Arbitrary Marginal Neural Ratio Estimation for Likelihood-free Inference

Abstract

In many areas of science, computer simulators are used to describe complex real-world phenomena. These simulators are stochastic forward models, meaning that they randomly generate synthetic realizations according to input parameters. A common task for scientists is to use such models to infer the parameters given observations. Due to their complexity, the likelihoods - essential for inference - implicitly defined by these simulators are typically not tractable. Consequently, scientists have relied on "likelihood-free" methods to perform parameter inference. In this thesis, we build upon one of these methods, the neural ratio estimation (NRE) of the likelihood-to-evidence (LTE) ratio, to enable inference over arbitrary subsets of the parameters. Called arbitrary marginal neural ratio estimation (AMNRE), this novel method is easy to use, efficient and can be implemented with basic neural network architectures. Trough a series of experiments, we demonstrate the applicability of AMNRE and find it to be competitive with baseline methods, despite using a fraction of the computing resources. We also apply AMNRE to the challenging problem of parameter inference of binary black hole systems from gravitational waves observation and obtain promising results. As a complement to this contribution, we discuss the problem of overconfidence in predictive models and propose regularization methods to induce uncertainty in neural predictions.