Matrix Completion with Noisy Entries and Outliers
This addresses robust matrix completion for applications like image inpainting, but it is incremental as it builds on existing robust statistics methods.
The paper tackles matrix completion with noisy entries and outliers by introducing a new optimization criterion using the Huber function to downweigh outliers, and develops a fast, monotonic convergent algorithm with theoretical stability and promising empirical performance in simulations like image inpainting.
This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to downweigh the effects of outliers. A practical algorithm is developed to solve the optimization involved. This algorithm is fast, straightforward to implement, and monotonic convergent. Furthermore, the proposed methodology is theoretically shown to be stable in a well defined sense. Its promising empirical performance is demonstrated via a sequence of simulation experiments, including image inpainting.