# Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlo

arXiv: https://arxiv.org/abs/2106.11561 · HTML: https://mlsanity.com/paper/2106.11561/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2021.

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

- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference](https://mlsanity.com/paper/2301.11674/) (2023)
- [Conditional Bayesian Quadrature](https://mlsanity.com/paper/2406.16530/) (2024)
- [Compositional simulation-based inference for time series](https://mlsanity.com/paper/2411.02728/) (2024)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [Cost-aware simulation-based inference](https://mlsanity.com/paper/2410.07930/) (2024)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks](https://mlsanity.com/paper/2303.02637/) (2023)
- [A Gradient Flow Perspective on Minimum MMD Estimation](https://mlsanity.com/paper/2607.03871/) (2026)
- [Kernel Quantile Embeddings and Associated Probability Metrics](https://mlsanity.com/paper/2505.20433/) (2025)

## Abstract (arXiv)

Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the generative model. This is for example the case for minimum distance estimation and approximate Bayesian computation. These approaches require sampling a high number of realisations from the model for different parameter values, which can be a significant challenge when simulating is an expensive operation. In this paper, we propose to enhance this approach by enforcing "sample diversity" in simulations of our models. This will be implemented through the use of quasi-Monte Carlo (QMC) point sets. Our key results are sample complexity bounds which demonstrate that, under smoothness conditions on the generator, QMC can significantly reduce the number of samples required to obtain a given level of accuracy when using three of the most common discrepancies: the maximum mean discrepancy, the Wasserstein distance, and the Sinkhorn divergence. This is complemented by a simulation study which highlights that an improved accuracy is sometimes also possible in some settings which are not covered by the theory.