# Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods

arXiv: https://arxiv.org/abs/2104.03384 · HTML: https://mlsanity.com/paper/2104.03384/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 92 references that are in the map.
- First posted on arXiv 7 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [Comparing Dynamics: Deep Neural Networks versus Glassy Systems](https://mlsanity.com/paper/1803.06969/) (2018)
- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Scaling limit of the Stein variational gradient descent: the mean field regime](https://mlsanity.com/paper/1805.04035/) (2018)
- [Deep Relaxation: partial differential equations for optimizing deep neural networks](https://mlsanity.com/paper/1704.04932/) (2017)
- [The prior can generally only be understood in the context of the likelihood](https://mlsanity.com/paper/1708.07487/) (2017)
- [Ensemble preconditioning for Markov chain Monte Carlo simulation](https://mlsanity.com/paper/1607.03954/) (2016)
- [Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families](https://mlsanity.com/paper/1506.02564/) (2015)
- [Ensemble Kalman Methods With Constraints](https://mlsanity.com/paper/1901.05668/) (2019)
- [Bayeslands: A Bayesian inference approach for parameter uncertainty quantification in Badlands](https://mlsanity.com/paper/1805.03696/) (2018)

## Built on by (most cited first, 8 of 8)

- [Learning About Structural Errors in Models of Complex Dynamical Systems](https://mlsanity.com/paper/2401.00035/) (2023)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC](https://mlsanity.com/paper/2108.00490/) (2021)
- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Optimality in Noisy Importance Sampling](https://mlsanity.com/paper/2201.02432/) (2022)
- [Batch Bayesian Optimization via Particle Gradient Flows](https://mlsanity.com/paper/2209.04722/) (2022)
- [The Ensemble Kalman Update is an Empirical Matheron Update](https://mlsanity.com/paper/2502.03048/) (2025)
- [Calibration of a neural network ocean closure for improved mean state and variability](https://mlsanity.com/paper/2604.06398/) (2026)

## Abstract (arXiv)

The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to parameter-to-data maps which are expensive to evaluate and are only available through noisy approximations. This paper is concerned with the use of interacting particle systems for the solution of the resulting inverse problems for parameters. Of particular interest is the case where the available forward model evaluations are subject to rapid fluctuations, in parameter space, superimposed on the smoothly varying large scale parametric structure of interest. {A motivating example from climate science is presented, and ensemble Kalman methods (which do not use the derivative of the parameter-to-data map) are shown, empirically, to perform well. Multiscale analysis is then used to analyze the behaviour of interacting particle system algorithms when rapid fluctuations, which we refer to as noise, pollute the large scale parametric dependence of the parameter-to-data map. Ensemble Kalman methods and Langevin-based methods} (the latter use the derivative of the parameter-to-data map) are compared in this light. The ensemble Kalman methods are shown to behave favourably in the presence of noise in the parameter-to-data map, whereas Langevin methods are adversely affected. On the other hand, Langevin methods have the correct equilibrium distribution in the setting of noise-free forward models, whilst ensemble Kalman methods only provide an uncontrolled approximation, except in the linear case. Therefore a new class of algorithms, ensemble Gaussian process samplers, which combine the benefits of both ensemble Kalman and Langevin methods, are introduced and shown to perform favourably.