Web: http://arxiv.org/abs/2010.02482

Jan. 26, 2022, 2:11 a.m. | Yuchen Zhou, Anru R. Zhang, Lili Zheng, Yazhen Wang

cs.LG updates on arXiv.org arxiv.org

This paper studies a general framework for high-order tensor SVD. We propose
a new computationally efficient algorithm, tensor-train orthogonal iteration
(TTOI), that aims to estimate the low tensor-train rank structure from the
noisy high-order tensor observation. The proposed TTOI consists of
initialization via TT-SVD (Oseledets, 2011) and new iterative backward/forward
updates. We develop the general upper bound on estimation error for TTOI with
the support of several new representation lemmas on tensor matricizations. By
developing a matching information-theoretic lower bound, …

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