Schrab, Antonin;
(2025)
Optimal Kernel Hypothesis Testing.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The thesis consists in proposing new kernel hypothesis tests and proving optimal power guarantees for them. Various testing frameworks such as the two-sample, independence and goodness-of-fit frameworks are considered. A strong focus is put on the, often ignored, crucial choice of the kernel which strongly impacts the test power. Two methods, namely kernel pooling and aggregation, are proposed to adaptively select the kernels in a parameter-free manner, and are shown to lead to minimax optimal separation rates with respect to the kernel and L2 metrics. Optimal kernel tests are also developed, and their power guarantees theoretically analysed, under various testing constraints such as, computation efficiency, differential privacy, and robustness to data corruption.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Optimal Kernel Hypothesis Testing |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2025. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| Keywords: | Machine Learning, Kernel Methods, Hypothesis Testing, Minimax Optimality |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10205846 |
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