Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption
Lihu Xu, Fang Yao, Qiuran Yao, Huiming Zhang; 24(92):1−46, 2023.
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 deep neural networks. Simulations and real data analysis demonstrate the robustness of log-truncated estimations over standard estimations.
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