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Abstract:
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In the era of High Dimensional Statistics, researchers frequently encounter data in the form of Multidimensional Arrays (Tensors). In this paper, we propose a Linear Tensor Regression Model with scalar response, tensor covariate and tensor coefficient, where, we assume that the coefficient-tensor is composed of a Low Tubal-Rank Tensor and a Sparse Tensor. In Tensor Regression framework, this low rank structure on the coefficient-tensor is quite distinct from the one by CP Decomposition and can be visualized as a potential extension of the usual “low-rank plus sparse” approach in matrix regression to the third-order tensor case. We develop a fast and scalable Alternating Minimization algorithm to solve a convex regularized program and provide theoretical results related to the upper bound of the estimation error, after addressing the issue of non-identifiability. The efficacy of our model is demonstrated on both synthetic and real data.
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