BayesFlow: Amortized Bayesian Workflows With Neural Networks

Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis (Bürkner et al., 2022; Gelman et al., 2020; Schad et al., 2021). Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. However, despite their theoretical appeal and utility, the practical execution of Bayesian workflows is often limited by computational bottlenecks: Obtaining even a single posterior may already take a long time, such that repeated estimation for the purpose of model validation or calibration becomes completely infeasible. BayesFlow provides a framework for simulation-based training of established neural network architectures, such as transformers (Vaswani et al., 2017) and normalizing flows (Papamakarios et al., 2021), for amortized data compression and inference. Amortized Bayesian inference (ABI), as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously (typically well below one second), the upfront neural network training is quickly amortized. For instance, amortized inference allows us to test a model's ability to recover its parameters (Schad et al., 2021) or assess its simulation-based calibration (Säilynoja et al., 2022; Talts et al., 2018) for different data set sizes in a matter of seconds, even though this may require the estimation of thousands of posterior distributions. BayesFlow offers a user-friendly API, which encapsulates the details of neural network architectures and training procedures that are less relevant for the practitioner and provides robust default implementations that work well across many applications. At the same time, BayesFlow implements a modular software architecture, allowing machine learning scientists to modify every component of the pipeline for custom applications as well as research at the frontier of Bayesian inference.