Bayesian kernel two-sample testing
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here,...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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Taylor and Francis
2022
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| _version_ | 1826312603355316224 |
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| author | Zhang, Q Wild, V Filippi, S Flaxman, S Sejdinovic, D |
| author_facet | Zhang, Q Wild, V Filippi, S Flaxman, S Sejdinovic, D |
| author_sort | Zhang, Q |
| collection | OXFORD |
| description | In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modeling the difference between kernel mean embeddings in the reproducing kernel Hilbert space using the framework established by Flaxman et al. The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e., testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach. |
| first_indexed | 2024-03-07T07:32:36Z |
| format | Journal article |
| id | oxford-uuid:e0839deb-73a9-4b21-91a1-007f9ba7d052 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-04-09T03:57:10Z |
| publishDate | 2022 |
| publisher | Taylor and Francis |
| record_format | dspace |
| spelling | oxford-uuid:e0839deb-73a9-4b21-91a1-007f9ba7d0522024-03-21T17:15:42ZBayesian kernel two-sample testingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e0839deb-73a9-4b21-91a1-007f9ba7d052EnglishSymplectic ElementsTaylor and Francis2022Zhang, QWild, VFilippi, SFlaxman, SSejdinovic, DIn modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modeling the difference between kernel mean embeddings in the reproducing kernel Hilbert space using the framework established by Flaxman et al. The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e., testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach. |
| spellingShingle | Zhang, Q Wild, V Filippi, S Flaxman, S Sejdinovic, D Bayesian kernel two-sample testing |
| title | Bayesian kernel two-sample testing |
| title_full | Bayesian kernel two-sample testing |
| title_fullStr | Bayesian kernel two-sample testing |
| title_full_unstemmed | Bayesian kernel two-sample testing |
| title_short | Bayesian kernel two-sample testing |
| title_sort | bayesian kernel two sample testing |
| work_keys_str_mv | AT zhangq bayesiankerneltwosampletesting AT wildv bayesiankerneltwosampletesting AT filippis bayesiankerneltwosampletesting AT flaxmans bayesiankerneltwosampletesting AT sejdinovicd bayesiankerneltwosampletesting |