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+
+
+
+ 20230922T033927-b00a71b076355f7f9368b35a7971c9c2c7983f77
+ 20230922033927
+
+ JOSS Admin
+ admin@theoj.org
+
+ The Open Journal
+
+
+
+
+ Journal of Open Source Software
+ JOSS
+ 2475-9066
+
+ 10.21105/joss
+ https://joss.theoj.org
+
+
+
+
+ 09
+ 2023
+
+
+ 8
+
+ 89
+
+
+
+ BayesFlow: Amortized Bayesian Workflows With Neural
+Networks
+
+
+
+ Stefan T.
+ Radev
+ https://orcid.org/0000-0002-6702-9559
+
+
+ Marvin
+ Schmitt
+ https://orcid.org/0000-0003-1293-820X
+
+
+ Lukas
+ Schumacher
+ https://orcid.org/0000-0003-1512-8288
+
+
+ Lasse
+ Elsemüller
+ https://orcid.org/0000-0003-0368-720X
+
+
+ Valentin
+ Pratz
+ https://orcid.org/0000-0001-8371-3417
+
+
+ Yannik
+ Schälte
+ https://orcid.org/0000-0003-1293-820X
+
+
+ Ullrich
+ Köthe
+ https://orcid.org/0000-0001-6036-1287
+
+
+ Paul-Christian
+ Bürkner
+ https://orcid.org/0000-0001-5765-8995
+
+
+
+ 09
+ 22
+ 2023
+
+
+ 5702
+
+
+ 10.21105/joss.05702
+
+
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+
+
+
+ Software archive
+ 10.5281/zenodo.8346393
+
+
+ GitHub review issue
+ https://github.com/openjournals/joss-reviews/issues/5702
+
+
+
+ 10.21105/joss.05702
+ https://joss.theoj.org/papers/10.21105/joss.05702
+
+
+ https://joss.theoj.org/papers/10.21105/joss.05702.pdf
+
+
+
+
+
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+
+
+
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+
+
diff --git a/joss.05702/10.21105.joss.05702.jats b/joss.05702/10.21105.joss.05702.jats
new file mode 100644
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@@ -0,0 +1,1105 @@
+
+
+
+
+
+
+
+Journal of Open Source Software
+JOSS
+
+2475-9066
+
+Open Journals
+
+
+
+5702
+10.21105/joss.05702
+
+BayesFlow: Amortized Bayesian Workflows With Neural
+Networks
+
+
+
+https://orcid.org/0000-0002-6702-9559
+
+Radev
+Stefan T.
+
+
+*
+
+
+https://orcid.org/0000-0003-1293-820X
+
+Schmitt
+Marvin
+
+
+
+
+https://orcid.org/0000-0003-1512-8288
+
+Schumacher
+Lukas
+
+
+
+
+https://orcid.org/0000-0003-0368-720X
+
+Elsemüller
+Lasse
+
+
+
+
+https://orcid.org/0000-0001-8371-3417
+
+Pratz
+Valentin
+
+
+
+
+https://orcid.org/0000-0003-1293-820X
+
+Schälte
+Yannik
+
+
+
+
+https://orcid.org/0000-0001-6036-1287
+
+Köthe
+Ullrich
+
+
+
+
+https://orcid.org/0000-0001-5765-8995
+
+Bürkner
+Paul-Christian
+
+
+
+
+
+
+Cluster of Excellence STRUCTURES, Heidelberg University,
+Germany
+
+
+
+
+Cluster of Excellence SimTech, University of Stuttgart,
+Germany
+
+
+
+
+Institute for Psychology, Heidelberg University,
+Germany
+
+
+
+
+Visual Learning Lab, Heidelberg University,
+Germany
+
+
+
+
+Life and Medical Sciences Institute, University of Bonn,
+Germany
+
+
+
+
+Department of Statistics, TU Dortmund University,
+Germany
+
+
+
+
+* E-mail:
+
+
+22
+6
+2023
+
+8
+89
+5702
+
+Authors of papers retain copyright and release the
+work under a Creative Commons Attribution 4.0 International License (CC
+BY 4.0)
+2022
+The article authors
+
+Authors of papers retain copyright and release the work under
+a Creative Commons Attribution 4.0 International License (CC BY
+4.0)
+
+
+
+simulation-based inference
+likelihood-free inference
+Bayesian inference
+amortized Bayesian inference
+Python
+
+
+
+
+
+ Summary
+
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.
