How SVMs can estimate quantiles and the median

Abstract

We investigate quantile regression based on the pinball loss and the ∊-insensitive loss. For the pinball loss a condition on the data-generating distribution P is given that ensures that the conditional quantiles are approximated with respect to ‖ · ‖1. This result is then used to derive an oracle inequality for an SVM based on the pinball loss. Moreover, we show that SVMs based on the ∊-insensitive loss estimate the conditional median only under certain conditions on P.