  In this paper we address the problem of learning the structure of a Bayesian
network in domains with continuous variables. This task requires a procedure
for comparing different candidate structures. In the Bayesian framework, this
is done by evaluating the {em marginal likelihood/} of the data given a
candidate structure. This term can be computed in closed-form for standard
parametric families (e.g., Gaussians), and can be approximated, at some
computational cost, for some semi-parametric families (e.g., mixtures of
Gaussians).
  We present a new family of continuous variable probabilistic networks that
are based on {em Gaussian Process/} priors. These priors are semi-parametric in
nature and can learn almost arbitrary noisy functional relations. Using these
priors, we can directly compute marginal likelihoods for structure learning.
The resulting method can discover a wide range of functional dependencies in
multivariate data. We develop the Bayesian score of Gaussian Process Networks
and describe how to learn them from data. We present empirical results on
artificial data as well as on real-life domains with non-linear dependencies.
