High Dimensional Quantile Regression

High-dimensional quantile regression extends traditional quantile regression to handle datasets with numerous predictor variables, offering robust statistical modeling resistant to outliers and data heterogeneity. Current research focuses on developing efficient distributed algorithms, particularly addressing the computational challenges posed by the non-smooth loss function, and extending the method to nonlinear models and vector-valued responses using techniques like optimal transport. These advancements improve the accuracy and scalability of quantile regression, impacting diverse fields such as robotics (e.g., safe and reliable teleoperation), and enabling more reliable uncertainty quantification in high-dimensional settings.