Robust Learning of Trimmed Estimators via Manifold Sampling

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss. Empirical results show that the method has favorable scaling properties. Although savings in time come at the expense of not certifying optimality, the algorithm consistently returns high-quality solutions on the trimmed linear regression and multiclass classification problems tested.