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

TL;DR

This paper introduces an iterative model selection method for biclustered matrix completion that leverages smoothness constraints and graph structures, improving scalability and accuracy in applications like imaging-genomics.

Contribution

It proposes a novel iterative procedure for direct model selection in biclustered matrix completion using information criteria and efficient scaling techniques.

Findings

Effective in simulation studies

Successful application to imaging-genomics data

Improves scalability of matrix completion methods

Abstract

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 in order to select an appropriate amount row and column smoothing, namely 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. We present simulation results and an application to predicting associations in imaging-genomics studies.