Robust Optimization of High-Dimensional Partially Linear Models Using Huber Loss and Elastic Net

Abstract

This paper proposes a new Huber-Elastic-Net regression model for partial linear models to address the complex and diverse characteristics of high-dimensional data. It combines the piecewise flexibility of Huber loss function and the mixed penalty term of elastic network to improve the anti-interference ability of outliers and alleviate multicollinearity among high-dimensional variables. Furthermore, we designed the Alternating Direction Method of Multipliers(ADMM) to solve this optimization problem and proved the convergence of this algorithm under certain conditions. Then, we conducted numerical simulations on two types of high-dimensional data, namely multicollinearity and outliers, to demonstrate the mitigating effect and anti-interference ability of the model, and compared and analyzed it with Lasso and Ridge regression methods. Finally, taking Boston housing price data as an example and comparing it with other models, we validated the effectiveness and practicality of the proposed model.