Universal Robust Regression via Maximum Mean Discrepancy

Abstract Many modern datasets are collected automatically and thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as adversarial contamination the data. However, most estimation methods designed for specific model. Notably, many were proposed recently obtain estimators linear models, or generalized few developed very settings, example beta regression sample selection models. In this paper we develop approach arbitrary based on maximum mean discrepancy minimization. We build two which both proven be Huber-type contamination. non-asymptotic error bound them show that it is also contamination, but estimator computationally more expensive use practice than other one. As by-product our theoretical analysis derive results kernel conditional embedding distributions independent interest.