Dynamic Survival Analysis with Controlled Latent States
Linus Bleistein, Van Tuan NGUYEN, Adeline Fermanian, Agathe Guilloux
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.
BibTeX
@inproceedings{
bleistein2024dynamic,
title={Dynamic Survival Analysis with Controlled Latent States},
author={Linus Bleistein and Van Tuan NGUYEN and Adeline Fermanian and Agathe Guilloux},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=xGlVkBSDdt}
}