Approximate Bayesian Computation with Path Signatures

Joel Dyer, Patrick Cannon, Sebastian M. Schmon
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:1207-1231, 2024.

Abstract

Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data through some distance measure, but existing approaches are often poorly suited to time series simulators, for example due to an independent and identically distributed data assumption. In this paper, we propose to use path signatures in approximate Bayesian computation to handle the sequential nature of time series. We provide theoretical guarantees on the resultant posteriors and demonstrate competitive Bayesian parameter inference for simulators generating univariate, multivariate, and irregularly spaced sequences of non-iid data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-dyer24a, title = {Approximate Bayesian Computation with Path Signatures}, author = {Dyer, Joel and Cannon, Patrick and Schmon, Sebastian M.}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {1207--1231}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/dyer24a/dyer24a.pdf}, url = {https://proceedings.mlr.press/v244/dyer24a.html}, abstract = {Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data through some distance measure, but existing approaches are often poorly suited to time series simulators, for example due to an independent and identically distributed data assumption. In this paper, we propose to use path signatures in approximate Bayesian computation to handle the sequential nature of time series. We provide theoretical guarantees on the resultant posteriors and demonstrate competitive Bayesian parameter inference for simulators generating univariate, multivariate, and irregularly spaced sequences of non-iid data.} }
Endnote
%0 Conference Paper %T Approximate Bayesian Computation with Path Signatures %A Joel Dyer %A Patrick Cannon %A Sebastian M. Schmon %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-dyer24a %I PMLR %P 1207--1231 %U https://proceedings.mlr.press/v244/dyer24a.html %V 244 %X Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data through some distance measure, but existing approaches are often poorly suited to time series simulators, for example due to an independent and identically distributed data assumption. In this paper, we propose to use path signatures in approximate Bayesian computation to handle the sequential nature of time series. We provide theoretical guarantees on the resultant posteriors and demonstrate competitive Bayesian parameter inference for simulators generating univariate, multivariate, and irregularly spaced sequences of non-iid data.
APA
Dyer, J., Cannon, P. & Schmon, S.M.. (2024). Approximate Bayesian Computation with Path Signatures. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:1207-1231 Available from https://proceedings.mlr.press/v244/dyer24a.html.

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