Fast and robust Bayesian inference using Gaussian processes with GPry

doi:10.1088/1475-7516/2023/10/021

Fast and robust Bayesian inference using Gaussian processes with GPry

2023-10-06

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DOI：10.1088/1475-7516/2023/10/021

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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 tradi-tional 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 def-inition 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 evalu-ation 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. JCAP10(2023)021

Keywords:

Machine learning

Statistical sampling techniques

Bayesian reasoning

Fast and robust Bayesian inference using Gaussian processes with GPry

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