BayesFlow: Learning complex stochastic models with invertible neural networks

• Main Authors: Radev, Stefan T, Mertens, Ulf K, Voss, Andreas, Ardizzone, Lynton, Köthe, Ullrich
• Format: Journal Article
• Language: English
• Published: 13-03-2020
• Subjects: Computer Science - Learning; Statistics - Machine Learning
• DOI: 10.48550/arxiv.2003.06281

Estimating the parameters of mathematical models is a common problem in
almost all branches of science. However, this problem can prove notably
difficult when processes and model descriptions become increasingly complex and
an explicit likelihood function is not available. With this work, we propose a
novel method for globally amortized Bayesian inference based on invertible
neural networks which we call BayesFlow. The method uses simulation to learn a
global estimator for the probabilistic mapping from observed data to underlying
model parameters. A neural network pre-trained in this way can then, without
additional training or optimization, infer full posteriors on arbitrary many
real datasets involving the same model family. In addition, our method
incorporates a summary network trained to embed the observed data into
maximally informative summary statistics. Learning summary statistics from data
makes the method applicable to modeling scenarios where standard inference
techniques with hand-crafted summary statistics fail. We demonstrate the
utility of BayesFlow on challenging intractable models from population
dynamics, epidemiology, cognitive science and ecology. We argue that BayesFlow
provides a general framework for building amortized Bayesian parameter
estimation machines for any forward model from which data can be simulated.