Chained generalisation bounds
This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between generalisation bounds based on the regularity of the loss function,...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Proceedings of Machine Learning Research
2022
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| _version_ | 1826308607864471552 |
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| author | Clerico, E Shidani, A Deligiannidis, G Doucet, A |
| author_facet | Clerico, E Shidani, A Deligiannidis, G Doucet, A |
| author_sort | Clerico, E |
| collection | OXFORD |
| description | This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between generalisation bounds based on the regularity of the loss function, and their chained counterparts, which can be obtained by lifting the regularity assumption from the loss onto its gradient. This allows us to re-derive the chaining mutual information bound from the literature, and to obtain novel chained information-theoretic generalisation bounds, based on the Wasserstein distance and other probability metrics. We show on some toy examples that the chained generalisation bound can be significantly tighter than its standard counterpart, particularly when the distribution of the hypotheses selected by the algorithm is very concentrated. |
| first_indexed | 2024-03-07T07:21:52Z |
| format | Conference item |
| id | oxford-uuid:ccb97caf-ec4a-41e9-bfc6-04c1d5b185e7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:21:52Z |
| publishDate | 2022 |
| publisher | Proceedings of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:ccb97caf-ec4a-41e9-bfc6-04c1d5b185e72022-10-14T11:10:49ZChained generalisation boundsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:ccb97caf-ec4a-41e9-bfc6-04c1d5b185e7EnglishSymplectic ElementsProceedings of Machine Learning Research2022Clerico, EShidani, ADeligiannidis, GDoucet, AThis work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between generalisation bounds based on the regularity of the loss function, and their chained counterparts, which can be obtained by lifting the regularity assumption from the loss onto its gradient. This allows us to re-derive the chaining mutual information bound from the literature, and to obtain novel chained information-theoretic generalisation bounds, based on the Wasserstein distance and other probability metrics. We show on some toy examples that the chained generalisation bound can be significantly tighter than its standard counterpart, particularly when the distribution of the hypotheses selected by the algorithm is very concentrated. |
| spellingShingle | Clerico, E Shidani, A Deligiannidis, G Doucet, A Chained generalisation bounds |
| title | Chained generalisation bounds |
| title_full | Chained generalisation bounds |
| title_fullStr | Chained generalisation bounds |
| title_full_unstemmed | Chained generalisation bounds |
| title_short | Chained generalisation bounds |
| title_sort | chained generalisation bounds |
| work_keys_str_mv | AT clericoe chainedgeneralisationbounds AT shidania chainedgeneralisationbounds AT deligiannidisg chainedgeneralisationbounds AT douceta chainedgeneralisationbounds |