Online Updating Huber Robust Regression for Big Data Streams

TL;DR

This paper introduces an online updating Huber robust regression method designed for big data streams, offering computational efficiency and robustness to outliers without needing to store historical data.

Contribution

It develops a novel online updating algorithm that is both computationally efficient and robust to outliers, suitable for high-volume streaming data.

Findings

Estimator is asymptotically equivalent to the Oracle estimator.

Method demonstrates high efficiency in numerical simulations.

Real data analysis confirms robustness and computational advantages.

Abstract

Big data streams are grasping increasing attention with the development of modern science and information technology. Due to the incompatibility of limited computer memory to high volume of streaming data, real-time methods without historical data storage is worth investigating. Moreover, outliers may occur with high velocity data streams generating, calling for more robust analysis. Motivated by these concerns, a novel Online Updating Huber Robust Regression algorithm is proposed in this paper. By extracting key features of new data subsets, it obtains a computational efficient online updating estimator without historical data storage. Meanwhile, by integrating Huber regression into the framework, the estimator is robust to contaminated data streams, such as heavy-tailed or heterogeneous distributed ones as well as cases with outliers. Moreover, the proposed online updating estimator is asymptotically equivalent to Oracle estimator obtained by the entire data and has a lower computation complexity. Extensive numerical simulations and a real data analysis are also conducted to evaluate the estimation and calculation efficiency of the proposed method.