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 type of robust estimators, the ridge log-truncated M-estimator and the elas...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Xu, Lihu, Yao, Fang, Yao, Qiuran, Zhang, Huiming
Format: Article
Language:English
Subjects:
Algorithms
Artificial neural networks
Data analysis
Estimators
Generalized linear models
Machine learning
Robustness (mathematics)
Statistical analysis
Statistical models
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422