41: An interpretable and efficient autoregressive model for high-dimensional tensor-valued time series

Music City Center 

The increasing availability of tensor-valued time series data has created new challenges for statistical modeling, particularly when both responses and covariates are high-dimensional and high-order tensors. To address the issues of over-parameterization and limited sample sizes, this paper introduces a novel CP-based low-rank structure for coefficient tensors in tensor-on-tensor regression and autoregressive models. The method uses CP decomposition to extract features from responses and covariates, enabling a supervised factor modeling framework that enhances both interpretability and estimation efficiency. The method further incorporates a sparse component to account for heterogeneous signals and potential model misspecifications. Estimation is performed using the alternating least squares (ALS) algorithm with updates cast as linear regression problems. Non-asymptotic estimation error bounds are established, and simulations and a real-world ENSO dataset confirm the method's effectiveness.

CP decomposition

ENSO area detection

High-dimensional time series data

Low-rank plus sparse modeling

Tensor autoregression 

Section on Statistical Learning and Data Science