  Gaussian processes constitute a very powerful and well-understood method for
non-parametric regression and classification. In the classical framework, the
training data consists of deterministic vector-valued inputs and the
corresponding (noisy) measurements whose joint distribution is assumed to be
Gaussian. In many practical applications, however, the inputs are either noisy,
i.e., each input is a vector-valued sample from an unknown probability
distribution, or the probability distributions are the inputs. In this paper,
we address Gaussian process regression with inputs given in form of probability
distributions and propose a framework that is based on distances between such
inputs. To this end, we review different admissible distance measures and
provide a numerical example that demonstrates our framework.
