Minimax Rates for Sparse Signal Detection under Correlation

Speaker: Chao Gao(University of Chicago)

Date: April 30 Sat. 10:00am

Venue: Tencent Meeting Room: 417 340 765     password: 13579

Abstract: We fully characterize the nonasymptotic minimnax 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.