An Efficient Dual ADMM for Huber Regression with Fused Lasso Penalty

TL;DR

This paper introduces an efficient dual ADMM algorithm for robust Huber regression with fused lasso penalty, improving robustness and variable selection in the presence of outliers and sequential sparsity.

Contribution

It develops a novel dual ADMM method for Huber regression with fused lasso, enhancing computational efficiency and robustness in high-dimensional settings.

Findings

Demonstrates superior robustness to outliers in simulations

Achieves accurate variable selection with fused lasso penalty

Shows improved computational efficiency over existing methods

Abstract

The ordinary least squares estimate in linear regression is sensitive to the influence of errors with large variance, which reduces its robustness, especially when dealing with heavy-tailed errors or outliers frequently encountered in real-world scenarios. To address this issue and accommodate the sparsity of coefficients along with their sequential disparities, we combine the adaptive robust Huber loss function with a fused lasso penalty. This combination yields a robust estimator capable of simultaneously achieving estimation and variable selection. Furthermore, we utilize an efficient alternating direction method of multipliers to solve this regression model from a dual perspective. The effectiveness and efficiency of our proposed approach is demonstrated through numerical experiments carried out on both simulated and real datasets.