Online multiple testing with e-values

Ziyu Xu, Aaditya Ramdas
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3997-4005, 2024.

Abstract

A scientist tests a continuous stream of hypotheses over time in the course of her investigation — she does not test a predetermined, fixed number of hypotheses. The scientist wishes to make as many discoveries as possible while ensuring the number of false discoveries is controlled — a well recognized way for accomplishing this is to control the false discovery rate (FDR). Prior methods for FDR control in the online setting have focused on formulating algorithms when specific dependency structures are assumed to exist between the test statistics of each hypothesis. However, in practice, these dependencies often cannot be known beforehand or tested after the fact. Our algorithm, e-LOND, provides FDR control under arbitrary, possibly unknown, dependence. We show that our method is more powerful than existing approaches to this problem through simulations. We also formulate extensions of this algorithm to utilize randomization for increased power and for constructing confidence intervals in online selective inference.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-xu24a, title = { Online multiple testing with e-values }, author = {Xu, Ziyu and Ramdas, Aaditya}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3997--4005}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/xu24a/xu24a.pdf}, url = {https://proceedings.mlr.press/v238/xu24a.html}, abstract = { A scientist tests a continuous stream of hypotheses over time in the course of her investigation — she does not test a predetermined, fixed number of hypotheses. The scientist wishes to make as many discoveries as possible while ensuring the number of false discoveries is controlled — a well recognized way for accomplishing this is to control the false discovery rate (FDR). Prior methods for FDR control in the online setting have focused on formulating algorithms when specific dependency structures are assumed to exist between the test statistics of each hypothesis. However, in practice, these dependencies often cannot be known beforehand or tested after the fact. Our algorithm, e-LOND, provides FDR control under arbitrary, possibly unknown, dependence. We show that our method is more powerful than existing approaches to this problem through simulations. We also formulate extensions of this algorithm to utilize randomization for increased power and for constructing confidence intervals in online selective inference. } }
Endnote
%0 Conference Paper %T Online multiple testing with e-values %A Ziyu Xu %A Aaditya Ramdas %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-xu24a %I PMLR %P 3997--4005 %U https://proceedings.mlr.press/v238/xu24a.html %V 238 %X A scientist tests a continuous stream of hypotheses over time in the course of her investigation — she does not test a predetermined, fixed number of hypotheses. The scientist wishes to make as many discoveries as possible while ensuring the number of false discoveries is controlled — a well recognized way for accomplishing this is to control the false discovery rate (FDR). Prior methods for FDR control in the online setting have focused on formulating algorithms when specific dependency structures are assumed to exist between the test statistics of each hypothesis. However, in practice, these dependencies often cannot be known beforehand or tested after the fact. Our algorithm, e-LOND, provides FDR control under arbitrary, possibly unknown, dependence. We show that our method is more powerful than existing approaches to this problem through simulations. We also formulate extensions of this algorithm to utilize randomization for increased power and for constructing confidence intervals in online selective inference.
APA
Xu, Z. & Ramdas, A.. (2024). Online multiple testing with e-values . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3997-4005 Available from https://proceedings.mlr.press/v238/xu24a.html.

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