2021/01/12 by Di Wang, Yao Zheng, Wang, Di +3 · 6 citations
Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2101.04276
openalex publication_date 2021/01/12 · openalex created_date 2023/11/05 · openalex updated_date 2026/07/28
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper provides a new modeling framework to accomplish this task via autoregression (AR). By considering a low-rank Tucker decomposition for the transition tensor, the proposed tensor AR can flexibly capture the underlying low-dimensional tensor dynamics, providing both substantial dimension reduction and meaningful multi-dimensional dynamic factor interpretations. For this model, we first study several nuclear-norm-regularized estimation methods and derive their non-asymptotic properties under the approximate low-rank setting. In particular, by leveraging the special balanced structure of the transition tensor, a novel convex regularization approach based on the sum of nuclear norms of square matricizations is proposed to efficiently encourage low-rankness of the coefficient tensor. To further improve the estimation efficiency under exact low-rankness, a non-convex estimator is proposed with a gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation studies and an empirical analysis of tensor-valued time series data from multi-category import-export networks demonstrate the advantages of the proposed approach.