Selecting Optimal Completion to Partial Matrix via Self Validation

In many applications such as film recommendation, one often encounters the problem of estimating the unseen entries in a partially observed matrix, formally known as matrix completion. Over the past several decades, lots of effective methods have been established in the literature, and each method may contain several hyper-parameters. For a partial matrix, one can use those methods with certain parametric settings to obtain a large number of completions. Now, a critical question is, how to select the optimal completion from a number of candidates ? This question is indeed a hard to answer, because in practice the true values of the missing entries are unknown. Thus far, the only approach for dealing with the issue is through data-validation , which is to first split the observations into two subsets, a training set and a validation set, and then choose the model that performs best on the validation set as the winner to …