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.
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