# High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data

arXiv: https://arxiv.org/abs/2211.11700 · HTML: https://mlsanity.com/paper/2211.11700/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [The Landscape of Empirical Risk for Non-convex Losses](https://mlsanity.com/paper/1607.06534/) (2016)
- [Estimating Time-varying Brain Connectivity Networks from Functional MRI Time Series](https://mlsanity.com/paper/1310.3863/) (2013)
- [High Dimensional Semiparametric Latent Graphical Model for Mixed Data](https://mlsanity.com/paper/1404.7236/) (2014)
- [High-dimensional Mixed Graphical Models](https://mlsanity.com/paper/1304.2810/) (2013)
- [On Semiparametric Exponential Family Graphical Models](https://mlsanity.com/paper/1412.8697/) (2014)
- [Selection and Estimation for Mixed Graphical Models](https://mlsanity.com/paper/1311.0085/) (2013)
- [Rank-based approach for estimating correlations in mixed ordinal data](https://mlsanity.com/paper/1809.06255/) (2018)
- [Regularized joint mixture models](https://mlsanity.com/paper/1908.07869/) (2019)
- [Fast computation of latent correlations](https://mlsanity.com/paper/2006.13875/) (2020)

## Abstract (arXiv)

Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or discrete, including in high-dimensions. However, in many applications data span variables of different types (e.g. continuous, count, binary, ordinal, etc.), whose principled joint analysis is nontrivial. Latent Gaussian copula models, in which all variables are modeled as transformations of underlying jointly Gaussian variables, represent a useful approach. Recent advances have shown how the binary-continuous case can be tackled, but the general mixed variable type regime remains challenging. In this work, we make the simple yet useful observation that classical ideas concerning polychoric and polyserial correlations can be leveraged in a latent Gaussian copula framework. Building on this observation we propose flexible and scalable methodology for data with variables of entirely general mixed type. We study the key properties of the approaches theoretically and empirically, via extensive simulations as well an illustrative application to data from the UK Biobank concerning COVID-19 risk factors.