# Stein Variational Inference for Discrete Distributions

arXiv: https://arxiv.org/abs/2003.00605 · HTML: https://mlsanity.com/paper/2003.00605/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2020.

## Built on by (most cited first, 16 of 16)

- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [Discrete Langevin Sampler via Wasserstein Gradient Flow](https://mlsanity.com/paper/2206.14897/) (2022)
- [Amortized Variational Inference: A Systematic Review](https://mlsanity.com/paper/2209.10888/) (2022)
- [Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling](https://mlsanity.com/paper/2205.14283/) (2022)
- [Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent](https://mlsanity.com/paper/2106.07832/) (2021)
- [Optimal Scaling for Locally Balanced Proposals in Discrete Spaces](https://mlsanity.com/paper/2209.08183/) (2022)
- [Efficient Informed Proposals for Discrete Distributions via Newton's Series Approximation](https://mlsanity.com/paper/2302.13929/) (2023)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [Stein Variational Gradient Descent with Multiple Kernel](https://mlsanity.com/paper/2107.09338/) (2021)
- [STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent](https://mlsanity.com/paper/2310.01775/) (2023)
- [Streaming Bayes GFlowNets](https://mlsanity.com/paper/2411.05899/) (2024)
- [CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver](https://mlsanity.com/paper/2403.03391/) (2024)
- [Factor Representation and Decision Making in Stock Markets Using Deep Reinforcement Learning](https://mlsanity.com/paper/2108.01758/) (2021)
- [Branching Stein Variational Gradient Descent for sampling multimodal distributions](https://mlsanity.com/paper/2506.13916/) (2025)

## Abstract (arXiv)

Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be directly applied to discrete distributions. In this work, we fill this gap by proposing a simple yet general framework that transforms discrete distributions to equivalent piecewise continuous distributions, on which the gradient-free SVGD is applied to perform efficient approximate inference. The empirical results show that our method outperforms traditional algorithms such as Gibbs sampling and discontinuous Hamiltonian Monte Carlo on various challenging benchmarks of discrete graphical models. We demonstrate that our method provides a promising tool for learning ensembles of binarized neural network (BNN), outperforming other widely used ensemble methods on learning binarized AlexNet on CIFAR-10 dataset. In addition, such transform can be straightforwardly employed in gradient-free kernelized Stein discrepancy to perform goodness-of-fit (GOF) test on discrete distributions. Our proposed method outperforms existing GOF test methods for intractable discrete distributions.