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.

Plus: Meta has been accused of burying research in VR's dangers In May, MIT Technology Review published an unprecedented and comprehensive look at how much energy the AI industry uses--down to a single query. Our reporters and editors traced where AI's carbon footprint stands now, and where it's headed, as AI barrels towards billions of daily users. We've just produced a short video to accompany that investigation. You can read the original full story here, and check out--and share-- the full video on YouTube here . AI is changing the grid. Could it help more than it harms?

Both of these problems have also received attention recently.

Bad actors, primarily distressed firms, have the incentive and desire to manipulate their financial reports to hide their distress and derive personal gains. As attackers, these firms are motivated by potentially millions of dollars and the availability of many publicly disclosed and used financial modeling frameworks. Existing attack methods do not work on this data due to anti-correlated objectives that must both be satisfied for the attacker to succeed. We introduce Maximum Violated Multi-Objective (MVMO) attacks that adapt the attacker's search direction to find $20\times$ more satisfying attacks compared to standard attacks. The result is that in $\approx50\%$ of cases, a company could inflate their earnings by 100-200%, while simultaneously reducing their fraud scores by 15%. By working with lawyers and professional accountants, we ensure our threat model is realistic to how such frauds are performed in practice.