Online updating Huber robust regression for big data streams

Abstract

ABSTRACT Big data streams have garnered significant attention in multiple industries. However, the immense volume and the presence of outliers in high-velocity streaming data pose great challenges to its analysis. To address these concerns, this paper introduces a novel Online Updating Huber Robust Regression algorithm. By efficiently capturing the salient features of new data subsets, a computationally efficient online updating estimator is proposed without the need for storing historical data. Furthermore, by incorporating Huber regression into its framework, the estimator exhibits robustness to heavy-tailed, heterogeneous as well as outlier-contaminated data. Theoretically, the proposed online updating estimator is asymptotically equivalent to an Oracle estimator derived from the entire dataset. Extensive numerical simulations and a real-world data analysis have been conducted to demonstrate the effectiveness and practicality of the proposed method.