Trustworthy regularized huber regression for outlier detection

Abstract

Machine learning has developed rapidly and involves many fields, such as signal detection and biological research. However, systems may exist outliers caused by the malicious violation of the attacker during the learning process, which makes machine learning instable and unreliable. Therefore, building a trustworthy model to meet robustness has become an urgent research topic. In this paper, we propose the trustworthy regularized Huber regression by Huber loss and decomposable regularizer under the mean shift model, which can identify and eliminate impacts on outliers and heavy-tailed errors. We establish the consistency and convergence rate of the regularized Huber estimators. The asymptotic property of outliers support recovery is explored in term of false and true discovery rates. Then we design an efficient algorithm by combining the alternating minimization and accelerated proximal gradient method to solve the trustworthy regularized Huber regression. Finally, extensive comparisons on simulation and real datasets demonstrate the superior performances.

Keywords:

• Trustworthy regularized Huber estimator
• outliers
• heavy-tailed errors
• alternating minimization
• accelerated proximal gradient

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 12071022].