# Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms

arXiv: https://arxiv.org/abs/1610.05683 · HTML: https://mlsanity.com/paper/1610.05683/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2016.

## Built on by (most cited first, 22 of 22)

- [Topic Modelling Meets Deep Neural Networks: A Survey](https://mlsanity.com/paper/2103.00498/) (2021)
- [Differentiable Annealed Importance Sampling and the Perils of Gradient Noise](https://mlsanity.com/paper/2107.10211/) (2021)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [The Sample Complexity of Approximate Rejection Sampling with Applications to Smoothed Online Learning](https://mlsanity.com/paper/2302.04658/) (2023)
- [Continuous normalizing flows on manifolds](https://mlsanity.com/paper/2104.14959/) (2021)
- [Gradient Estimation for Binary Latent Variables via Gradient Variance Clipping](https://mlsanity.com/paper/2208.06124/) (2022)
- [Decorrelate Irrelevant, Purify Relevant: Overcome Textual Spurious Correlations from a Feature Perspective](https://mlsanity.com/paper/2202.08048/) (2022)
- [Reparameterized Variational Rejection Sampling](https://mlsanity.com/paper/2309.14612/) (2023)
- [Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixing](https://mlsanity.com/paper/2310.02340/) (2023)
- [Deep generative modelling of canonical ensemble with differentiable thermal properties](https://mlsanity.com/paper/2404.18404/) (2024)
- [Enhancing Uncertainty Estimation and Interpretability via Bayesian Non-negative Decision Layer](https://mlsanity.com/paper/2505.22199/) (2025)
- [BaRA: Bayesian Adaptive Rank Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2606.29184/) (2026)
- [Optimization of Annealed Importance Sampling Hyperparameters](https://mlsanity.com/paper/2209.13226/) (2022)
- [An Overview on Controllable Text Generation via Variational Auto-Encoders](https://mlsanity.com/paper/2211.07954/) (2022)
- [Spherical Cauchy Variational Autoencoders: Heavy Angular Tails and Exact KL Evaluation](https://mlsanity.com/paper/2506.21278/) (2025)
- [Variational Rejection Particle Filtering](https://mlsanity.com/paper/2103.15343/) (2021)
- [Towards Controllable Agent in MOBA Games with Generative Modeling](https://mlsanity.com/paper/2112.08093/) (2021)
- [A variational autoencoder-based nonnegative matrix factorisation model for deep dictionary learning](https://mlsanity.com/paper/2301.07272/) (2023)
- [Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approach](https://mlsanity.com/paper/2308.16092/) (2023)
- [Distributional Sensitivity Analysis: Enabling Differentiability in Sample-Based Inference](https://mlsanity.com/paper/2508.09347/) (2025)
- [Reparameterization through Coverings and Topological Weight Priors](https://mlsanity.com/paper/2604.23804/) (2026)
- [Implicit Variational Rejection Sampling](https://mlsanity.com/paper/2606.14235/) (2026)

## Abstract (arXiv)

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.