Distributionally Robust Quickest Change Detection using Wasserstein Uncertainty Sets

Liyan Xie, Yuchen Liang, Venugopal V. Veeravalli
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1063-1071, 2024.

Abstract

The problem of quickest detection of a change in the distribution of streaming data is considered. It is assumed that the pre-change distribution is known, while the only information about the post-change is through a (small) set of labeled data. This post-change data is used in a data-driven minimax robust framework, where an uncertainty set for the post-change distribution is constructed. The robust change detection problem is studied in an asymptotic setting where the mean time to false alarm goes to infinity. It is shown that the least favorable distribution (LFD) is an exponentially tilted version of the pre-change density and can be obtained efficiently. A Cumulative Sum (CuSum) test based on the LFD, which is referred to as the distributionally robust (DR) CuSum test, is then shown to be asymptotically robust. The results are extended to the case with multiple post-change uncertainty sets and validated using synthetic and real data examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-xie24a, title = {Distributionally Robust Quickest Change Detection using {W}asserstein Uncertainty Sets}, author = {Xie, Liyan and Liang, Yuchen and V. Veeravalli, Venugopal}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1063--1071}, 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/xie24a/xie24a.pdf}, url = {https://proceedings.mlr.press/v238/xie24a.html}, abstract = {The problem of quickest detection of a change in the distribution of streaming data is considered. It is assumed that the pre-change distribution is known, while the only information about the post-change is through a (small) set of labeled data. This post-change data is used in a data-driven minimax robust framework, where an uncertainty set for the post-change distribution is constructed. The robust change detection problem is studied in an asymptotic setting where the mean time to false alarm goes to infinity. It is shown that the least favorable distribution (LFD) is an exponentially tilted version of the pre-change density and can be obtained efficiently. A Cumulative Sum (CuSum) test based on the LFD, which is referred to as the distributionally robust (DR) CuSum test, is then shown to be asymptotically robust. The results are extended to the case with multiple post-change uncertainty sets and validated using synthetic and real data examples.} }
Endnote
%0 Conference Paper %T Distributionally Robust Quickest Change Detection using Wasserstein Uncertainty Sets %A Liyan Xie %A Yuchen Liang %A Venugopal V. Veeravalli %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-xie24a %I PMLR %P 1063--1071 %U https://proceedings.mlr.press/v238/xie24a.html %V 238 %X The problem of quickest detection of a change in the distribution of streaming data is considered. It is assumed that the pre-change distribution is known, while the only information about the post-change is through a (small) set of labeled data. This post-change data is used in a data-driven minimax robust framework, where an uncertainty set for the post-change distribution is constructed. The robust change detection problem is studied in an asymptotic setting where the mean time to false alarm goes to infinity. It is shown that the least favorable distribution (LFD) is an exponentially tilted version of the pre-change density and can be obtained efficiently. A Cumulative Sum (CuSum) test based on the LFD, which is referred to as the distributionally robust (DR) CuSum test, is then shown to be asymptotically robust. The results are extended to the case with multiple post-change uncertainty sets and validated using synthetic and real data examples.
APA
Xie, L., Liang, Y. & V. Veeravalli, V.. (2024). Distributionally Robust Quickest Change Detection using Wasserstein Uncertainty Sets. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1063-1071 Available from https://proceedings.mlr.press/v238/xie24a.html.

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