Statistics and Its Interface

Volume 17 (2024)

Number 2

Special issue on statistical learning of tensor data

Bayesian methods in tensor analysis

Pages: 249 – 274

DOI: https://dx.doi.org/10.4310/23-SII802

Authors

Shi Yiyao (Department of Statistics, University of California, Irvine, Calif., U.S.A.)

Shen Weining (Department of Statistics, University of California, Irvine, Calif., U.S.A.)

Abstract

Tensors, also known as multidimensional arrays, are useful data structures in machine learning and statistics. In recent years, Bayesian methods have emerged as a popular direction for analyzing tensor-valued data since they provide a convenient way to introduce sparsity into the model and conduct uncertainty quantification. In this article, we provide an overview of frequentist and Bayesian methods for solving tensor completion and regression problems, with a focus on Bayesian methods. We review common Bayesian tensor approaches including model formulation, prior assignment, posterior computation, and theoretical properties.We also discuss potential future directions in this field.

Keywords

imaging analysis, posterior inference, recommender system, tensor completion, tensor decomposition, tensor regression

Received 12 February 2023

Accepted 2 June 2023

Published 1 February 2024