Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two types of robust estimators, the ridge log-truncated M-estimator and the elastic net log-truncated M-estimator. The first estimator is applied to convex regressions such as quantile regression and generalized linear models, while the other one is applied to high dimensional non-convex learning problems such as regressions via …

analysis data data analysis generalized linear machine machine learning networks neural networks paper quantile regression ridge simulations statistical statistics types variance