Robust and covariance-assisted tensor response regression

Tensor data analysis is gaining increasing popularity in modern multivariate statistics. When analyzing real-world tensor data, many existing tensor estimation approaches are sensitive to heavy-tailed data and outliers, in addition to the apparent high-dimensionality. In this article, we develop a robust and covariance-assisted tensor response regression model based on a recently proposed tensor t‑distribution to address these issues in tensor data. This model assumes that the tensor regression coefficient has a low-rank structure that can be learned more effectively using the additional covariance information. This enables a fast and robust decomposition-based estimation method. Theoretical analysis and numerical experiments demonstrate the superior performance of our approach. By addressing the heavy-tail, high-order, and high-dimensional issues, our work contributes to robust and effective estimation methods for tensor response regression, with broad applicability in various domains.

Keywords

dimension reduction, envelope method, t-distributions, tensor decomposition

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Research for this paper was supported in part by grants CCF-1908969 and DMS-2053697 from the U.S. National Science Foundation.

Received 29 September 2022

Published 1 February 2024