However,thisoperation can greatly impair the performance of stochastic methods, e.g.

Additionally, prompt-based FT with the PCP outperforms state-of-the-art semi-supervised approaches with greater simplicity, eliminating the need for an iterative process and extra data augmentation. Our further analysis explores the performance lower bound of the PCP and reveals that the advantages of PCP persist across different sizes of models and datasets.

Motivated by this issue, we revisit this classical matrix recovery problem.

Additionally, prompt-based FT with the PCP outperforms state-of-the-art semi-supervised approaches with greater simplicity, eliminating the need for an iterative process and extra data augmentation. Our further analysis explores the performance lower bound of the PCP and reveals that the advantages of PCP persist across different sizes of models and datasets.

We investigate the robust PCA problem of decomposing an observed matrix into the sum of a low-rank and a sparse error matrices via convex programming Principal Component Pursuit (PCP). In contrast to previous studies that assume the support of the error matrix is generated by uniform Bernoulli sampling, we allow non-uniform sampling, i.e., entries of the low-rank matrix are corrupted by errors with unequal probabilities. We characterize conditions on error corruption of each individual entry based on the local incoherence of the low-rank matrix, under which correct matrix decomposition by PCP is guaranteed. Such a refined analysis of robust PCA captures how robust each entry of the low rank matrix combats error corruption. In order to deal with non-uniform error corruption, our technical proof introduces a new weighted norm and develops/exploits the concentration properties that such a norm satisfies.