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

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 lack of meaningful 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 has a long range dependence among its entries, 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.