50th Anniv. Seminar Series on 'Computationally efficient tensor completion with...' by Dr. Dong XIA
posted by Department of Statistics and Actuarial Science for HKU and Public
Event Type: Public Lecture/Forum/Seminar/Workshop/Conference/Symposium
Event Nature: Science & Technology
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
THE UNIVERSITY OF HONG KONG
50th Anniversary Seminar Series
Dr. Dong XIA
Department of Statistics
will give a talk
COMPUTATIONALLY EFFICIENT TENSOR COMPLETION WITH STATISTICAL OPTIMALITY
We develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of noisy tensor completion. Much of the attention has been focused on the fundamental computational challenges often associated with problems involving higher order tensors, yet very little is known about their statistical performance. To fill in this void, in this article, we characterize the fundamental statistical limits of noisy tensor completion by establishing minimax optimal rates of convergence for estimating a k-th order low rank tensor which suggest significant room for improvement over the existing approaches. Furthermore, we propose a polynomial-time computable estimating procedure based upon power iteration and a second-order spectral initialization that achieves the optimal rates of convergence. Our method is fairly easy to implement and numerical experiments are presented to further demonstrate the practical merits of our estimator.
|Venue||Room 301, Run Run Shaw Building, HKU|
Registration is not required.