# Deep Conditional Transformation Models

arXiv: https://arxiv.org/abs/2010.07860 · HTML: https://mlsanity.com/paper/2010.07860/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 23 of 23)

- [deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression](https://mlsanity.com/paper/2104.02705/) (2021)
- [A New PHO-rmula for Improved Performance of Semi-Structured Networks](https://mlsanity.com/paper/2306.00522/) (2023)
- [Combining Graph Neural Networks and Spatio-temporal Disease Models to Predict COVID-19 Cases in Germany](https://mlsanity.com/paper/2101.00661/) (2021)
- [Probabilistic Time Series Forecasts with Autoregressive Transformation Models](https://mlsanity.com/paper/2110.08248/) (2021)
- [Robust normalizing flows using Bernstein-type polynomials](https://mlsanity.com/paper/2102.03509/) (2021)
- [Distributional Gradient Boosting Machines](https://mlsanity.com/paper/2204.00778/) (2022)
- [Deep interpretable ensembles](https://mlsanity.com/paper/2205.12729/) (2022)
- [Interpretable Neural Causal Models with TRAM-DAGs](https://mlsanity.com/paper/2503.16206/) (2025)
- [TranSUN: A Preemptive Paradigm to Eradicate Retransformation Bias Intrinsically from Regression Models in Recommender Systems](https://mlsanity.com/paper/2505.13881/) (2025)
- [Bernstein Flows for Flexible Posteriors in Variational Bayes](https://mlsanity.com/paper/2202.05650/) (2022)
- [Deep conditional transformation models for survival analysis](https://mlsanity.com/paper/2210.11366/) (2022)
- [Bayesian Semi-structured Subspace Inference](https://mlsanity.com/paper/2401.12950/) (2024)
- [How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression](https://mlsanity.com/paper/2405.05429/) (2024)
- [Additive Higher-Order Factorization Machines](https://mlsanity.com/paper/2205.14515/) (2022)
- [An interpretable neural network-based non-proportional odds model for ordinal regression](https://mlsanity.com/paper/2303.17823/) (2023)
- [Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks](https://mlsanity.com/paper/2511.14455/) (2025)
- [Transformation Models for Flexible Posteriors in Variational Bayes](https://mlsanity.com/paper/2106.00528/) (2021)
- [Generalizing Orthogonalization for Models with Non-Linearities](https://mlsanity.com/paper/2405.02475/) (2024)
- [A Functional Extension of Semi-Structured Networks](https://mlsanity.com/paper/2410.05430/) (2024)
- [Explainability in mulimodal deep transformation models for stroke outcome prediction](https://mlsanity.com/paper/2504.06299/) (2025)
- [Hybrid Bernstein Normalizing Flows for Flexible Multivariate Density Regression with Interpretable Marginals](https://mlsanity.com/paper/2505.14164/) (2025)
- [Conditional Rank-Rank Regression via Deep Conditional Transformation Models](https://mlsanity.com/paper/2603.07230/) (2026)
- [Transfer Learning in Nonparametric Regression with Deep ReLU Networks](https://mlsanity.com/paper/2608.20255/) (2026)

## Abstract (arXiv)

Learning the cumulative distribution function (CDF) of an outcome variable conditional on a set of features remains challenging, especially in high-dimensional settings. Conditional transformation models provide a semi-parametric approach that allows to model a large class of conditional CDFs without an explicit parametric distribution assumption and with only a few parameters. Existing estimation approaches within this class are, however, either limited in their complexity and applicability to unstructured data sources such as images or text, lack interpretability, or are restricted to certain types of outcomes. We close this gap by introducing the class of deep conditional transformation models which unifies existing approaches and allows to learn both interpretable (non-)linear model terms and more complex neural network predictors in one holistic framework. To this end we propose a novel network architecture, provide details on different model definitions and derive suitable constraints as well as network regularization terms. We demonstrate the efficacy of our approach through numerical experiments and applications.