Online learning for quantile regression and support vector regression

We consider for quantile regression and support vector regression a kernel-based online learning algorithm associated with a sequence of insensitive pinball loss functions. Our error analysis and derived learning rates show quantitatively that the statistical performance of the learning algorithm may vary with the quantile parameter τ$\tau$. In our analysis we overcome the technical difficulty caused by the varying insensitive parameter introduced with a motivation of sparsity.