# A Copula Graphical Model for Multi-Attribute Data using Optimal Transport

arXiv: https://arxiv.org/abs/2404.06735 · HTML: https://mlsanity.com/paper/2404.06735/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Plugin Estimation of Smooth Optimal Transport Maps](https://mlsanity.com/paper/2107.12364/) (2021)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance](https://mlsanity.com/paper/2012.05199/) (2020)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation](https://mlsanity.com/paper/1909.08733/) (2019)
- [Large-scale optimal transport map estimation using projection pursuit](https://mlsanity.com/paper/2106.05838/) (2021)
- [Learning Graphs with Monotone Topology Properties and Multiple Connected Components](https://mlsanity.com/paper/1705.10934/) (2017)
- [High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach](https://mlsanity.com/paper/2105.02487/) (2021)
- [An additive graphical model for discrete data](https://mlsanity.com/paper/2112.14674/) (2021)

## Built on by (most cited first, 1 of 1)

- [Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects](https://mlsanity.com/paper/2607.28981/) (2026)

## Abstract (arXiv)

Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional independence between vectors is characterized by blockwise zeros in the precision matrix. To relax the restrictive Gaussian assumption, in this paper, we introduce a novel semiparametric multi-attribute graphical model based on a new copula named Cyclically Monotone Copula. This new copula treats the distribution of the node vectors as multivariate marginals and transforms them into Gaussian distributions based on the optimal transport theory. Since the model allows the node vectors to have arbitrary continuous distributions, it is more flexible than the classical Gaussian copula method that performs coordinatewise Gaussianization. We establish the concentration inequalities of the estimated covariance matrices and provide sufficient conditions for selection consistency of the group graphical lasso estimator. For the setting with high-dimensional attributes, a {Projected Cyclically Monotone Copula} model is proposed to address the curse of dimensionality issue that arises from solving high-dimensional optimal transport problems. Numerical results based on synthetic and real data show the efficiency and flexibility of our methods.