2021/10/25 by Subhodh Kotekal, Chao Gao, Kotekal, Subhodh +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Bayesian Methods and Mixture Models #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Fractal and DNA sequence analysis #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2110.12966
openalex publication_date 2021/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 √(p) and p-√(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.