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Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates. (arXiv:2211.08580v2 [math.ST] UPDATED)
Nov. 24, 2022, 7:14 a.m. | Julien Chhor, Rajarshi Mukherjee, Subhabrata Sen
stat.ML updates on arXiv.org arxiv.org
Given a heterogeneous Gaussian sequence model with unknown mean $\theta \in
\mathbb R^d$ and known covariance matrix $\Sigma =
\operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$, we study the signal
detection problem against sparse alternatives, for known sparsity $s$. Namely,
we characterize how large $\epsilon^*>0$ should be, in order to distinguish
with high probability the null hypothesis $\theta=0$ from the alternative
composed of $s$-sparse vectors in $\mathbb R^d$, separated from $0$ in $L^t$
norm ($t \geq 1$) by at least $\epsilon^*$. We find minimax upper …
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