The paper establishes matching non-asymptotic minimax upper and lower bounds for the minimal signal strength μ needed to detect an s1 × s2 submatrix in a d1 × d2 Gaussian noise matrix for arbitrary parameter values.
We haveψ12 = log ( 1 + d2 s2 2 log(ed1) ) , and •ϕ12 =d 1 log ( 1 + d2 s2 2 ) ≥ψ12 by Lemma 25.(ii)
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Minimax optimal submatrix detection: Sharp non-asymptotic rates
The paper establishes matching non-asymptotic minimax upper and lower bounds for the minimal signal strength μ needed to detect an s1 × s2 submatrix in a d1 × d2 Gaussian noise matrix for arbitrary parameter values.