Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration. (arXiv:2010.02482v2 [math.ST] UPDATED)

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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