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SUMMARY:Singular Value Decomposition for High-dimensional High-order Data 
 - Anru Zhang (University of Wisconsin-Madison)
DTSTART:20180123T110000Z
DTEND:20180123T120000Z
UID:TALK99025@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:High-dimensional high-order data arise in many modern scientif
 ic applications including genomics\, brain imaging\, and social science. I
 n this talk\, we consider the methods\, theories\, and computations for te
 nsor 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 computatio
 nal limits for tensor SVD under the general scenario. This problem exhibit
 s three different phases according to signal-noise-ratio (SNR)\, and the m
 inimax-optimal statistical and/or computational results are developed&nbsp
 \;in each of the regimes. In addition\, we further consider the sparse ten
 sor singular value decomposition which allows more robust estimation under
  sparsity structural assumptions. A novel sparse tensor alternating thresh
 olding algorithm is proposed. Both the optimal theoretical results and num
 erical analyses are provided to guarantee the performance of the proposed 
 procedure.<br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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