Minimax rates for sparse signal detection under correlation
Minimax rates for sparse signal detection under correlation
复制标题
相关下稀疏信号检测的极小极大率
DOI：
10.1093/imaiai/iaad044
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Gao, Chao
中科院分区：
文献类型：
--
作者：
Kotekal, Subhodh;Gao, Chao
我们充分刻画了高斯序列模型中稀疏信号检测的非渐近极大极小分离率，推广了Collier，Comminges和Tsybakov的一个结果。作为速率表征的结果，我们发现强相关性是好事，适度相关性是诅咒，而弱相关性是无关的。此外，产生祝福的阈值关联能级在稀疏水平上呈现相变.我们还建立了新的相变出现在极小极大分离率与相关水平的微妙依赖。此外，我们还研究了群结构相关性，并在一个包含多个随机效应的模型中导出了极小极大分离率。结果表明，群结构从根本上改变了等相关情况下的检测问题，在分离率上出现了不同的现象。
We fully characterize the nonasymptotic minimax separation rate for sparse signal detection in the Gaussian sequence model withequicorrelated 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 theandsparsity 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.