Change-point detection in Vector-Tensor linear model

Abstract

For high-throughput low-rank data, CANDECOMP/PARAFAC ($\mathrm{CP}$) decomposition is frequently employed to reduce the dimensionality to a manageable level. In this article, we consider a Vector-Tensor linear regression model, where the low-rank structure is expressed through CP decomposition, and the change-point structure is incorporated into the multi-array coefficients. A novel procedure is proposed to jointly detect the change-point and estimate the tensor structure by minimizing the sum of squared residuals. The associated algorithm is developed based on Alternating Least Squares (ALS) algorithm, and is computationally efficient and scalable. Furthermore, we establish the consistency of the change-point estimator under a set of general conditions. Simulations and empirical studies illustrate the validity and effectiveness.