  Gaussian processes (GPs) are distributions over functions, which provide a
Bayesian nonparametric approach to regression and classification. In spite of
their success, GPs have limited use in some applications, for example, in some
cases a symmetric distribution with respect to its mean is an unreasonable
model. This implies, for instance, that the mean and the median coincide, while
the mean and median in an asymmetric (skewed) distribution can be different
numbers. In this paper, we propose Skew-Gaussian processes (SkewGPs) as a
non-parametric prior over functions. A SkewGP extends the multivariate Unified
Skew-Normal distribution over finite dimensional vectors to a stochastic
processes. The SkewGP class of distributions includes GPs and, therefore,
SkewGPs inherit all good properties of GPs and increase their flexibility by
allowing asymmetry in the probabilistic model. By exploiting the fact that
SkewGP and probit likelihood are conjugate model, we derive closed form
expressions for the marginal likelihood and predictive distribution of this new
nonparametric classifier. We verify empirically that the proposed SkewGP
classifier provides a better performance than a GP classifier based on either
Laplace's method or Expectation Propagation.
