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

Lihu Xu; Fang Yao; Qiuran Yao; Huiming Zhang

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arXiv · 2201.03182

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

Lihu Xu·Fang Yao·Qiuran Yao·Huiming Zhang

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Abstract

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 type 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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BibTeX RIS

Lihu Xu, Fang Yao, Qiuran Yao, Huiming Zhang. 2022-01-10. Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption. https://arxiv.org/abs/2201.03182

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