# Probabilistic Inference and Learning with Stein's Method

arXiv: https://arxiv.org/abs/2603.07467 · HTML: https://mlsanity.com/paper/2603.07467/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [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 Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Global Non-convex Optimization with Discretized Diffusions](https://mlsanity.com/paper/1810.12361/) (2018)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [Stein Point Markov Chain Monte Carlo](https://mlsanity.com/paper/1905.03673/) (2019)
- [Measuring Sample Quality with Diffusions](https://mlsanity.com/paper/1611.06972/) (2016)
- [Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget](https://mlsanity.com/paper/1304.5299/) (2013)
- [Random Feature Stein Discrepancies](https://mlsanity.com/paper/1806.07788/) (2018)
- [Sampling with Mirrored Stein Operators](https://mlsanity.com/paper/2106.12506/) (2021)
- [Black-box Importance Sampling](https://mlsanity.com/paper/1610.05247/) (2016)

## Built on by (most cited first, 5 of 5)

- [Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scales](https://mlsanity.com/paper/2607.03367/) (2026)
- [Closing the Approximation Gap in Simulation-free Latent SDEs](https://mlsanity.com/paper/2606.16138/) (2026)
- [When Does Trimming Help Conformal Prediction? A Retained-Law Diagnostic under Calibration Contamination](https://mlsanity.com/paper/2605.06204/) (2026)
- [TASER: Task-Aware Stein Regularisation for Geometry-Driven Robustness](https://mlsanity.com/paper/2605.30601/) (2026)
- [Conditional Kernel Stein Discrepancy](https://mlsanity.com/paper/2610.11863/) (2026)

## Abstract (arXiv)

This monograph provides a rigorous overview of theoretical and methodological aspects of probabilistic inference and learning with Stein's method. Recipes are provided for constructing Stein discrepancies from Stein operators and Stein sets, and properties of these discrepancies such as computability, separation, convergence detection, and convergence control are discussed. Further, the connection between Stein operators and Stein variational gradient descent is set out in detail. The main definitions and results are precisely stated, and references to all proofs are provided.