Web: http://arxiv.org/abs/2206.08756

June 20, 2022, 1:12 a.m. | Yuetian Luo, Anru R. Zhang

stat.ML updates on arXiv.org arxiv.org

We study the tensor-on-tensor regression, where the goal is to connect tensor
responses to tensor covariates with a low Tucker rank parameter tensor/matrix
without the prior knowledge of its intrinsic rank. We propose the Riemannian
gradient descent (RGD) and Riemannian Gauss-Newton (RGN) methods and cope with
the challenge of unknown rank by studying the effect of rank
over-parameterization. We provide the first convergence guarantee for the
general tensor-on-tensor regression by showing that RGD and RGN respectively
converge linearly and quadratically …

arxiv computational gap math on optimization regression statistical tensor

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