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Minimax rates for sparse signal detection under correlation

2022-04-22

Speaker: GAO ChaoAssistant Professor, Department of Statistics and the College, University of Chicago

Venue: Tencent meeting ID: 417-340-765 (Code: 13579)

Abstract:

We fully characterize the nonasymptotic minimax separation rate for sparse signal detection in the Gaussian sequence model with p equicorrelated observations, generalizing a result of Collier, Comminges, and Tsybakov. As a consequence of the rate characterization, we find that strong correlation is a blessing, moderate correlation is a curse, and weak correlation is irrelevant. Moreover, the threshold correlation level yielding a blessing exhibits phase transitions at the \sqrt{p} and p-\sqrt{p} sparsity levels. We also establish the emergence of new phase transitions in the minimax separation rate with a subtle dependence on the correlation level. Additionally, we study group structured correlations and derive the minimax separation rate in a model including multiple random effects. The group structure turns out to fundamentally change the detection problem from the equicorrelated case and different phenomena appear in the separation rate.