Dynamical Survival Analysis with Controlled Latent States
This work addresses survival analysis tasks in domains like finance and predictive maintenance, offering a novel modeling approach but appears incremental as it builds on existing neural controlled differential equations.
The authors tackled the problem of learning individual-specific intensities of counting processes from static variables and irregular time series by introducing a model where intensity is the solution to a controlled differential equation, resulting in neural and signature-based estimators with theoretical guarantees and performance demonstrated on simulated and real-world datasets.
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.