Dynamic Survival Analysis with Controlled Latent States

Linus Bleistein, Van Tuan Nguyen, Adeline Fermanian, Agathe Guilloux
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:4160-4204, 2024.

Abstract

We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-bleistein24a, title = {Dynamic Survival Analysis with Controlled Latent States}, author = {Bleistein, Linus and Nguyen, Van Tuan and Fermanian, Adeline and Guilloux, Agathe}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {4160--4204}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/bleistein24a/bleistein24a.pdf}, url = {https://proceedings.mlr.press/v235/bleistein24a.html}, abstract = {We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.} }
Endnote
%0 Conference Paper %T Dynamic Survival Analysis with Controlled Latent States %A Linus Bleistein %A Van Tuan Nguyen %A Adeline Fermanian %A Agathe Guilloux %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-bleistein24a %I PMLR %P 4160--4204 %U https://proceedings.mlr.press/v235/bleistein24a.html %V 235 %X We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.
APA
Bleistein, L., Nguyen, V.T., Fermanian, A. & Guilloux, A.. (2024). Dynamic Survival Analysis with Controlled Latent States. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:4160-4204 Available from https://proceedings.mlr.press/v235/bleistein24a.html.

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