Going off the Grid: Iterative Model Selection for Biclustered Matrix Completion
This work addresses matrix completion challenges in domains like imaging-genomics, though it is incremental as it builds on existing graph-based smoothing methods.
The paper tackles the problem of matrix completion with side information by introducing an iterative model selection procedure to determine optimal row and column smoothing, resulting in improved performance as demonstrated in simulations and an imaging-genomics application.
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.