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Singular Value Decomposition for High-dimensional High-order Data

Presented by: 
Anru Zhang University of Wisconsin-Madison
Tuesday 23rd January 2018 - 11:00 to 12:00
INI Seminar Room 2
High-dimensional high-order data arise in many modern scientific applications including genomics, brain imaging, and social science. In this talk, we consider the methods, theories, and computations for tensor singular value decomposition (tensor SVD), which aims to extract the hidden low-rank structure from high-dimensional high-order data. First, comprehensive results are developed on both the statistical and computational limits for tensor SVD under the general scenario. This problem exhibits three different phases according to signal-noise-ratio (SNR), and the minimax-optimal statistical and/or computational results are developed in each of the regimes. In addition, we further consider the sparse tensor singular value decomposition which allows more robust estimation under sparsity structural assumptions. A novel sparse tensor alternating thresholding algorithm is proposed. Both the optimal theoretical results and numerical analyses are provided to guarantee the performance of the proposed procedure.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons