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.
Then if µ2 <C−1 ∗ d1 s2 1 log ( cd2 s2 ) + cµ s2 log (C∗ 2e ) , it holds E [ exp(µ2XY)1 ( X≥⌈C∗ s2 1 d1 ⌉ )] <α
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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.