"Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functions"Ke WeiExisting analysis of the non-convex methods for robust matrix completion (RMC) problem either requires the explicit but empirically redundant regularization in the algorithm or requires sample splitting in the analysis. In contrast, we provide the first projection and sample splitting free analysis on a nonconvex RMC method with general thresholding functions through the leave-one-out technique. When applying our result to low rank matrix completion, it substantially improves the sampling complexity of existing result for the singular value projection method. The theoretical result is achieved by a refined analysis that relaxes the requirement on the distance to the ground truth, as well as more effective technique tools we adopt and develop. |
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