# Quasi-stationary Monte Carlo and the ScaLE Algorithm

arXiv: https://arxiv.org/abs/1609.03436 · HTML: https://mlsanity.com/paper/1609.03436/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2016.

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

- [Fast Bayesian Coresets via Subsampling and Quasi-Newton Refinement](https://mlsanity.com/paper/2203.09675/) (2022)
- [Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics](https://mlsanity.com/paper/2207.12395/) (2022)
- [Bayesian Pseudo-Coresets via Contrastive Divergence](https://mlsanity.com/paper/2303.11278/) (2023)
- [Divide-and-Conquer Fusion](https://mlsanity.com/paper/2110.07265/) (2021)
- [Automated design of compound lenses with discrete-continuous optimization](https://mlsanity.com/paper/2509.23572/) (2025)

## Abstract (arXiv)

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo methods which simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for the exact simulation of diffusions. The methodology introduced here is particularly promising in that it is applicable to the same class of problems as gradient based Markov chain Monte Carlo algorithms but entirely circumvents the need to conduct Metropolis-Hastings type accept/reject steps whilst retaining exactness: the paper gives theoretical guarantees ensuring the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing na"ive sub-sampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size.