Conditional quantile regression with ?1-regularization and e-insensitive pinball loss

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.