Robust multi-outcome regression with correlated covariate blocks using fused LAD-lasso

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• High-dimensional regression models often face challenges with non-normal outcome distributions and outlying observations.
• Simultaneous estimation and variable selection are crucial for understanding complex datasets.
• Covariate data frequently exhibits natural correlation structures, such as in sequential or spatial measurements.

Purpose of the Study:

• To present a robust fused LAD-lasso method designed for multiple outcomes.
• To address the limitations of existing methods when dealing with non-normal data and outliers.
• To incorporate a group fusion penalty for handling correlated covariate blocks in regression.

Main Methods:

• A robust fused Least Absolute Deviations-Lasso (LAD-Lasso) approach for multiple outcomes.
• Implementation of a group fusion penalty to manage correlated covariate blocks and encourage coefficient similarity.
• Utilizing Bayesian Information Criterion (BIC)-type criteria for model selection.

Main Results:

• The proposed method demonstrates robustness against non-normal outcome distributions and outlying observations.
• The group fusion penalty effectively handles correlated covariate structures, particularly in sequential data.
• Extensive simulations confirm the properties and performance of the developed approach.

Conclusions:

• The robust fused LAD-Lasso method offers a powerful tool for variable selection and estimation in high-dimensional, multi-outcome regression.
• The inclusion of a group fusion penalty enhances the method's applicability to data with inherent covariate correlation.
• The approach shows promise for real-world applications, including the analysis of skewed longitudinal data.