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+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5776 +10.21105/joss.05776 + +BlackBIRDS: Black-Box Inference foR Differentiable +Simulators + + + +https://orcid.org/0000-0001-5055-9863 + +Quera-Bofarull +Arnau + + + +* + + +https://orcid.org/0000-0002-8304-8450 + +Dyer +Joel + + + +* + + +https://orcid.org/0000-0003-2082-734X + +Calinescu +Anisoara + + + + +https://orcid.org/0000-0001-7871-073X + +Farmer +J. Doyne + + + + + + +https://orcid.org/0000-0002-9329-8410 + +Wooldridge +Michael + + + + + +Department of Computer Science, University of Oxford, +UK + + + + +Institute for New Economic Thinking, University of Oxford, +UK + + + + +Mathematical Institute, University of Oxford, +UK + + + + +Santa Fe Institute, USA + + + + +* E-mail: +* E-mail: + + +14 +7 +2023 + +8 +89 +5776 + +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) + + + +Python +Bayesian inference +differentiable simulators +variational inference +Markov chain Monte Carlo + + + + + + Summary +

BlackBIRDS is a Python package consisting of + generically applicable, black-box inference methods for differentiable + simulation models. It facilitates both (a) the differentiable + implementation of simulation models by providing a common + object-oriented framework for their implementation in + PyTorch + (Paszke + et al., 2019), and (b) the use of a variety of + gradient-assisted inference procedures for these simulation models, + allowing researchers to easily exploit the differentiable nature of + their simulator in parameter estimation tasks. The package consists of + both Bayesian and non-Bayesian inference methods, and relies on + well-supported software libraries (e.g., + normflows, + Stimper + et al., 2023) to provide this broad functionality.

+ + + Statement of need +

Across scientific disciplines and application domains, simulation + is used extensively as a means to studying complex mathematical models + of real-world systems. A simulation-based approach to modelling such + systems provides the modeller with significant benefits, permitting + them to specify their model in the way that they believe most + faithfully represents the true data-generating process and relieving + them from concerns regarding the mathematical tractability of the + resulting model. However, this additional flexibility comes at a + price: the resulting model can be too complex to easily perform + optimisation and inference tasks on the corresponding simulator, which + in many cases necessitates the use of approximate, simulation-based + inference and optimisation methods to perform these tasks + inexactly.

+

The complicated and black-box nature of many simulation models can + present a significant barrier to the successful deployment of these + simulation-based inference and optimisation techniques. Consequently, + there has been increasing interest within various scientific + communities in constructing differentiable simulation + models (see e.g., + Baydin + et al., 2020; + Chopra + et al., 2023): simulation models for which the gradient of the + model output with respect to the model’s input parameters can be + easily obtained. The primary motivation for this is that access to + this additional information, which captures the sensitivity of the + output of the simulator to changes in the input, can enable the use of + more efficient simulation-based optimisation and inference procedures, + helping to reduce the total runtime of such algorithms, their overall + consumption of valuable computational resources, and their concomitant + financial and environmental costs.

+

To this end, BlackBIRDS was designed to + provide researchers with easy access to a set of parameter inference + methods that exploit the gradient information provided by + differentiable simulators. The package provides support for a variety + of approaches to gradient-assisted parameter inference, including:

+ + +

Simulated Minimum Distance + (Franke, + 2009; SMD, see e.g., + Gourieroux + et al., 1993), in which parameter point estimates + + + 𝛉̂ + are obtained as

+

+ + 𝛉̂=argmin𝛉∈𝚯ℓ(𝛉,𝐲), + where + + 𝛉 + are the simulator’s parameters, which take values in some set + + + 𝚯, + and + + ℓ + is a loss function capturing the compatibility between the + observed data + + 𝐲 + and the simulator’s behaviour at parameter vector + + + 𝛉;

