Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm

TL;DR

This paper introduces a new statistical method called SERA for detecting changes in tensor dependence structures, improving testing power and false discovery control in high-dimensional tensor data analysis.

Contribution

The paper proposes a novel sparsity-exploited reranking algorithm (SERA) for tensor dependence alteration detection, applicable to large-scale inference with sparsity, and establishes its theoretical properties.

Findings

SERA effectively controls false discovery rates.

The method shows superior power in simulations.

Applications demonstrate practical utility in scientific data analysis.

Abstract

Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.