Vine copulas for mixed data : multi-view clustering for mixed data beyond meta-Gaussian dependencies

Abstract

Copulas enable flexible parameterization of multivariate distributions in terms of constituent marginals and dependence families. Vine copulas, hierarchical collections of bivariate copulas, can model a wide variety of dependencies in multivariate data including asymmetric and tail dependencies which the more widely used Gaussian copulas, used in Meta-Gaussian distributions, cannot. However, current inference algorithms for vines cannot fit data with mixed--a combination of continuous, binary and ordinal--features that are common in many domains. We design a new inference algorithm to fit vines on mixed data thereby extending their use to several applications. We illustrate our algorithm by developing a dependency-seeking multi-view clustering model based on Dirichlet Process mixture of vines that generalizes previous models to arbitrary dependencies as well as to mixed marginals. Empirical results on synthetic and real datasets demonstrate the performance on clustering single-view and multi-view data with asymmetric and tail dependencies and with mixed marginals.