# De-randomizing MCMC dynamics with the diffusion Stein operator

arXiv: https://arxiv.org/abs/2110.03768 · HTML: https://mlsanity.com/paper/2110.03768/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 33 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence](https://mlsanity.com/paper/2006.02509/) (2020)
- [Gradient Estimators for Implicit Models](https://mlsanity.com/paper/1705.07107/) (2017)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [A Unified Particle-Optimization Framework for Scalable Bayesian Sampling](https://mlsanity.com/paper/1805.11659/) (2018)
- [Accelerated Information Gradient flow](https://mlsanity.com/paper/1909.02102/) (2019)
- [High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm](https://mlsanity.com/paper/1908.10859/) (2019)
- [Measuring Sample Quality with Diffusions](https://mlsanity.com/paper/1611.06972/) (2016)
- [Riemannian Stein Variational Gradient Descent for Bayesian Inference](https://mlsanity.com/paper/1711.11216/) (2017)
- [Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory](https://mlsanity.com/paper/1809.01293/) (2018)
- [Is There an Analog of Nesterov Acceleration for MCMC?](https://mlsanity.com/paper/1902.00996/) (2019)
- [Stochastic Gradient MCMC with Repulsive Forces](https://mlsanity.com/paper/1812.00071/) (2018)
- [Understanding MCMC Dynamics as Flows on the Wasserstein Space](https://mlsanity.com/paper/1902.00282/) (2019)

## Built on by (most cited first, 3 of 3)

- [GAD-PVI: A General Accelerated Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2312.16429/) (2023)
- [Input-gradient space particle inference for neural network ensembles](https://mlsanity.com/paper/2306.02775/) (2023)
- [Energy based diffusion generator for efficient sampling of Boltzmann distributions](https://mlsanity.com/paper/2401.02080/) (2024)

## Abstract (arXiv)

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples from a diffusion process because the time evolution of its marginal distributions constitutes a curve that minimizes the KL-divergence via steepest descent in the Wasserstein space. Parallel to LD, Stein variational gradient descent (SVGD) similarly minimizes the KL, albeit endowed with a novel Stein-Wasserstein distance, by deterministically transporting a set of particle samples, thus de-randomizes the stochastic diffusion process. We propose de-randomized kernel-based particle samplers to all diffusion-based samplers known as MCMC dynamics. Following previous work in interpreting MCMC dynamics, we equip the Stein-Wasserstein space with a fiber-Riemannian Poisson structure, with the capacity of characterizing a fiber-gradient Hamiltonian flow that simulates MCMC dynamics. Such dynamics discretizes into generalized SVGD (GSVGD), a Stein-type deterministic particle sampler, with particle updates coinciding with applying the diffusion Stein operator to a kernel function. We demonstrate empirically that GSVGD can de-randomize complex MCMC dynamics, which combine the advantages of auxiliary momentum variables and Riemannian structure, while maintaining the high sample quality from an interacting particle system.