期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 66, 期 9, 页码 5927-5964出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2020.2982499
关键词
Tensors; Estimation; Matrix decomposition; Sparse matrices; Noise measurement; Probability; Image coding; Finite-sample analysis; non-convex optimization; tensor estimation
资金
- NSF [DMS-1712907, DMS-1811812, DMS-1821183, CAREER-1944904, DMS-1811868]
- NIH [R01 GM131399]
- Office of Naval Research (ONR) [N00014-18-2759]
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy case with high probability. The non-asymptotic analysis sheds light on an interplay between optimization error and statistical error. The proposed procedure is shown to be rate-optimal under certain conditions. As a technical by-product, novel high-order concentration inequalities are derived for studying high-moment sub-Gaussian tensors. An interesting tensor formulation illustrates the potential application to high-order interaction pursuit in high-dimensional linear regression.
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