Alignment and matching tests for high-dimensional tensor signals via tensor contraction

TL;DR

This paper introduces a new framework for hypothesis testing of high-dimensional tensor signals using tensor contraction and eigenvalue analysis, addressing challenges posed by high dimensionality and dependence structures.

Contribution

It proposes a novel tensor contraction-based method for hypothesis testing in high-dimensional tensor signals, handling complex dependence structures.

Findings

Effective test statistics derived from eigenvalues of contracted tensors

Addresses long-range dependence in data matrix entries

Provides a new analytical framework for tensor signal testing

Abstract

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and the lack of suitable test statistics. By exploiting a recent tensor contraction method, we propose and validate relevant test statistics using eigenvalues of a data matrix resulting from the tensor contraction. The matrix entries exhibit long-range dependence, which makes the analysis of the matrix challenging, involved, and distinct from standard random matrix theory. Our approach provides a novel framework for addressing hypothesis testing problems in the context of high-dimensional tensor signals.