Maurer, Andreas;
Parletta, Daniela Angela;
Paudice, Andrea;
Pontil, Massimiliano;
(2021)
Robust Unsupervised Learning via L-statistic Minimization.
In: Meila, Marina and Zhang, Tong, (eds.)
Proceedings of the 38th International Conference on Machine Learning.
(pp. pp. 7524-7533).
PMLR
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Abstract
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised learning. The key assumption is that the perturbing distribution is characterized by larger losses relative to a given class of admissible models. This is exploited by a general descent algorithm which minimizes an L - statistic criterion over the model class, weighting small losses more. Our analysis characterizes the robustness of the method in terms of bounds on the reconstruction error relative to the underlying unperturbed distribution. As a byproduct, we prove uniform convergence bounds with respect to the proposed criterion for several popular models in unsupervised learning, a result which may be of independent interest. Numerical experiments with \textsc{kmeans} clustering and principal subspace analysis demonstrate the effectiveness of our approach.
| Type: | Proceedings paper |
|---|---|
| Title: | Robust Unsupervised Learning via L-statistic Minimization. |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.mlr.press/v139/maurer21a.html |
| 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 > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10164244 |
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