A Distributionally Robust Optimization Approach for Outlier Detection

We consider the outlier detection problem in a linear regression setting. Outlying observations can be detected by large residuals but this approach is not robust to large outliers which tend to shift the residual function. Instead, we propose a new Distributionally Robust Optimization (DRO) method addressing this issue. The robust optimization problem reduces to solving a second-order cone programming problem. We prove several generalization guarantees for our solution under mild conditions. Extensive numerical experiments demonstrate that our approach outperforms Huber's robust regression approach.