DSI/Department of Statistics Colloquium: Frederic Koehler (UChicago)

Abstract: Suppose we have n i.i.d. random vectors X_1,\ldots, X_n in d dimensions. How large can n be, as a function of d, such that there exists an ellipsoid interpolating all n points? Saunderson, Parrilo, and Willsky conjectured an explicit answer (n ~ d^2/4) for Gaussian data.  Subsequently, many authors made rigorous progress on this question. We study a natural least-squares generalization of ellipsoid fitting, over a general class of data distributions, and solve its high-dimensional limit—- this proves the Gaussian conjecture as a special case. The solution combines in a nice way ideas from high-dimensional probability, statistical learning, and convex geometry + optimization. Based on a joint work with Youngtak Sohn.

Bio: Frederic Koehler is an Assistant Professor of Statistics and Data Science at the University of Chicago. Before joining the University of Chicago, Frederic was a Motwani Postdoctoral Fellow at Stanford University. Prior, he was a research fellow in UC Berkeley’s Simons Institute in the Program on Computational Complexity of Statistical Inference. He received his PHD in Mathematics and Statistics from MIT, where he was coadvised by Ankur Moitra and Elchanan Mossel. Before that, he received his undergraduate degree in Mathematics at Princeton University.

His current research interests include computational learning theory and related topics: probability theory, high-dimensional statistics, optimization, related aspects of statistical physics, etc. In particular, he is very interested in learning and inference in graphical models.