+
+
BayesFlow defines a formal
+ workflow for data generation, neural approximation, and model
+ criticism.
+
+
+
+
+ Statement of Need
+
BayesFlow embodies functionality that is
+ specifically designed for building and validating amortized Bayesian
+ workflows with the help of neural networks.
+ [fig:figure1]
+ outlines a typical workflow in the context of amortized posterior and
+ likelihood estimation. A simulator coupled with a prior defines a
+ generative Bayesian model. The generative model may depend on various
+ (optional) context variates like varying numbers of observations,
+ design matrices, or positional encodings. The generative scope of the
+ model and the range of context variables determine the scope
+ of amortization, that is, over which types of data the neural
+ approximator can be applied without re-training. The neural
+ approximators interact with model outputs (parameters, data) and
+ context variates through a configurator. The configurator is
+ responsible for carrying out transformations (e.g., input
+ normalization, double-to-float conversion, etc.) that are not part of
+ the model but may facilitate neural network training and
+ convergence.
+
[fig:figure1]
+ also illustrates an example configuration of four neural networks: 1)
+ a summary network to compress simulation outcomes (individual data
+ points, sets, or time series) into informative embeddings; 2) a
+ posterior network to learn an amortized approximate posterior; and 3)
+ another summary network to compress simulation inputs (parameters)
+ into informative embeddings; and 4) a likelihood network to learn an
+ amortized approximate likelihood.
+ [fig:figure1]
+ depicts the standalone and joint capabilities of the networks when
+ applied in isolation or in tandem. The input conditions for the
+ posterior and likelihood networks are partitioned by the configurator:
+ Complex (“summary”) conditions are processed by the respective summary
+ network into embeddings, while very simple (“direct”) conditions can
+ bypass the summary network and flow straight into the neural
+ approximator.
+
Currently, the software features four key capabilities for
+ enhancing Bayesian workflows, which have been described in the
+ referenced works:
+
+
+
Amortized posterior estimation: Train a generative
+ network to efficiently infer full posteriors (i.e., solve the
+ inverse problem) for all existing and future data compatible with
+ a simulation model
+ (Radev,
+ Mertens, et al., 2020).
+
+
+
Amortized likelihood estimation: Train a
+ generative network to efficiently emulate a simulation model
+ (i.e., solve the forward problem) for all possible parameter
+ configurations or interact with external probabilistic programs
+ (Boelts
+ et al., 2022;
+ Radev
+ et al., 2023).
+
+
+
Amortized model comparison: Train a neural
+ classifier to recognize the “best” model in a set of competing
+ candidates
+ (Elsemüller
+ et al., 2023;
+ Radev,
+ D’Alessandro, et al., 2020;
+ Schmitt
+ et al., 2022) or combine amortized posterior and likelihood
+ estimation to compute Bayesian evidence and out-of-sample
+ predictive performance
+ (Radev
+ et al., 2023).
+
+
+
Model misspecification detection: Ensure that the
+ resulting posteriors are faithful approximations of the otherwise
+ intractable target posterior, even when simulations do not
+ perfectly represent reality
+ (Radev
+ et al., 2023;
+ Schmitt
+ et al., 2023).
+
+
+
BayesFlow has been used for amortized
+ Bayesian inference in various areas of applied research, such as
+ epidemiology
+ (Radev
+ et al., 2021), cognitive modeling
+ (Krause
+ et al., 2022;
+ Schumacher
+ et al., 2023;
+ Sokratous
+ et al., 2023;
+ Wieschen
+ et al., 2020), computational psychiatry
+ (D’Alessandro
+ et al., 2020), neuroscience
+ (Ghaderi-Kangavari
+ et al., 2022), particle physics
+ (Bieringer
+ et al., 2021), agent-based econometrics models
+ (Shiono,
+ 2021), seismic imaging
+ (Siahkoohi
+ et al., 2023), user behavior
+ (Moon
+ et al., 2023), structural health monitoring
+ (Zeng
+ et al., 2023), aerospace
+ (Tsilifis
+ et al., 2022) and wind turbine design
+ (Noever-Castelos
+ et al., 2022), micro-electro-mechanical systems testing
+ (Heringhaus
+ et al., 2022), and fractional Brownian motion
+ (Verdier
+ et al., 2022).
