Canal-LASSO: A sparse noise-resilient online linear regression model

Least absolute shrinkage and selection operator (LASSO) is one of the most commonly used methods for shrinkage estimation and variable selection. Robust variable selection methods via penalized regression, such as least absolute deviation LASSO (LAD-LASSO), etc., have gained growing attention in works of literature. However those penalized regression procedures are still sensitive to noisy data. Furthermore, "concept drift" makes learning from streaming data fundamentally different from the traditional batch learning. Focusing on the shrinkage estimation and variable selection tasks on noisy streaming data, this paper presents a noise-resilient online learning regression model, i.e. canal-LASSO. Comparing with the LASSO and LAD-LASSO, canal-LASSO is resistant to noisy data in both explanatory variables and response variables. Extensive simulation studies demonstrate satisfactory sparseness and noise-resilient performances of canal-LASSO.