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Graphical models are an important tool in exploring relationships betweenvariables in complex, multivariate data. Methods for learning such graphicalmodels are well developed in the case where all variables are either continuousor discrete, including in high-dimensions. However, in many applications dataspan variables of different types (e.g. continuous, count, binary, ordinal,etc.), whose principled joint analysis is nontrivial. Latent Gaussian copulamodels, in which all variables are modeled as transformations of underlyingjointly Gaussian variables, represent a useful approach. Recent advances haveshown how the binary-continuous case can be tackled, but the general mixedvariable type regime remains challenging. In this work, we make the simple yetuseful observation that classical ideas concerning polychoric and polyserialcorrelations can be leveraged in a latent Gaussian copula framework. Buildingon this observation we propose flexible and scalable methodology for data withvariables of entirely general mixed type. We study the key properties of theapproaches theoretically and empirically, via extensive simulations as well anillustrative application to data from the UK Biobank concerning COVID-19 riskfactors.

High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data