Application of kernel hypothesis testing on set-valued data

Alexis Bellot, Mihaela van der Schaar
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:194-204, 2021.

Abstract

We present a general framework for kernel hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of images of a given phenomenon. This observation pattern, however, differs from the common assumptions required for hypothesis testing: each set differs in size, may have differing levels of noise, and also may incorporate nuisance variability, irrelevant for the analysis of the phenomenon of interest; all features that bias test decisions if not accounted for. In this paper, we propose to interpret sets as independent samples from a collection of latent probability distributions, and introduce kernel two-sample and independence tests in this latent space of distributions. We prove the consistency of these tests and observe them to outperform in a wide range of synthetic and real data experiments, where previously heuristics were needed for feature extraction and testing.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-bellot21a, title = {Application of kernel hypothesis testing on set-valued data}, author = {Bellot, Alexis and van der Schaar, Mihaela}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {194--204}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/bellot21a/bellot21a.pdf}, url = {https://proceedings.mlr.press/v161/bellot21a.html}, abstract = {We present a general framework for kernel hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of images of a given phenomenon. This observation pattern, however, differs from the common assumptions required for hypothesis testing: each set differs in size, may have differing levels of noise, and also may incorporate nuisance variability, irrelevant for the analysis of the phenomenon of interest; all features that bias test decisions if not accounted for. In this paper, we propose to interpret sets as independent samples from a collection of latent probability distributions, and introduce kernel two-sample and independence tests in this latent space of distributions. We prove the consistency of these tests and observe them to outperform in a wide range of synthetic and real data experiments, where previously heuristics were needed for feature extraction and testing.} }
Endnote
%0 Conference Paper %T Application of kernel hypothesis testing on set-valued data %A Alexis Bellot %A Mihaela van der Schaar %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-bellot21a %I PMLR %P 194--204 %U https://proceedings.mlr.press/v161/bellot21a.html %V 161 %X We present a general framework for kernel hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of images of a given phenomenon. This observation pattern, however, differs from the common assumptions required for hypothesis testing: each set differs in size, may have differing levels of noise, and also may incorporate nuisance variability, irrelevant for the analysis of the phenomenon of interest; all features that bias test decisions if not accounted for. In this paper, we propose to interpret sets as independent samples from a collection of latent probability distributions, and introduce kernel two-sample and independence tests in this latent space of distributions. We prove the consistency of these tests and observe them to outperform in a wide range of synthetic and real data experiments, where previously heuristics were needed for feature extraction and testing.
APA
Bellot, A. & van der Schaar, M.. (2021). Application of kernel hypothesis testing on set-valued data. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:194-204 Available from https://proceedings.mlr.press/v161/bellot21a.html.

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