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.
In this case, the problem roughly reduces to the sparse signal detection problem in a standard Gaussian sequence model
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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.