Mining gold: Improving simulation-based inference with latent information

We summarize and discuss new inference techniques for systems that are described by a simulator with an intractable likelihood function. The key idea is that additional information that characterizes the latent process can often be extracted from the simulator. It can then be used to augment the training data for neural surrogates of the likelihood function. These methods have been applied to problems in particle physics and astrophysics, and the initial results demonstrate their potential to improve sample efficiency and quality of inference. 1 Simulation-based inference Phenomena across many domains of science are most accurately described by complicated computer simulations. These simulators typically implement a forward mode: given some model parameters θ as input, they generate potential outcomes or observations x, sampled from a probability density or likelihood function x ∼ p(x|θ). Often the true values of these model parameters θ are not known, and the inverse problem of inferring the likely values of θ from measured values of the observables x is an important goal. Both in a frequentist and a Bayesian setup, the central object for this inference task is the likelihood function, which can be schematically written as p(x|θ) = ∫ dz p(x, z|θ) . (1) Here we are integrating over all possible values of the latent variables z that describe the generative process, and p(x, z|θ) is the joint probability density or joint likelihood function of observables and latent variables. Realistic scientific simulators often involve a large number of latent variables, and the integral over such a high-dimensional space cannot be calculated explicitly (nor can it be sampled efficiently for a fixed x). The likelihood function is therefore intractable. This is a major challenge for scientific inference in fields ranging from particle physics to cosmology, epidemiology, genetics, and climate science. Inference in this case requires simulation-based (or likelihood-free) inference techniques. Some approaches, including the well-known Approximate Bayesian Computation (ABC) technique [1, 2] as well as methods based on density estimation [3], rely on reducing the observations to low-dimensional summary statistics. Standard choices of these summary statistics discard information and reduce the power of a measurement. In another approach, neural networks are trained as surrogates for the likelihood, the likelihood ratio, or the posterior [4–30]. Usually these methods are agnostic about the latent process in the simulator and only use its output x during training. Second Workshop on Machine Learning and the Physical Sciences (NeurIPS 2019), Vancouver, Canada. Here we review a recently proposed family of techniques that extracts more information from the simulator and uses this augmented data to train neural networks to either learn the likelihood or likelihood ratio function efficiently or to define powerful summary statistics that are statistically optimal in a well-defined approximation [31–34]. In Sec. 3 we point to software tools that automate this process. We then discuss the application of these ideas to various problems in Sec. 4. We conclude with a brief discussion of this approach in Sec. 5. This submission reviews the ideas originally presented in Refs. [31–34] and presents an overview of the application of these ideas to the physical sciences [35–37]. It is intentionally kept brief, aiming for an “extended abstract” style. For a camera-ready version, we would expand it into a more typical paper form and add new, so far unpublished results demonstrating the power of these methods.