Robust PCA: Fundamental Limits and Algorithms

We consider the problem of how to best estimate the low rank component of a low-rank-signal-plus-noise-plus-outliers matrix in the dense and sparse outlier regimes. We derive oracle performance limits and use these to compare the performance of low rank estimation algorithms that utilize hard or soft thresholding for outlier suppression. Hard thresholding is shown to be provably better than soft thresholding in a sense we make precise. This is joint work with Brian Moore.
Since Fall 2009, I am an assistant professor in the Department of Electrical Engineering and Computer Science at the University of Michigan. Prior to that I was at MIT where I received my Masters and PhD in Electrical Engineering and Computer Science as part of the MIT/WHOI Joint Program in Ocean Science and Engineering. I work at the interface of statistical signal processing and random matrix theory with applications such as sonar, radar, wireless communications and machine learning in mind.

I particularly enjoy using random matrix theory to address problems that arise in statistical signal processing. An important component of my work is applying it in real-world settings to tease out low-level signals from sensor, oceanographic, financial and econometric time/frequency measurements/time series. In addition to the satisfaction derived from transforming the theory into practice, real-world settings give us insight into how the underlying techniques can be refined and/or made more robust.