Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks

Louis Béthune, Paul Novello, Guillaume Coiffier, Thibaut Boissin, Mathieu Serrurier, Quentin Vincenot, Andres Troya-Galvis
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:2245-2271, 2023.

Abstract

We propose a new method, dubbed One Class Signed Distance Function (OCSDF), to perform One Class Classification (OCC) by provably learning the Signed Distance Function (SDF) to the boundary of the support of any distribution. The distance to the support can be interpreted as a normality score, and its approximation using 1-Lipschitz neural networks provides robustness bounds against $l2$ adversarial attacks, an under-explored weakness of deep learning-based OCC algorithms. As a result, OCSDF comes with a new metric, certified AUROC, that can be computed at the same cost as any classical AUROC. We show that OCSDF is competitive against concurrent methods on tabular and image data while being way more robust to adversarial attacks, illustrating its theoretical properties. Finally, as exploratory research perspectives, we theoretically and empirically show how OCSDF connects OCC with image generation and implicit neural surface parametrization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-bethune23a, title = {Robust One-Class Classification with Signed Distance Function using 1-{L}ipschitz Neural Networks}, author = {B\'{e}thune, Louis and Novello, Paul and Coiffier, Guillaume and Boissin, Thibaut and Serrurier, Mathieu and Vincenot, Quentin and Troya-Galvis, Andres}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {2245--2271}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/bethune23a/bethune23a.pdf}, url = {https://proceedings.mlr.press/v202/bethune23a.html}, abstract = {We propose a new method, dubbed One Class Signed Distance Function (OCSDF), to perform One Class Classification (OCC) by provably learning the Signed Distance Function (SDF) to the boundary of the support of any distribution. The distance to the support can be interpreted as a normality score, and its approximation using 1-Lipschitz neural networks provides robustness bounds against $l2$ adversarial attacks, an under-explored weakness of deep learning-based OCC algorithms. As a result, OCSDF comes with a new metric, certified AUROC, that can be computed at the same cost as any classical AUROC. We show that OCSDF is competitive against concurrent methods on tabular and image data while being way more robust to adversarial attacks, illustrating its theoretical properties. Finally, as exploratory research perspectives, we theoretically and empirically show how OCSDF connects OCC with image generation and implicit neural surface parametrization.} }
Endnote
%0 Conference Paper %T Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks %A Louis Béthune %A Paul Novello %A Guillaume Coiffier %A Thibaut Boissin %A Mathieu Serrurier %A Quentin Vincenot %A Andres Troya-Galvis %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-bethune23a %I PMLR %P 2245--2271 %U https://proceedings.mlr.press/v202/bethune23a.html %V 202 %X We propose a new method, dubbed One Class Signed Distance Function (OCSDF), to perform One Class Classification (OCC) by provably learning the Signed Distance Function (SDF) to the boundary of the support of any distribution. The distance to the support can be interpreted as a normality score, and its approximation using 1-Lipschitz neural networks provides robustness bounds against $l2$ adversarial attacks, an under-explored weakness of deep learning-based OCC algorithms. As a result, OCSDF comes with a new metric, certified AUROC, that can be computed at the same cost as any classical AUROC. We show that OCSDF is competitive against concurrent methods on tabular and image data while being way more robust to adversarial attacks, illustrating its theoretical properties. Finally, as exploratory research perspectives, we theoretically and empirically show how OCSDF connects OCC with image generation and implicit neural surface parametrization.
APA
Béthune, L., Novello, P., Coiffier, G., Boissin, T., Serrurier, M., Vincenot, Q. & Troya-Galvis, A.. (2023). Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:2245-2271 Available from https://proceedings.mlr.press/v202/bethune23a.html.

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