  Direct quantile regression involves estimating a given quantile of a response
variable as a function of input variables. We present a new framework for
direct quantile regression where a Gaussian process model is learned,
minimising the expected tilted loss function. The integration required in
learning is not analytically tractable so to speed up the learning we employ
the Expectation Propagation algorithm. We describe how this work relates to
other quantile regression methods and apply the method on both synthetic and
real data sets. The method is shown to be competitive with state of the art
methods whilst allowing for the leverage of the full Gaussian process
probabilistic framework.
