# Deep Generative Quantile Bayes

arXiv: https://arxiv.org/abs/2410.08378 · HTML: https://mlsanity.com/paper/2410.08378/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 59 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [On the regularization of Wasserstein GANs](https://mlsanity.com/paper/1709.08894/) (2017)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)](https://mlsanity.com/paper/2103.01678/) (2021)
- [2-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANs](https://mlsanity.com/paper/1902.07197/) (2019)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Autoregressive Quantile Networks for Generative Modeling](https://mlsanity.com/paper/1806.05575/) (2018)
- [Discriminator optimal transport](https://mlsanity.com/paper/1910.06832/) (2019)
- [Quantile regression with deep ReLU Networks: Estimators and minimax rates](https://mlsanity.com/paper/2010.08236/) (2020)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [Probabilistic Time Series Forecasting with Implicit Quantile Networks](https://mlsanity.com/paper/2107.03743/) (2021)
- [ABC random forests for Bayesian parameter inference](https://mlsanity.com/paper/1605.05537/) (2016)
- [Neural Copula: A unified framework for estimating generic high-dimensional Copula functions](https://mlsanity.com/paper/2205.15031/) (2022)
- [Generative Bayesian Inference with GANs](https://mlsanity.com/paper/2208.12113/) (2022)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [Generative Quantile Regression with Variability Penalty](https://mlsanity.com/paper/2301.03661/) (2023)
- [Tree Bandits for Generative Bayes](https://mlsanity.com/paper/2404.10436/) (2024)

## Built on by (most cited first, 2 of 2)

- [Conditional Flow Matching for Bayesian Posterior Inference](https://mlsanity.com/paper/2510.09534/) (2025)
- [Two-way Guidance: Simultaneous Learning of Summary Statistics for Generative Bayes](https://mlsanity.com/paper/2610.12850/) (2026)

## Abstract (arXiv)

We develop a multivariate posterior sampling procedure through deep generative quantile learning. Simulation proceeds implicitly through a push-forward mapping that can transform i.i.d. random vector samples from the posterior. We utilize Monge-Kantorovich depth in multivariate quantiles to directly sample from Bayesian credible sets, a unique feature not offered by typical posterior sampling methods. To enhance the training of the quantile mapping, we design a neural network that automatically performs summary statistic extraction. This additional neural network structure has performance benefits, including support shrinkage (i.e., contraction of our posterior approximation) as the observation sample size increases. We demonstrate the usefulness of our approach on several examples where the absence of likelihood renders classical MCMC infeasible. Finally, we provide the following frequentist theoretical justifications for our quantile learning framework: {consistency of the estimated vector quantile, of the recovered posterior distribution, and of the corresponding Bayesian credible sets.