Distribution-Free, Size Adaptive Submatrix Detection with Acceleration

TL;DR

This paper introduces a distribution-free, size-adaptive submatrix detection method that uses permutation tests and an approximation net to efficiently identify elevated submatrices without prior size knowledge, maintaining high statistical power.

Contribution

It presents a novel Bonferroni-type permutation testing procedure that is both distribution-free and adaptive to unknown submatrix sizes, with computational acceleration via an approximation net.

Findings

The proposed test achieves asymptotic power comparable to methods with known submatrix size.

The approximation net accelerates computation without sacrificing first-order power.

The method is distribution-free and adaptable to various data distributions.

Abstract

Given a large matrix containing independent data entries, we consider the problem of detecting a submatrix inside the data matrix that contains larger-than-usual values. Different from previous literature, we do not have exact information about the dimension of the potential elevated submatrix. We propose a Bonferroni type testing procedure based on permutation tests, and show that our proposed test loses no first-order asymptotic power compared to tests with full knowledge of potential elevated submatrix. In order to speed up the calculation during the test, an approximation net is constructed and we show that Bonferroni type permutation test on the approximation net loses no power on the first order asymptotically.