Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data

Anru Zhang and Rungang Han

Journal of the American Statistical Association, 2019, vol. 114, issue 528, 1708-1725

Abstract: In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named sparse tensor alternating thresholding for singular value decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates. Supplementary materials for this article are available online.

Date: 2019
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DOI: 10.1080/01621459.2018.1527227

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