# Graphical Transformation Models

arXiv: https://arxiv.org/abs/2503.17845 · HTML: https://mlsanity.com/paper/2503.17845/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 22 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Most Likely Transformations](https://mlsanity.com/paper/1508.06749/) (2015)
- [Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas](https://mlsanity.com/paper/1503.03305/) (2015)
- [Copula & Marginal Flows: Disentangling the Marginal from its Joint](https://mlsanity.com/paper/1907.03361/) (2019)
- [Multivariate Conditional Transformation Models](https://mlsanity.com/paper/1906.03151/) (2019)
- [Bayesian Conditional Transformation Models](https://mlsanity.com/paper/2012.11016/) (2020)
- [Selection of Sparse Vine Copulas in High Dimensions with the Lasso](https://mlsanity.com/paper/1705.05877/) (2017)
- [Bayesian Penalized Transformation Models: Structured Additive Location-Scale Regression for Arbitrary Conditional Distributions](https://mlsanity.com/paper/2404.07440/) (2024)

## Built on by (most cited first, 2 of 2)

- [Hybrid Bernstein Normalizing Flows for Flexible Multivariate Density Regression with Interpretable Marginals](https://mlsanity.com/paper/2505.14164/) (2025)
- [Scalable Learning of Multivariate Distributions via Coresets](https://mlsanity.com/paper/2603.19792/) (2026)

## Abstract (arXiv)

Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the identification of varying conditional independencies. GTMs extend multivariate transformation models by replacing the Gaussian copula with a custom-designed multivariate transformation, offering two major advantages. Firstly, GTMs can capture more complex interdependencies using penalized splines, which also provide an efficient regularization scheme. Secondly, we demonstrate how to approximately regularize GTMs towards pairwise conditional independencies using a lasso penalty, akin to Gaussian graphical models. The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn complex dependencies and identify conditional independencies. Additionally, the model is applied to a benchmark astrophysics dataset, where the GTM demonstrates favorable performance compared to non-parametric vine copulas in learning complex multivariate distributions.