Sampling-Based Accuracy Testing of Posterior Estimators for General Inference

Pablo Lemos, Adam Coogan, Yashar Hezaveh, Laurence Perreault-Levasseur
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:19256-19273, 2023.

Abstract

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce "Tests of Accuracy with Random Points" (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-lemos23a, title = {Sampling-Based Accuracy Testing of Posterior Estimators for General Inference}, author = {Lemos, Pablo and Coogan, Adam and Hezaveh, Yashar and Perreault-Levasseur, Laurence}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {19256--19273}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/lemos23a/lemos23a.pdf}, url = {https://proceedings.mlr.press/v202/lemos23a.html}, abstract = {Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce "Tests of Accuracy with Random Points" (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.} }
Endnote
%0 Conference Paper %T Sampling-Based Accuracy Testing of Posterior Estimators for General Inference %A Pablo Lemos %A Adam Coogan %A Yashar Hezaveh %A Laurence Perreault-Levasseur %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-lemos23a %I PMLR %P 19256--19273 %U https://proceedings.mlr.press/v202/lemos23a.html %V 202 %X Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce "Tests of Accuracy with Random Points" (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.
APA
Lemos, P., Coogan, A., Hezaveh, Y. & Perreault-Levasseur, L.. (2023). Sampling-Based Accuracy Testing of Posterior Estimators for General Inference. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:19256-19273 Available from https://proceedings.mlr.press/v202/lemos23a.html.

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