# DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework

arXiv: https://arxiv.org/abs/2112.00945 · HTML: https://mlsanity.com/paper/2112.00945/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 21 of 21)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [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)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020)
- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [Accelerating Langevin Sampling with Birth-death](https://mlsanity.com/paper/1905.09863/) (2019)
- [A Unified Particle-Optimization Framework for Scalable Bayesian Sampling](https://mlsanity.com/paper/1805.11659/) (2018)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Accelerated Information Gradient flow](https://mlsanity.com/paper/1909.02102/) (2019)
- [Riemannian Stein Variational Gradient Descent for Bayesian Inference](https://mlsanity.com/paper/1711.11216/) (2017)
- [Global convergence of neuron birth-death dynamics](https://mlsanity.com/paper/1902.01843/) (2019)
- [Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory](https://mlsanity.com/paper/1809.01293/) (2018)
- [Stein Variational Gradient Descent as Moment Matching](https://mlsanity.com/paper/1810.11693/) (2018)
- [Understanding MCMC Dynamics as Flows on the Wasserstein Space](https://mlsanity.com/paper/1902.00282/) (2019)
- [Variance Reduction in Stochastic Particle-Optimization Sampling](https://mlsanity.com/paper/1811.08052/) (2018)
- [Unbalanced Sobolev Descent](https://mlsanity.com/paper/2009.14148/) (2020)
- [Particle Optimization in Stochastic Gradient MCMC](https://mlsanity.com/paper/1711.10927/) (2017)

## Built on by (most cited first, 7 of 7)

- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [GAD-PVI: A General Accelerated Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2312.16429/) (2023)
- [Neural Sinkhorn Gradient Flow](https://mlsanity.com/paper/2401.14069/) (2024)
- [Wasserstein Gradient Flow over Variational Parameter Space for Variational Inference](https://mlsanity.com/paper/2310.16705/) (2023)
- [Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flow](https://mlsanity.com/paper/2406.15762/) (2024)
- [Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective](https://mlsanity.com/paper/2602.01179/) (2026)
- [Bayesian three-dimensional seismic travel-time tomography for active- and passive-source seismic data using physics-informed neural network](https://mlsanity.com/paper/2606.21789/) (2026)

## Abstract (arXiv)

The recently developed Particle-based Variational Inference (ParVI) methods drive the empirical distribution of a set of fixed-weight particles towards a given target distribution π by iteratively updating particles' positions. However, the fixed weight restriction greatly confines the empirical distribution's approximation ability, especially when the particle number is limited. In this paper, we propose to dynamically adjust particles' weights according to a Fisher-Rao reaction flow. We develop a general Dynamic-weight Particle-based Variational Inference (DPVI) framework according to a novel continuous composite flow, which evolves the positions and weights of particles simultaneously. We show that the mean-field limit of our composite flow is actually a Wasserstein-Fisher-Rao gradient flow of certain dissimilarity functional F, which leads to a faster decrease of F than the Wasserstein gradient flow underlying existing fixed-weight ParVIs. By using different finite-particle approximations in our general framework, we derive several efficient DPVI algorithms. The empirical results demonstrate the superiority of our derived DPVI algorithms over their fixed-weight counterparts.