# A stochastic Stein Variational Newton method

arXiv: https://arxiv.org/abs/2204.09039 · HTML: https://mlsanity.com/paper/2204.09039/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 19 Apr 2022.

## Builds on (most cited first, 22 of 22)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [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)
- [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)
- [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)
- [Projected Stein Variational Gradient Descent](https://mlsanity.com/paper/2002.03469/) (2020)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Riemannian Stein Variational Gradient Descent for Bayesian Inference](https://mlsanity.com/paper/1711.11216/) (2017)
- [Information Newton's flow: second-order optimization method in probability space](https://mlsanity.com/paper/2001.04341/) (2020)
- [Projected Stein Variational Newton: A Fast and Scalable Bayesian Inference Method in High Dimensions](https://mlsanity.com/paper/1901.08659/) (2019)
- [Stochastic Gradient MCMC with Repulsive Forces](https://mlsanity.com/paper/1812.00071/) (2018)
- [Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation](https://mlsanity.com/paper/1704.03459/) (2017)
- [Stein Variational Gradient Descent as Moment Matching](https://mlsanity.com/paper/1810.11693/) (2018)
- [Stochastic Quasi-Newton Langevin Monte Carlo](https://mlsanity.com/paper/1602.03442/) (2016)
- [Understanding MCMC Dynamics as Flows on the Wasserstein Space](https://mlsanity.com/paper/1902.00282/) (2019)
- [Online, Informative MCMC Thinning with Kernelized Stein Discrepancy](https://mlsanity.com/paper/2201.07130/) (2022)
- [Stein Variational Gaussian Processes](https://mlsanity.com/paper/2009.12141/) (2020)
- [Variations of Q-Q Plots -- The Power of our Eyes!](https://mlsanity.com/paper/1503.02098/) (2015)

## Built on by (most cited first, 4 of 4)

- [Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learning](https://mlsanity.com/paper/2405.09536/) (2024)
- [Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network models](https://mlsanity.com/paper/2407.00761/) (2024)
- [Condensed Stein Variational Gradient Descent for Uncertainty Quantification of Neural Networks](https://mlsanity.com/paper/2412.16462/) (2024)
- [Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversion](https://mlsanity.com/paper/2212.14595/) (2022)

## Abstract (arXiv)

Stein variational gradient descent (SVGD) is a general-purpose optimization-based sampling algorithm that has recently exploded in popularity, but is limited by two issues: it is known to produce biased samples, and it can be slow to converge on complicated distributions. A recently proposed stochastic variant of SVGD (sSVGD) addresses the first issue, producing unbiased samples by incorporating a special noise into the SVGD dynamics such that asymptotic convergence is guaranteed. Meanwhile, Stein variational Newton (SVN), a Newton-like extension of SVGD, dramatically accelerates the convergence of SVGD by incorporating Hessian information into the dynamics, but also produces biased samples. In this paper we derive, and provide a practical implementation of, a stochastic variant of SVN (sSVN) which is both asymptotically correct and converges rapidly. We demonstrate the effectiveness of our algorithm on a difficult class of test problems -- the Hybrid Rosenbrock density -- and show that sSVN converges using three orders of magnitude fewer gradient evaluations of the log likelihood than its stochastic SVGD counterpart. Our results show that sSVN is a promising approach to accelerating high-precision Bayesian inference tasks with modest-dimension, d~O(10).