l₁-Norm Quantile Regression Screening Rule via the Dual Circumscribed Sphere

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• L₁-norm quantile regression is valuable for high-dimensional data with outliers or heavy-tailed errors.
• Existing methods face computational challenges with ultra-high dimensional datasets due to the non-differentiability of the quantile function.
• Current screening rules are ineffective for accelerating l₁-norm quantile regression computations.

Purpose of the Study:

• To develop a novel and computationally efficient screening rule for l₁-norm quantile regression.
• To address the computational expense associated with ultra-high dimensional data in quantile regression.
• To improve the speed and scalability of l₁-norm quantile regression analysis.

Main Methods:

• Introduction of the dual circumscribed sphere technique.
• Development of a novel screening rule expressed as a closed-form function of the data.
• Elimination of inactive features using the proposed screening rule.

Main Results:

• The proposed screening rule effectively eliminates a significant portion of inactive features.
• Numerical experiments demonstrate the rule's efficiency on both simulated and real-world datasets.
• Computational time reductions of up to 23 times were observed compared to computations without the screening rule.

Conclusions:

• The novel screening rule offers a computationally efficient solution for l₁-norm quantile regression in high-dimensional settings.
• This technique significantly accelerates the analysis of datasets with outliers or heavy-tailed errors.
• The proposed method enhances the practical applicability of l₁-norm quantile regression for large-scale data.