Sharp non-asymptotic minimax rates are derived for submatrix detection in Gaussian matrices, with matching upper and lower bounds on the critical signal strength μ* for all parameter configurations.
Then we have ψ12 = 1 s1 log ( 1 +d2s1 s2 2 log (d1 s1 )) ≥1 s1 log ( 1 +d2 s2 ) ≥β12, which yields the desired result
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Minimax optimal submatrix detection: Sharp non-asymptotic rates
Sharp non-asymptotic minimax rates are derived for submatrix detection in Gaussian matrices, with matching upper and lower bounds on the critical signal strength μ* for all parameter configurations.