# Minimax rates for sparse signal detection under correlation

arXiv: https://arxiv.org/abs/2110.12966 · HTML: https://mlsanity.com/paper/2110.12966/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates](https://mlsanity.com/paper/2211.08580/) (2022)
- [Optimal community detection in dense bipartite graphs](https://mlsanity.com/paper/2505.18372/) (2025)
- [Minimax Signal Detection in Sparse Additive Models](https://mlsanity.com/paper/2304.09398/) (2023)

## Abstract (arXiv)

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.