Structural tensor-on-tensor regression with interaction effects and its application to a hot rolling process
Huihui Miao, Andi Wang, Bing Li, Jianjun Shi
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.
Topics & Concepts
Curse of dimensionalityTensor (intrinsic definition)Regularization (linguistics)Process (computing)RegressionComputer scienceRegression analysisMathematicsAlgorithmMathematical optimizationArtificial intelligenceMachine learningStatisticsOperating systemPure mathematicsTensor decomposition and applicationsAdvanced Neuroimaging Techniques and ApplicationsSparse and Compressive Sensing Techniques