Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly m...

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Bibliographic Details
Published in:Journal of computational and graphical statistics 2019-01, Vol.28 (1), p.36-47
Main Authors: Chi, Eric C., Hu, Liuyi, Saibaba, Arvind K., Rao, Arvind U. K.
Format: Article
Language:English
Subjects:
Convex optimization
Degrees of freedom
Hutchinson estimator
Information criterion
Iterative methods
Penalization
Smoothness
Sparse linear systems
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Summary:We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2018.1482763