Parallelized Acquisition for Active Learning using Monte Carlo Sampling

Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the posterior. Recent attention has been directed towards the use of emulators of the posterior based on Gaussian Process (GP) regression combined with active sampling to achieve comparable precision with far fewer costly likelihood evaluations. Key to this approach is the batched acquisition of proposals, so that the true posterior can be evaluated in parallel. This is usually achieved via sequential maximization of the highly multimodal acquisition function. Unfortunately, this approach parallelizes poorly and is prone to getting stuck in local maxima. Our approach addresses this issue by generating nearly-optimal batches of candidates using an almost-embarrassingly parallel Nested Sampler on the mean prediction of the GP. The resulting nearly-sorted Monte Carlo sample is used to generate a batch of candidates ranked according to their sequentially conditioned acquisition function values at little cost. The final sample can also be used for inferring marginal quantities. Our proposed implementation (NORA) demonstrates comparable accuracy to sequential conditioned acquisition optimization and efficient parallelization in various synthetic and cosmological inference problems.

Fast and robust Bayesian Inference using Gaussian Processes with GPry

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.