Beyond Moments - Robust Certificates for Affine Transformations

Explore a groundbreaking algorithm for recovering unknown affine transformations of a standard unit hypercube from corrupted random samples in this 49-minute lecture by Santosh Vempala at the Hausdorff Center for Mathematics. Delve into the challenges of robust statistics and learn why traditional moment-based methods fall short in this context. Discover how the presented polynomial-time algorithm achieves optimal total variation distance guarantees in recovering both the transformation and the uncorrupted distribution. Examine the novel robust certificate for affine transformations and its implications for the field. Engage with intriguing open problems in this area of research, based on joint work with He Jia and Pravesh Kothari.