Non UBC
DSpace
Takeru Matsuda
2019-10-09T08:24:02Z
2019-04-11T09:40
I talk about two recent studies on singular value shrinkage.
1. We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are a natural generalization of the Stein prior. Bayes estimators and Bayesian predictive densities based on our priors are minimax and dominate those based on the uniform prior in finite samples. In particular, our priors work well when the true value of the parameter has low rank.
2. We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris. Numerical results demonstrate that the EB algorithm attains at least comparable accuracy to existing algorithms for matrices not close to square and that it works particularly well when the rank is relatively large or the proportion of observed entries is small.
Application to real data also shows the practical utility of the EB algorithm.
https://circle.library.ubc.ca/rest/handle/2429/71866?expand=metadata
30.0 minutes
video/mp4
Author affiliation: University of Tokyo
Banff (Alta.)
10.14288/1.0383325
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Statistics
Singular value shrinkage priors and empirical Bayes matrix completion
Moving Image
http://hdl.handle.net/2429/71866