Quantile Regression with Gaussian Kernels

This paper aims at the error analysis of stochastic gradient descent (SGD) for quantile regression, which is associated with a sequence of varying ε-insensitive pinball loss functions and flexible Gaussian kernels. Analyzing sparsity and learning rates will be provided when the target function lies in some Sobolev spaces and a noise condition is satisfied for the underlying probability measure. Our results show that selecting the variance of the Gaussian kernel plays a crucial role in the learning performance of quantile regression algorithms.