# Multivariate Conditional Transformation Models

arXiv: https://arxiv.org/abs/1906.03151 · HTML: https://mlsanity.com/paper/1906.03151/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2019.

## Built on by (most cited first, 8 of 8)

- [Probabilistic Time Series Forecasts with Autoregressive Transformation Models](https://mlsanity.com/paper/2110.08248/) (2021)
- [Distributional Gradient Boosting Machines](https://mlsanity.com/paper/2204.00778/) (2022)
- [Bernstein Flows for Flexible Posteriors in Variational Bayes](https://mlsanity.com/paper/2202.05650/) (2022)
- [Graphical Transformation Models](https://mlsanity.com/paper/2503.17845/) (2025)
- [Additive Covariance Matrix Models: Modelling Regional Electricity Net-Demand in Great Britain](https://mlsanity.com/paper/2211.07451/) (2022)
- [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)
- [Generalized Engression Models](https://mlsanity.com/paper/2610.01823/) (2026)

## Abstract (arXiv)

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that they often rely on rather simplistic assumptions, e.g. a constant dependency structure that is not allowed to vary with the covariates or the restriction to linear dependence between the responses only. We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way conditional on nonlinear effects of covariates. The framework can be embedded into likelihood-based inference, including results on asymptotic normality, and allows the dependence structure to vary with covariates. In addition, the framework scales well beyond bivariate response situations, which were the main focus of most earlier investigations. We illustrate the application of multivariate conditional transformation models in a trivariate analysis of childhood undernutrition and demonstrate empirically that our approach can be beneficial compared to existing benchmarks such that complex truly multivariate data-generating processes can be inferred from observations.