Sequential Kernelized Stein Discrepancy

Diego Martinez-Taboada, Aaditya Ramdas
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1288-1296, 2025.

Abstract

We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the sample size need not be fixed prior to data collection; the practitioner can choose whether to stop the test or continue to gather evidence at any time while controlling the false discovery rate. In stark contrast to related literature, we do not impose uniform boundedness on the Stein kernel. Instead, we exploit the potential boundedness of the Stein kernel at arbitrary point evaluations to define test martingales, that give way to the subsequent novel sequential tests. We prove the validity of the test, as well as an asymptotic lower bound for the logarithmic growth of the wealth process under the alternative. We further illustrate the empirical performance of the test with a variety of distributions, including restricted Boltzmann machines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-martinez-taboada25a, title = {Sequential Kernelized Stein Discrepancy}, author = {Martinez-Taboada, Diego and Ramdas, Aaditya}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1288--1296}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/martinez-taboada25a/martinez-taboada25a.pdf}, url = {https://proceedings.mlr.press/v258/martinez-taboada25a.html}, abstract = {We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the sample size need not be fixed prior to data collection; the practitioner can choose whether to stop the test or continue to gather evidence at any time while controlling the false discovery rate. In stark contrast to related literature, we do not impose uniform boundedness on the Stein kernel. Instead, we exploit the potential boundedness of the Stein kernel at arbitrary point evaluations to define test martingales, that give way to the subsequent novel sequential tests. We prove the validity of the test, as well as an asymptotic lower bound for the logarithmic growth of the wealth process under the alternative. We further illustrate the empirical performance of the test with a variety of distributions, including restricted Boltzmann machines.} }
Endnote
%0 Conference Paper %T Sequential Kernelized Stein Discrepancy %A Diego Martinez-Taboada %A Aaditya Ramdas %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-martinez-taboada25a %I PMLR %P 1288--1296 %U https://proceedings.mlr.press/v258/martinez-taboada25a.html %V 258 %X We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the sample size need not be fixed prior to data collection; the practitioner can choose whether to stop the test or continue to gather evidence at any time while controlling the false discovery rate. In stark contrast to related literature, we do not impose uniform boundedness on the Stein kernel. Instead, we exploit the potential boundedness of the Stein kernel at arbitrary point evaluations to define test martingales, that give way to the subsequent novel sequential tests. We prove the validity of the test, as well as an asymptotic lower bound for the logarithmic growth of the wealth process under the alternative. We further illustrate the empirical performance of the test with a variety of distributions, including restricted Boltzmann machines.
APA
Martinez-Taboada, D. & Ramdas, A.. (2025). Sequential Kernelized Stein Discrepancy. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1288-1296 Available from https://proceedings.mlr.press/v258/martinez-taboada25a.html.

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