Title: A New Approach to Robustness and Flexibility in High-dimensions
Abstract: High-dimensional problems are those where the number of variables to estimate/decide on vastly outnumber the number of observations. Several popular methods for the same impose structural models on the data (e.g. low-rank, sparse, Markov assumptions etc.). These methods however are both very fragile to gross/adversarial corruptions, and overly restrictive in their modeling capability.
We propose the simultaneous use of more than structural model for high-dimensional problems. Our approach yields several new methods that are much more widely applicable, and significantly more robust, than existing ones - often with only slightly larger computational complexity. We present new methods, and corresponding analytical results, for (a) PCA in the presence of arbitrary outliers and corruptions (b) Robust Collaborative filtering © Multiple sparse regression/compressed sensing with partially shared sparsity (d) Graph clustering Our methods are based on convex optimization.
Bio: Sujay Sanghavi is an Assistant Professor in ECE at UT Austin. He obtained his PhD from UIUC in 2006, and was a postdoctoral associate in LIDS, MIT until 2008. Sujay's research lies at the intersection of large-scale networks (communication and social), and statistical machine learning and inference. He got the NSF CAREER award in 2010.