Structural tensor-on-tensor regression with interaction effects and its application to a hot rolling process

Abstract This paper proposes a method of Structural Tensor-On-Tensosr regression considering the Interaction effects (STOTI). To alleviate the curse of dimensionality and resolve computational challenge, the STOTI method describes the specific structure of the main and interaction effect tensors indicated by the prior knowledge of the data using corresponding regularization terms on their appropriate modes. We designed an ADMM consensus algorithm to estimate these coefficient tensors. Extensive simulations and a real case study of the hot rolling process verified the superiority of the proposed method in terms of estimation and prediction accuracy.