is based on joint work with Sumit Mukherjee and Ming Yuan.