A Robust Optimization Approach to Statistics and Beyond

Apostolos Fertis
Institute for Operations Research, ETH, Zurich, Switzerland

Thursday, October 15 at 1:00pm
Engr IV Room 57-124

Abstract
Statistical estimators are highly dependent on the accuracy of the data used to produce them. Early on, the need for statistical estimators that are less affected by small deviations from the model which describes the data has been realized. Huber has constructed a qualitative and a quantitative framework to form robust estimators and Hampel has defined the influence curve as a heuristic tool to assess the robustness of estimators. In the meanwhile, regularization has been theoretically and experimentally proved to yield successful statistical estimators, as in the cases of lasso, ridge regression and support vector machines.

In this talk, I present the idea of applying robust optimization to construct statistical estimators that are resistent in errors. I provide a general framework which connects regularized regression estimators with a robust optimization approach and show how to compute robust estimators for logistic regression and the normal distribution parameters. Finally, I extend the same idea to risk management. Coherent risk measures, such as Conditional Value at Risk (CVaR), are calculated through a statistical procedure called sample average approximation. I design robust coherent risk measures in an attempt to make coherent risk measures resistent in the errors of the sample data used to compute them. Finally, I present the idea of applying fast gradient and smoothing techniques to speed up the computation of the robust estimators defined.

Biography
Apostolos Fertis received his Diploma in Electrical and Computer Engineering from the National Technical University of Athens and his MsC and PhD in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology. He is currently a postdoctoral researcher at the Institute for Operations Research in ETH Zurich. His research interests include robust optimization, statistics, risk management, optimization algorithms and economics. He is a member of IEEE, INFORMS and the Mathematical Programming Society.