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Computational and statistical boundaries for submatrix localization in a large noisy matrix. (English) Zbl 1392.62017

The paper deals with the analysis of the interplay between computational efficiency and statistical accuracy in submatrix localization based on a noisy observation of a large matrix. In this respect the authors propose and analyse a new linear time spectral algorithm that identifies the submatrix. They show that the localization problem requires larger signal-to-noise ratio. They also consider a new analysis of a known method that is based on a convex relaxation for comparison with the spectral method.

MSC:

62C20 Minimax procedures in statistical decision theory
90C27 Combinatorial optimization