Gaussian Process Vine Copulas for Multivariate Dependence
This work addresses a limitation in multivariate dependence modeling for statisticians and data scientists, though it is incremental as it builds on existing vine copula methods.
The paper tackles the problem of simplifying inference in high-dimensional copula modeling by relaxing the assumption that conditional bivariate copulas are independent from their conditioning variables, resulting in better estimates of the underlying copula on real-world datasets.
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.