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Title: Global testing against sparse alternatives under Ising models Authors:  Rajarshi Mukherjee - Harvard T.H. Chan School of Public Health (United States) [presenting]
Sumit Mukherjee - Columbia University (United States)
Ming Yuan - Columbia University (United States)
Gourab Ray - University of Victoria (Canada)
Abstract: The effect of dependence on detecting sparse signals is studied. In particular, we focus on global testing against sparse alternatives for the magnetizations of an Ising models 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 and underlying network of the Ising model). Moreover, we provide evidence that certain critical states of the model exhibit a subtle ``blessing of dependence'' phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop testing procedures that are broadly applicable to account for general network dependence and show that they are asymptotically minimax-separation optimal in many examples.