Conditional quantile regression with ℓ1-regularization and e-insensitive pinball loss

Abstract

This paper considers the regularized learning schemes based on ℓ1-regularizer and the ε-insensitive pinball loss in a data dependent hypothesis space. The target is the error analysis for the conditional quantile regression learning. Except for continuity and boundedness, the kernel function is not necessary to satisfy any further regularity conditions. The data dependent nature of the algorithm leads to an extra error term called hypothesis error. By concentration inequality with ℓ2-empirical covering numbers and operator decomposition techniques, satisfied error bounds and convergence rates are explicitly derived.