Gaussian Process Vine Copulas for Multivariate Dependence

TL;DR

This paper introduces a Bayesian method using sparse Gaussian processes to model conditional dependencies in vine copulas, improving multivariate dependence estimation in high-dimensional data.

Contribution

It relaxes the common independence assumption in vine copulas by learning latent functions for conditional dependencies using Gaussian processes.

Findings

Better estimates of the underlying copula when modeling all conditional dependencies.

Scalable Bayesian inference with expectation propagation.

Improved multivariate dependence modeling on real-world datasets.

Abstract

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.