mlsanityData to 7 Oct 2026

Wasserstein Generative Learning of Conditional Distribution

arXiv 2112.10039 ↗First posted 19 Dec 2021cs.LG math.ST stat.THcited by 24

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Abstract (arXiv)

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a conditional generator to transform a known distribution to the target conditional distribution. The conditional generator is estimated by matching a joint distribution involving the conditional generator and the target joint distribution, using the Wasserstein distance as the discrepancy measure for these joint distributions. We establish non-asymptotic error bound of the conditional sampling distribution generated by the proposed method and show that it is able to mitigate the curse of dimensionality, assuming that the data distribution is supported on a lower-dimensional set. We conduct numerical experiments to validate proposed method and illustrate its applications to conditional sample generation, nonparametric conditional density estimation, prediction uncertainty quantification, bivariate response data, image reconstruction and image generation.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 17 of its 50 references that are in the map. First posted on arXiv 19 Dec 2021.

Builds on

17 of 50 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  3. 2017Improved Training of Wasserstein GANscited by 2,223
  4. 2014Conditional Generative Adversarial Netscited by 2,152
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5 more
  1. 2019Nonlinear Approximation via Compositionscited by 37
  2. 2017Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimationcited by 34
  3. 2019Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inferencecited by 21
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  5. 2021On the capacity of deep generative networks for approximating distributionscited by 19

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Citing papers per year: 2022: 1; 2023: 9; 2024: 7; 2025: 5; 2026: 2.

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  1. 2022CARD: Classification and Regression Diffusion Modelscited by 102
  2. 2023Conditional Optimal Transport on Function Spacescited by 26
  3. 2023Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inferencecited by 19
  4. 2023Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problemscited by 12
  5. 2023Wasserstein Generative Regressioncited by 12
  6. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  7. 2023A generative flow for conditional sampling via optimal transportcited by 7
  8. 2023Consistent Optimal Transport with Empirical Conditional Measurescited by 6
  9. 2024A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)cited by 5
  10. 2023Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distancescited by 3
  11. 2024DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecastingcited by 3
  12. 2024A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Modelscited by 3
12 more
  1. 2025Wasserstein Distributionally Robust Nonparametric Regressioncited by 3
  2. 2023Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Modelscited by 2
  3. 2024Diffusion Boosted Treescited by 2
  4. 2024Deep Limit Model-free Prediction in Regressioncited by 2
  5. 2024Penalized Generative Variable Selectioncited by 1
  6. 2024Deep Generative Demand Learning for Newsvendor and Pricingcited by 0
  7. 2025Learning Counterfactually Fair Models via Improved Generation with Neural Causal Modelscited by 0
  8. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  9. 2025Calibration Prediction Interval for Non-parametric Regression and Neural Networkscited by 0
  10. 2025One-shot Conditional Sampling: MMD meets Nearest Neighborscited by 0
  11. 2026DenoiseRank: Learning to Rank by Diffusion Modelscited by 0
  12. 2026Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensionscited by 0