# Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect

arXiv: https://arxiv.org/abs/2109.13891 · HTML: https://mlsanity.com/paper/2109.13891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 28 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Recursive Estimation for Sparse Gaussian Process Regression](https://mlsanity.com/paper/1905.11711/) (2019)
- [Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels](https://mlsanity.com/paper/1403.5496/) (2014)
- [Adaptive, delayed-acceptance MCMC for targets with expensive likelihoods](https://mlsanity.com/paper/1509.00172/) (2015)
- [Scalable Gaussian Process Classification via Expectation Propagation](https://mlsanity.com/paper/1507.04513/) (2015)

## Abstract (arXiv)

We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).