Likelihood-free MCMC with Amortized Approximate Ratio Estimators

Joeri Hermans, Volodimir Begy, Gilles Louppe
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4239-4248, 2020.

Abstract

Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing practitioners to rely on approximations. This work introduces a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible amortized estimator which approximates the likelihood-to-evidence ratio. We demonstrate that the learned ratio estimator can be embedded in \textsc{mcmc} samplers to approximate likelihood-ratios between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability and to measure the quality of an approximation. The accuracy of our approach is demonstrated on a variety of benchmarks against well-established techniques. Scientific applications in physics show its applicability.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-hermans20a, title = {Likelihood-free {MCMC} with Amortized Approximate Ratio Estimators}, author = {Hermans, Joeri and Begy, Volodimir and Louppe, Gilles}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {4239--4248}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/hermans20a/hermans20a.pdf}, url = { http://proceedings.mlr.press/v119/hermans20a.html }, abstract = {Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing practitioners to rely on approximations. This work introduces a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible amortized estimator which approximates the likelihood-to-evidence ratio. We demonstrate that the learned ratio estimator can be embedded in \textsc{mcmc} samplers to approximate likelihood-ratios between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability and to measure the quality of an approximation. The accuracy of our approach is demonstrated on a variety of benchmarks against well-established techniques. Scientific applications in physics show its applicability.} }
Endnote
%0 Conference Paper %T Likelihood-free MCMC with Amortized Approximate Ratio Estimators %A Joeri Hermans %A Volodimir Begy %A Gilles Louppe %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-hermans20a %I PMLR %P 4239--4248 %U http://proceedings.mlr.press/v119/hermans20a.html %V 119 %X Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing practitioners to rely on approximations. This work introduces a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible amortized estimator which approximates the likelihood-to-evidence ratio. We demonstrate that the learned ratio estimator can be embedded in \textsc{mcmc} samplers to approximate likelihood-ratios between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability and to measure the quality of an approximation. The accuracy of our approach is demonstrated on a variety of benchmarks against well-established techniques. Scientific applications in physics show its applicability.
APA
Hermans, J., Begy, V. & Louppe, G.. (2020). Likelihood-free MCMC with Amortized Approximate Ratio Estimators. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:4239-4248 Available from http://proceedings.mlr.press/v119/hermans20a.html .

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