Signature Isolation Forest

Marta Campi, Guillaume Staerman, Gareth W. Peters, Tomoko Masui
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:532-540, 2025.

Abstract

Functional Isolation Forest (FIF) is a recent state-of-the-art Anomaly Detection (AD) algorithm designed for functional data. It relies on a tree partition procedure where an abnormality score is computed by projecting each curve observation on a drawn dictionary through a linear inner product. Such linear inner product and the dictionary are a priori choices that highly influence the algorithm’s performances and might lead to unreliable results, particularly with complex datasets. This work aims to target such challenges by introducing Signature Isolation Forest, a novel class of AD algorithm leveraging the signature transform arising from rough path theory. Our objective is to remove the constraints imposed by FIF through the proposition of two algorithms which specifically target the linearity of the FIF inner product and the choice of the dictionary. We provide several numerical experiments, including a real-world applications benchmark showing the relevance of our methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-campi25a, title = {Signature Isolation Forest}, author = {Campi, Marta and Staerman, Guillaume and Peters, Gareth W. and Masui, Tomoko}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {532--540}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/campi25a/campi25a.pdf}, url = {https://proceedings.mlr.press/v258/campi25a.html}, abstract = {Functional Isolation Forest (FIF) is a recent state-of-the-art Anomaly Detection (AD) algorithm designed for functional data. It relies on a tree partition procedure where an abnormality score is computed by projecting each curve observation on a drawn dictionary through a linear inner product. Such linear inner product and the dictionary are a priori choices that highly influence the algorithm’s performances and might lead to unreliable results, particularly with complex datasets. This work aims to target such challenges by introducing Signature Isolation Forest, a novel class of AD algorithm leveraging the signature transform arising from rough path theory. Our objective is to remove the constraints imposed by FIF through the proposition of two algorithms which specifically target the linearity of the FIF inner product and the choice of the dictionary. We provide several numerical experiments, including a real-world applications benchmark showing the relevance of our methods.} }
Endnote
%0 Conference Paper %T Signature Isolation Forest %A Marta Campi %A Guillaume Staerman %A Gareth W. Peters %A Tomoko Masui %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-campi25a %I PMLR %P 532--540 %U https://proceedings.mlr.press/v258/campi25a.html %V 258 %X Functional Isolation Forest (FIF) is a recent state-of-the-art Anomaly Detection (AD) algorithm designed for functional data. It relies on a tree partition procedure where an abnormality score is computed by projecting each curve observation on a drawn dictionary through a linear inner product. Such linear inner product and the dictionary are a priori choices that highly influence the algorithm’s performances and might lead to unreliable results, particularly with complex datasets. This work aims to target such challenges by introducing Signature Isolation Forest, a novel class of AD algorithm leveraging the signature transform arising from rough path theory. Our objective is to remove the constraints imposed by FIF through the proposition of two algorithms which specifically target the linearity of the FIF inner product and the choice of the dictionary. We provide several numerical experiments, including a real-world applications benchmark showing the relevance of our methods.
APA
Campi, M., Staerman, G., Peters, G.W. & Masui, T.. (2025). Signature Isolation Forest. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:532-540 Available from https://proceedings.mlr.press/v258/campi25a.html.

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