+ + +

Markov chain Monte Carlo (MCMC), in which samples from a + parameter posterior

+

+ + π(𝛉∣𝐲)∝e−ℓ(𝛉,𝐲)π(𝛉),

+

corresponding to a choice of loss function + + + ℓ + and a prior density + + π + over + + 𝚯 + are generated by executing a Markov chain on + + + 𝚯. + Currently, support is provided for Metropolis-adjusted Langevin + Dynamics + (Roberts + & Tweedie, 1996), although nothing prevents the + inclusion of additional gradient-assisted MCMC algorithms such as + Hamiltonian Monte Carlo + (Duane + et al., 1987);

+ + +

Variational Inference (VI), in which a parameteric + approximation + + q* + to the intractable posterior is obtained by solving the following + optimisation problem over a variational family + + + 𝒬 + + + q*=argminq∈𝒬𝔼q[−ℓ(𝛉,𝐲)]+𝔼q[logq(𝛉)π(𝛉)], + where + + ℓ + is defined as above and + + π + is a prior density over + + 𝚯.

+ + +

The package is written such that the user is free to specify their + choice of + + ℓ + and + + π + (in the case of Bayesian methods), under the constraint that both + choices are differentiable with respect to + + + 𝛉. + This allows the user to target a wide variety of parameter point + estimators, and both classical and generalised (see e.g., + Bissiri + et al., 2016; + Knoblauch + et al., 2022) posteriors. We provide a number of + tutorials + demonstrating (a) how to implement a simulator in a differentiable + framework in PyTorch and (b) how to apply the different parameter + inference methods supported by BlackBIRDS to + these differentiable simulators. Our package provides the user with + flexible posterior density estimators with the use of normalising + flows, and has already been used in scientific research to calibrate + differentiable simulators + (Quera-Bofarull, + Chopra, et al., 2023; + Quera-Bofarull, + Dyer, et al., 2023).

+ + Related software +

BlackBIRDS offers complementary + functionality to a number of existing Python packages. + sbi + (Tejero-Cantero + et al., 2020) is a package offering PyTorch-based + implementations of numerous simulation-based inference algorithms, + including those based on the use of MCMC and neural conditional + density estimators. Our package differs significantly, however: in + contrast to sbi, + BlackBIRDS provides support for both Bayesian + and non-Bayesian inference methods, and permits the researcher to + exploit gradients of the simulator, loss function, and/or posterior + density with respect to parameters + + 𝛉 + during inference tasks. The same comparison applies to the the + BayesFlow package + (Radev + et al., 2023). black-it + (Benedetti + et al., 2022) is a further recent Python package that + collects some recently developed parameter estimation methods from + the agent-based modelling community; the focus of this package is, + however, on non-Bayesian methods, and the package does not currently + support the exploitation of simulator gradients. + PyVBMC + (Huggins + et al., 2023) provides a Python implementation of the + Variational Bayesian Monte Carlo algorithm using Gaussian processes, + but differs from our package in that it does not exploit simulator + gradients and is focused on Bayesian inference alone. Additional + older packages (e.g., + Dutta + et al., 2021; + Schälte + et al., 2022) also focus on approximate Bayesian inference + methods for non-differentiable simulators. Beyond this, we are + unaware of other mature software projects in Python that support + parameter inference in the specific case of differentiable + simulation models.

+ + + + Features + + +

User-friendly and flexible API: SMD only requires the loss + function + + ℓ + and the optimiser to use, while MCMC (resp. VI) requires only the + loss + + ℓ, + the prior density + + π, + and the MCMC method (resp. posterior approximator) to be + specified. However, additional arguments can be provided to + straightforwardly customise hyperparameters of the different + methods.

+ + +

Multi-GPU parallelisation support with MPI.

+ + +

Support for both forward-mode and reverse-mode + auto-differentiation.

+ + +

Continuous integration and unit tests.

+ + + + + Acknowledgements +

This research was supported by a UKRI AI World Leading Researcher + Fellowship awarded to Wooldridge (grant EP/W002949/1). M. Wooldridge + and A. Calinescu acknowledge funding from Trustworthy AI - Integrating + Learning, Optimisation and Reasoning + (TAILOR), + a project funded by European Union Horizon2020 research and innovation + program under Grant Agreement 952215.

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