Dimension selection in tensor decompositions and envelope models

Abstract

The statistical analysis of tensor-valued data has emerged as an area of increasing methodological focus. Tensor decomposition models and low-rank tensor regression models often assume that there exists a low-rank structure of the tensor data or tensor coefficient. Consistent selection of structural dimensions or tensor ranks constitutes a problem of significant theoretical and practical importance. This paper introduces a unified framework for addressing this challenge, applicable across multiple tensor decomposition frameworks and envelope regression models.