Fast inference for slow likelihoods with probabilistic machine-learning

Abstract: Inference for slow likelihoods can require weeks or months, if possible at all, with traditional Monte Carlo samplers. This would be the case, for example, when fitting expensive non-linear matter spectrum models, or when characterizing individual long-duration GW events. I will introduce a fast machine-learning Bayesian inference algorithm for general non-Gaussian posteriors with a moderate number of parameters. I will present a pedagogical discussion of some general aspects of it, such as dealing with the curse of dimensionality, characterizing a region of interest, or parallelising active learning. I will show that the total number of expensive likelihood evaluations can be reduced by at least two orders of magnitude compared to traditional Monte Carlo methods, at low overhead costs and no pre-training. I will demonstrate its performance on a couple of real cosmological and GW problems.