  Copulas allow to learn marginal distributions separately from the
multivariate dependence structure (copula) that links them together into a
density function. Vine factorizations ease the learning of high-dimensional
copulas by constructing a hierarchy of conditional bivariate copulas. However,
to simplify inference, it is common to assume that each of these conditional
bivariate copulas is independent from its conditioning variables. In this
paper, we relax this assumption by discovering the latent functions that
specify the shape of a conditional copula given its conditioning variables We
learn these functions by following a Bayesian approach based on sparse Gaussian
processes with expectation propagation for scalable, approximate inference.
Experiments on real-world datasets show that, when modeling all conditional
dependencies, we obtain better estimates of the underlying copula of the data.