+
The software is built on top of TensorFlow
+ (Abadi
+ et al., 2016) and thereby enables off-the-shelf support for GPU
+ and TPU acceleration. Furthermore, it can seamlessly interact with
+ TensorFlow Probability
+ (Dillon
+ et al., 2017) for flexible latent distributions and a variety
+ of joint priors.
+
+
+ Related Software
+
When a non-amortized inference procedure does not create a
+ computational bottleneck, approximate Bayesian computation (ABC) might
+ be an appropriate tool. This is the case if a single data set needs to
+ be analyzed, if an infrastructure for parallel computing is readily
+ available, or if repeated re-fits of a model (e.g., cross-validation)
+ are not desired. A variety of mature Python packages for ABC exist,
+ such as PyMC
+ (Salvatier
+ et al., 2016), pyABC
+ (Schälte
+ et al., 2022), ABCpy
+ (Dutta
+ et al., 2021), or ELFI
+ (Lintusaari
+ et al., 2018). In contrast to these packages,
+ BayesFlow focuses on amortized inference, but
+ can also interact with ABC samplers (e.g., use BayesFlow to learn
+ informative summary statistics for an ABC analysis).
+
When it comes to simulation-based inference with neural networks,
+ the sbi toolkit enables both likelihood and
+ posterior estimation using different inference algorithms, such as
+ Neural Posterior Estimation
+ (Papamakarios
+ et al., 2021), Sequential Neural Posterior Estimation
+ (Greenberg
+ et al., 2019) and Sequential Neural Likelihood Estimation
+ (Papamakarios
+ et al., 2019). BayesFlow and
+ sbi can be viewed as complementary toolkits,
+ where sbi implements a variety of different
+ approximators for standard modeling scenarios, while
+ BayesFlow focuses on amortized workflows with
+ user-friendly default settings and optional customization. The
+ Swyft library focuses on Bayesian parameter
+ inference in physics and astronomy. Swyft uses
+ a specific type of simulation-based neural inference technique,
+ namely, Truncated Marginal Neural Ratio Estimation
+ (Miller
+ et al., 2021). This method improves on standard Markov chain
+ Monte Carlo (MCMC) methods for ABC by learning the
+ likelihood-to-evidence ratio with neural density estimators. Finally,
+ the Lampe library provides implementations for
+ a subset of the methods for posterior estimation in the
+ sbi library, aiming to expose all components
+ (e.g., network architectures, optimizers) in order to provide a
+ customizable interface for creating neural approximators. All of these
+ libraries are built on top of PyTorch.
+
+
+ Availability, Development, and Documentation
+
BayesFlow is available through PyPI via
+ pip install bayesflow, the development version
+ is available via GitHub. GitHub Actions manage continuous integration
+ through automated code testing and documentation. The documentation is
+ hosted at
+ www.bayesflow.org.
+ Currently, BayesFlow features seven tutorial
+ notebooks. These notebooks showcase different aspects of the software,
+ ranging from toy examples to applied modeling scenarios, and
+ illustrating both posterior estimation and model comparison
+ workflows.
+
+
+ Acknowledgments
+
We thank Ulf Mertens, Marco D’Alessandro, René Bucchia, The-Gia Leo
+ Nguyen, Jonas Arruda, Lea Zimmermann, and Leonhard Volz for
+ contributing to the GitHub repository. STR was funded by the Deutsche
+ Forschungsgemeinschaft (DFG, German Research Foundation) under
+ Germany’s Excellence Strategy - EXC-2181 - 390900948 (the Heidelberg
+ Cluster of Excellence STRUCTURES), MS and PCB were supported by the
+ Cyber Valley Research Fund (grant number: CyVy-RF-2021-16) and the DFG
+ EXC-2075 - 390740016 (the Stuttgart Cluster of Excellence SimTech). LS
+ and LE were supported by a grant from the DFG (GRK 2277) to the
+ research training group Statistical Modeling in Psychology (SMiP). YS
+ acknowledges support from the Joachim Herz Foundation. UK was
+ supported by the Informatics for Life initiative funded by the Klaus
+ Tschira Foundation. YS and UK were supported by the EMUNE project
+ (“Invertierbare Neuronale Netze für ein verbessertes Verständnis von
+ Infektionskrankheiten”, BMBF, 031L0293A-D).
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