Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models (or generalized linear models), and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on Maximum Mean Discrepancy minimization. We build two estimators which are both proven to be robust to Huber-type contamination. We obtain a non-asymptotic error bound for one them and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators we derive new results on kernel conditional mean embedding of distributions which are of independent interest.
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；Université Paris-Saclay, CNRS, Univ Evry, Laboratoire de Mathématiques et Modélisation d’Evry（巴黎萨克雷大学，法国国家科学研究中心，埃夫里大学，埃夫里数学与建模实验室）；Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189, CRIStAL（里尔大学，法国国家信息与自动化研究所，法国国家科学研究中心，里尔中央理工学院，CRIStAL实验室）；LPSM of Sorbonne University（索邦大学LPSM）
本文提出了学习理论中回归问题的通用估计的一般研究方法，它在Binev，P.的“Universalgorithms for learning theory Part I：piecewise常数函数“和“Universalgorithms for learning theory Part II：piecewise常数函数“中已有讨论，Cohen，A.，Dahmen，W.，德沃尔河，Temlyakov，V.这种新方法使我们能够改善结果。
