# Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions

arXiv: https://arxiv.org/abs/1703.09930 · HTML: https://mlsanity.com/paper/1703.09930/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2017.

## Built on by (most cited first, 9 of 9)

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- [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)
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- [Fast and robust Bayesian Inference using Gaussian Processes with GPry](https://mlsanity.com/paper/2211.02045/) (2022)
- [Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC](https://mlsanity.com/paper/2104.03942/) (2021)
- [Meta-Learning an Inference Algorithm for Probabilistic Programs](https://mlsanity.com/paper/2103.00737/) (2021)
- [Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2303.00573/) (2023)
- [Parallelized Acquisition for Active Learning using Monte Carlo Sampling](https://mlsanity.com/paper/2305.19267/) (2023)
- [Measuring the right thing: justifying metrics in AI impact assessments](https://mlsanity.com/paper/2504.05007/) (2025)

## Abstract (arXiv)

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.