Bayesian Methods in Tensor Analysis

TL;DR

This paper reviews Bayesian methods for tensor analysis, focusing on tensor completion and regression, highlighting their formulation, computation, and theoretical aspects, and discussing future research directions.

Contribution

It provides a comprehensive overview of Bayesian tensor methods, including model formulation, prior choices, and theoretical properties, with insights into future developments.

Findings

Bayesian methods effectively handle tensor completion and regression.

Theoretical properties of Bayesian tensor models are established.

Future research directions include scalable algorithms and new prior models.

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.