Meunier, Dimitri;
Pontil, Massimiliano;
Ciliberto, Carlo;
(2022)
Distribution Regression with Sliced Wasserstein Kernels.
In: Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan, (eds.)
Proceedings of the 39th International Conference on Machine Learning.
(pp. pp. 15501-15523).
Proceedings of Machine Learning Research (PMLR): Baltimore, Maryland, USA.
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Abstract
The problem of learning functions over spaces of probabilities – or distribution regression – is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation capturing all relevant properties of the underlying functional mapping. A principled approach to distribution regression is provided by kernel mean embeddings, which lifts kernel-induced similarity on the input domain at the probability level. This strategy effectively tackles the two-stage sampling nature of the problem, enabling one to derive estimators with strong statistical guarantees, such as universal consistency and excess risk bounds. However, kernel mean embeddings implicitly hinge on the maximum mean discrepancy (MMD), a metric on probabilities, which may fail to capture key geometrical relations between distributions. In contrast, optimal transport (OT) metrics, are potentially more appealing. In this work, we propose an OT-based estimator for distribution regression. We build on the Sliced Wasserstein distance to obtain an OT-based representation. We study the theoretical properties of a kernel ridge regression estimator based on such representation, for which we prove universal consistency and excess risk bounds. Preliminary experiments complement our theoretical findings by showing the effectiveness of the proposed approach and compare it with MMD-based estimators.
| Type: | Proceedings paper |
|---|---|
| Title: | Distribution Regression with Sliced Wasserstein Kernels |
| Event: | 39th International Conference on Machine Learning |
| Location: | MD, Baltimore |
| Dates: | 17 Jul 2022 - 23 Jul 2022 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.mlr.press/v162/ |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10199640 |
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