4.6 Article

AN OPTIMAL STATISTICAL AND COMPUTATIONAL FRAMEWORK FOR GENERALIZED TENSOR ESTIMATION

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STATISTICALLY OPTIMAL AND COMPUTATIONALLY EFFICIENT LOW RANK TENSOR COMPLETION FROM NOISY ENTRIES

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Summary: In this article, the author develops methods to estimate a low rank tensor from noisy observations to achieve statistical and computational efficiencies. The fundamental statistical limits of noisy tensor completion are characterized by establishing minimax optimal rates of convergence for estimating a kth order low rank tensor. Additionally, a polynomial-time computable estimating procedure is proposed based on power iteration and a second-order spectral initialization achieving optimal rates of convergence.

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