mlsanityData to 14 Oct 2026

Wasserstein Generative Regression

arXiv 2306.15163 ↗First posted 27 Jun 2023stat.ML cs.LGcited by 12

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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.

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

10 of 73 references.

References · 10

  1. 2017Improved Training of Wasserstein GANscited by 2,235
  2. 2014Conditional Generative Adversarial Netscited by 2,162
  3. 2016Generative Adversarial Text to Image Synthesiscited by 735
  4. 2019Conformalized Quantile Regressioncited by 629
  5. 2020Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Userscited by 338
  6. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 311
  7. 2021Conformalized Survival Analysiscited by 53
  8. 2021An error analysis of generative adversarial networks for learning distributionscited by 36
  9. 2021Wasserstein Generative Learning of Conditional Distributioncited by 24
  10. 2021Inferential Wasserstein Generative Adversarial Networkscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 8.

12 papers.

  1. 2024A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)cited by 7
  2. 2026Theoretical Analysis of Engression and Reverse Markov Engressioncited by 4
  3. 2026Error Analysis of Neural-Network-Based Engressioncited by 4
  4. 2025Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networkscited by 1
  5. 2026Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regressioncited by 1
  6. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  7. 2025Wasserstein Regression as a Variational Approximation of Probabilistic Trajectories through the Bernstein Basiscited by 0
  8. 2026Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensionscited by 0
  9. 2026Distributional Causal Mediation via Conditional Generative Modelingcited by 0
  10. 2026Generative Predictive Distributions for Time Seriescited by 0
  11. 2026Optimal Mixture-of-Experts Model Averaging for Conditional Generative Modelscited by 0
  12. 2026Semi-Supervised Conditional Diffusion via Label Augmentationcited by 0