# Online, Informative MCMC Thinning with Kernelized Stein Discrepancy

arXiv: https://arxiv.org/abs/2201.07130 · HTML: https://mlsanity.com/paper/2201.07130/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 18 Jan 2022.

## Builds on (most cited first, 17 of 17)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (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)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Dimension-independent likelihood-informed MCMC](https://mlsanity.com/paper/1411.3688/) (2014)
- [Stein Point Markov Chain Monte Carlo](https://mlsanity.com/paper/1905.03673/) (2019)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [Optimal quantisation of probability measures using maximum mean discrepancy](https://mlsanity.com/paper/2010.07064/) (2020)
- [Parsimonious Online Learning with Kernels via Sparse Projections in Function Space](https://mlsanity.com/paper/1612.04111/) (2016)
- [Consistent Online Gaussian Process Regression Without the Sample Complexity Bottleneck](https://mlsanity.com/paper/2004.11094/) (2020)

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

- [Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2206.01162/) (2022)
- [A stochastic Stein Variational Newton method](https://mlsanity.com/paper/2204.09039/) (2022)
- [STEERING: Stein Information Directed Exploration for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2301.12038/) (2023)

## Abstract (arXiv)

A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many non-parametric approaches do so by sampling a large number of points using variants of Markov Chain Monte Carlo (MCMC). We propose an MCMC variant that retains only those posterior samples which exceed a KSD threshold, which we call KSD Thinning. We establish the convergence and complexity tradeoffs for several settings of KSD Thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. Finally, we provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations, and observe superior consistency/complexity tradeoffs. Code is available at github.com/colehawkins/KSD-Thinning.