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Learning the joint dependence of discrete variables is a fundamental problemin machine learning, with many applications including prediction, clusteringand dimensionality reduction. More recently, the framework of copula modelinghas gained popularity due to its modular parametrization of jointdistributions. Among other properties, copulas provide a recipe for combiningflexible models for univariate marginal distributions with parametric familiessuitable for potentially high dimensional dependence structures. Moreradically, the extended rank likelihood approach of Hoff (2007) bypasseslearning marginal models completely when such information is ancillary to thelearning task at hand as in, e.g., standard dimensionality reduction problemsor copula parameter estimation. The main idea is to represent data by theirobservable rank statistics, ignoring any other information from the marginals.Inference is typically done in a Bayesian framework with Gaussian copulas, andit is complicated by the fact this implies sampling within a space where thenumber of constraints increases quadratically with the number of data points.The result is slow mixing when using off-the-shelf Gibbs sampling. We presentan efficient algorithm based on recent advances on constrained HamiltonianMarkov chain Monte Carlo that is simple to implement and does not requirepaying for a quadratic cost in sample size.

Flexible sampling of discrete data correlations without the marginal distributions