# Wasserstein Generative Regression

arXiv: https://arxiv.org/abs/2306.15163 · HTML: https://mlsanity.com/paper/2306.15163/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 73 references that are in the map.
- First posted on arXiv 27 Jun 2023.

## Builds on (most cited first, 10 of 10)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [An error analysis of generative adversarial networks for learning distributions](https://mlsanity.com/paper/2105.13010/) (2021)
- [Wasserstein Generative Learning of Conditional Distribution](https://mlsanity.com/paper/2112.10039/) (2021)
- [Inferential Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/2109.05652/) (2021)

## Built on by (most cited first, 12 of 12)

- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [Theoretical Analysis of Engression and Reverse Markov Engression](https://mlsanity.com/paper/2606.01002/) (2026)
- [Error Analysis of Neural-Network-Based Engression](https://mlsanity.com/paper/2607.27723/) (2026)
- [Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks](https://mlsanity.com/paper/2511.14455/) (2025)
- [Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression](https://mlsanity.com/paper/2609.23789/) (2026)
- [Boosting Statistic Learning with Synthetic Data from Pretrained Large Models](https://mlsanity.com/paper/2505.04992/) (2025)
- [Wasserstein Regression as a Variational Approximation of Probabilistic Trajectories through the Bernstein Basis](https://mlsanity.com/paper/2510.26607/) (2025)
- [Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensions](https://mlsanity.com/paper/2604.21849/) (2026)
- [Distributional Causal Mediation via Conditional Generative Modeling](https://mlsanity.com/paper/2605.01765/) (2026)
- [Generative Predictive Distributions for Time Series](https://mlsanity.com/paper/2606.16773/) (2026)
- [Optimal Mixture-of-Experts Model Averaging for Conditional Generative Models](https://mlsanity.com/paper/2607.04360/) (2026)
- [Semi-Supervised Conditional Diffusion via Label Augmentation](https://mlsanity.com/paper/2607.16685/) (2026)

## Abstract (arXiv)

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning framework, where a conditional generator is a function that can generate samples from a conditional distribution. The main idea is to estimate a conditional generator that satisfies the constraint that it produces a good regression function estimator. We use deep neural networks to model the conditional generator. Our approach can handle problems with multivariate outcomes and covariates, and can be used to construct prediction intervals. We provide theoretical guarantees by deriving non-asymptotic error bounds and the distributional consistency of our approach under suitable assumptions. We also perform numerical experiments with simulated and real data to demonstrate the effectiveness and superiority of our approach over some existing approaches in various scenarios.