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 by our assumption onµ2, we have µ2 < cµ s2 log (s2d1 log(cd2 s2 ) cµ2es2 1 ) ≤min k∈A f(k) ≤min k∈A g(k)
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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.