Outlier Detection Using Robust Optimization with Uncertainty Sets Constructed from Risk Measures

Abstract

We consider a robust optimization formulation for the problem of outlier detection, with an uncertainty set determined by the risk preference of the decision maker. This connection between risk measures and uncertainty sets is established in 3. Inspired by this methodology for uncertainty set construction under a distortion risk measure, we propose a regularized optimization problem with a finite number of constraints to estimate a robust regression plane that is less sensitive to outliers. An alternating minimization scheme is applied to solve for the optimal solution. We show that in three different scenarios differentiated by the location of outliers, our Risk Measure-based Robust Optimization (RMRO) approach outperforms the traditionally used robust regression 12 in terms of the estimation accuracy and detection rates.