Title:An Efficient Dual ADMM for Huber Regression with Fused Lasso Penalty

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.