Streaming data recovery via Bayesian tensor train decomposition

In this paper, we study a Bayesian tensor train (TT) decomposition method to recover streaming data by approximating the latent structure in high-order streaming data. Drawing on the streaming variational Bayes method, we introduce the TT format into Bayesian tensor decomposition methods for streaming data, and formulate posteriors of TT cores. Thanks to the Bayesian framework of the TT format, the proposed algorithm (SPTT) excels in recovering streaming data with high-order, incomplete, and noisy properties. The experiments in synthetic and real-world datasets show the accuracy of our method compared to state-of-the-art Bayesian tensor decomposition methods for streaming data

Bayesian Methods in Tensor Analysis

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.Comment: 32 pages, 8 figures, 2 table