# Optimal Thinning of MCMC Output

arXiv: https://arxiv.org/abs/2005.03952 · HTML: https://mlsanity.com/paper/2005.03952/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2020.

## Built on by (most cited first, 26 of 26)

- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Generalized Kernel Thinning](https://mlsanity.com/paper/2110.01593/) (2021)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Distribution Compression in Near-linear Time](https://mlsanity.com/paper/2111.07941/) (2021)
- [Sampling with Mirrored Stein Operators](https://mlsanity.com/paper/2106.12506/) (2021)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Controlling Moments with Kernel Stein Discrepancies](https://mlsanity.com/paper/2211.05408/) (2022)
- [Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference](https://mlsanity.com/paper/2301.11674/) (2023)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)
- [Universal Functional Regression with Neural Operator Flows](https://mlsanity.com/paper/2404.02986/) (2024)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [A stochastic Stein Variational Newton method](https://mlsanity.com/paper/2204.09039/) (2022)
- [Online, Informative MCMC Thinning with Kernelized Stein Discrepancy](https://mlsanity.com/paper/2201.07130/) (2022)
- [Bayesian Numerical Integration with Neural Networks](https://mlsanity.com/paper/2305.13248/) (2023)
- [Local and Mixing-Based Algorithms for Gaussian Graphical Model Selection from Glauber Dynamics](https://mlsanity.com/paper/2412.18594/) (2024)
- [Bayes Hilbert Spaces for Posterior Approximation](https://mlsanity.com/paper/2304.09053/) (2023)
- [Optimizing Kernel Discrepancies via Subset Selection](https://mlsanity.com/paper/2511.02706/) (2025)
- [Position: The Time for Sampling Is Now! Charting a New Course for Bayesian Deep Learning](https://mlsanity.com/paper/2605.21765/) (2026)
- [Stein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2502.03587/) (2025)
- [Copula Discrepancy: Benchmarking Dependence Structure](https://mlsanity.com/paper/2507.21434/) (2025)
- [StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow](https://mlsanity.com/paper/2605.16486/) (2026)
- [Amortized quadrature for posterior expectations in inverse problems](https://mlsanity.com/paper/2606.15871/) (2026)
- [On the Optimisation Landscape of Overparameterised Weighted MMD](https://mlsanity.com/paper/2610.19861/) (2026)

## Abstract (arXiv)

The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to "burn in" and removed, whilst the remainder of the chain is "thinned" if compression is also required. In this paper we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.