Fast and robust Bayesian Inference using Gaussian Processes with GPry

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.

39 pages, 13 figures. Submitted to JCAP

References in corpus (28)

• PolyChord: nested sampling for cosmology
• Fast likelihood-free cosmology with neural density estimators and active learning
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• The Ecological Impact of High-performance Computing in Astrophysics
• Fast cosmological parameter estimation using neural networks
• {\sc CosmoNet}: fast cosmological parameter estimation in non-flat models using neural networks
• CONNECT: A neural network based framework for emulating cosmological observables and cosmological parameter inference
• Novel Method for Incorporating Model Uncertainties into Gravitational Wave Parameter Estimates
• Geometric variational inference
• CosmicNet II: Emulating extended cosmologies with efficient and accurate neural networks
• Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS
• Real-Time Likelihood-Free Inference of Roman Binary Microlensing Events with Amortized Neural Posterior Estimation
• Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes
• Robust Simulation-Based Inference in Cosmology with Bayesian Neural Networks
• $\text{matryoshka}$: Halo Model Emulator for the Galaxy Power Spectrum
• Parameter Inference for Weak Lensing using Gaussian Processes and MOPED
• LINNA: Likelihood Inference Neural Network Accelerator
• $\text{matryoshka}$ II: Accelerating Effective Field Theory Analyses of the Galaxy Power Spectrum
• Unbiased likelihood-free inference of the Hubble constant from light standard sirens
• Accurate X-ray Timing in the Presence of Systematic Biases With Simulation-Based Inference
• Accelerating cosmological inference with Gaussian processes and neural networks -- an application to LSST Y1 weak lensing and galaxy clustering
• Bayesian evidence-driven likelihood selection for sky-averaged 21-cm signal extraction
• Normalizing flows for random fields in cosmology
• PyVBMC: Efficient Bayesian inference in Python
• Fast emulation of two-point angular statistics for photometric galaxy surveys
• Bayesian error propagation for neural-net based parameter inference
• Estimating Cosmological Constraints from Galaxy Cluster Abundance using Simulation-Based Inference
• Parallelized Acquisition for Active Learning using Monte Carlo Sampling

Cited by in corpus (9)

• CONNECT: A neural network based framework for emulating cosmological observables and cosmological parameter inference
• Capse.jl: efficient and auto-differentiable CMB power spectra emulation
• Halo Occupation Distribution of Emission Line Galaxies: fitting method with Gaussian Processes
• Fast and effortless computation of profile likelihoods using CONNECT
• PyVBMC: Efficient Bayesian inference in Python
• Calculating Bayesian evidence for inflationary models using CONNECT
• Accelerating LISA inference with Gaussian processes
• On the accuracy of posterior recovery with neural network emulators
• ABCMB: A Python+JAX Package for the Cosmic Microwave Background Power Spectrum