# Improved Stein Variational Gradient Descent with Importance Weights

arXiv: https://arxiv.org/abs/2210.00462 · HTML: https://mlsanity.com/paper/2210.00462/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 2 Oct 2022.

## Builds on (most cited first, 23 of 23)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [Stein Variational Policy Gradient](https://mlsanity.com/paper/1704.02399/) (2017)
- [Federated Generalized Bayesian Learning via Distributed Stein Variational Gradient Descent](https://mlsanity.com/paper/2009.06419/) (2020)
- [Stein Variational Gradient Descent With Matrix-Valued Kernels](https://mlsanity.com/paper/1910.12794/) (2019)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [Training Deep Energy-Based Models with f-Divergence Minimization](https://mlsanity.com/paper/2003.03463/) (2020)
- [Variational Inference with Tail-adaptive f-Divergence](https://mlsanity.com/paper/1810.11943/) (2018)
- [Sampling with Mirrored Stein Operators](https://mlsanity.com/paper/2106.12506/) (2021)
- [Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Condition](https://mlsanity.com/paper/2206.00508/) (2022)
- [Black-box Importance Sampling](https://mlsanity.com/paper/1610.05247/) (2016)
- [A stochastic version of Stein Variational Gradient Descent for efficient sampling](https://mlsanity.com/paper/1902.03394/) (2019)
- [Stein Variational Adaptive Importance Sampling](https://mlsanity.com/paper/1704.05201/) (2017)
- [Scalable Thompson Sampling via Optimal Transport](https://mlsanity.com/paper/1902.07239/) (2019)
- [Learning Structural Weight Uncertainty for Sequential Decision-Making](https://mlsanity.com/paper/1801.00085/) (2017)

## Built on by (most cited first, 2 of 2)

- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [Towards a Better Theoretical Understanding of Independent Subnetwork Training](https://mlsanity.com/paper/2306.16484/) (2023)

## Abstract (arXiv)

Stein Variational Gradient Descent (SVGD) is a popular sampling algorithm used in various machine learning tasks. It is well known that SVGD arises from a discretization of the kernelized gradient flow of the Kullback-Leibler divergence DKLleft(·midπright), where π is the target distribution. In this work, we propose to enhance SVGD via the introduction of importance weights, which leads to a new method for which we coin the name β-SVGD. In the continuous time and infinite particles regime, the time for this flow to converge to the equilibrium distribution π, quantified by the Stein Fisher information, depends on ρ0 and π very weakly. This is very different from the kernelized gradient flow of Kullback-Leibler divergence, whose time complexity depends on DKLleft(ρ0midπright). Under certain assumptions, we provide a descent lemma for the population limit β-SVGD, which covers the descent lemma for the population limit SVGD when β→ 0. We also illustrate the advantages of β-SVGD over SVGD by experiments.