Fast and robust Bayesian Inference using Gaussian Processes with GPry

TL;DR

GPry is a fast, robust Bayesian inference algorithm that uses Gaussian Processes and active learning to significantly reduce the number of likelihood evaluations needed, outperforming traditional Monte Carlo methods especially for expensive likelihoods.

Contribution

The paper introduces GPry, a novel Gaussian Process-based Bayesian inference method that requires no pre-training or special hardware, and employs active learning to drastically cut down on likelihood evaluations.

Findings

GPry reduces posterior evaluations by two orders of magnitude.

GPry outperforms traditional Monte Carlo methods for likelihood evaluations taking seconds.

GPry enables inference in days for complex models that would take months with traditional methods.

Abstract

We present the GPry algorithm for fast Bayesian inference of general (non-Gaussian) posteriors with a moderate number of parameters. GPry does not need any pre-training, special hardware such as GPUs, and is intended as a drop-in replacement for traditional Monte Carlo methods for Bayesian inference. Our algorithm is based on generating a Gaussian Process surrogate model of the log-posterior, aided by a Support Vector Machine classifier that excludes extreme or non-finite values. An active learning scheme allows us to reduce the number of required posterior evaluations by two orders of magnitude compared to traditional Monte Carlo inference. Our algorithm allows for parallel evaluations of the posterior at optimal locations, further reducing wall-clock times. We significantly improve performance using properties of the posterior in our active learning scheme and for the definition of the GP prior. In particular we account for the expected dynamical range of the posterior in different dimensionalities. We test our model against a number of synthetic and cosmological examples. GPry outperforms traditional Monte Carlo methods when the evaluation time of the likelihood (or the calculation of theoretical observables) is of the order of seconds; for evaluation times of over a minute it can perform inference in days that would take months using traditional methods. GPry is distributed as an open source Python package (pip install gpry) and can also be found at https://github.com/jonaselgammal/GPry.