Fast and robust Bayesian inference using Gaussian processes with GPry

Journal of Cosmology and Astroparticle Physics, vol. 2023, pp. 021

Abstract

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 .

Authors 4

1. Jonas El Gammal corresponding

   University of Stavanger

   Affiliation as printed

   Department of Mathematics and Physics, University of Stavanger, Kristine Bonnevies vei 22, Stavanger 4021, Norway

2. Nils Schöneberg corresponding

   Institut de Ciències del Cosmos · Universitat de Barcelona

   Affiliation as printed

   Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, Barcelona E08028, Spain

3. Jesús Torrado corresponding

   University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova

   Affiliation as printed

   Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova, Via Marzolo 8, Padova I-35131, Italy

   INFN, Sezione di Padova, Via Marzolo 8, Padova I-35131, Italy

   Dipartimento di Fisica e Astronomia "G. Galilei", Università degli Studi di Padova, Via Marzolo 8, Padova I-35131, Italy

4. Christian Fidler corresponding Aachen Institute for Theoretical Particle Physics and Cosmology

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, Sommerfeldstraße 16, Aachen 52074, Germany