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Rajarshi MUKHERJEE (University of Berkeley) – “Global Testing Against Sparse Alternatives under Ising Models”
March 5, 2:00 pm - 3:15 pm
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The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 5th of March 2018
Place: Room 3001.
Rajarshi MUKHERJEE (University of Berkeley) “Global Testing Against Sparse Alternatives under Ising Models“
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 is best illustrated under the Curie-Weiss model where we observe 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 optimal under fairly general regularity conditions.
This talk is based on joint work with Sumit Mukherjee and Ming Yuan.
Cristina BUTUCEA, Alexandre TSYBAKOV, Eric MOULINES, Mathieu ROSENBAUM