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.

翻译：我们考虑从一组静态变量和非均匀采样的时间序列中学习计数过程的个体特异性强度的任务。我们引入了一种新颖的建模方法，其中强度是受控微分方程的解。我们首先通过构建神经受控微分方程来设计一个神经估计器。随后，我们展示了在足够正则性条件下，我们的模型可以在签名空间中被线性化，从而产生一个基于签名的估计器，我们称之为CoxSig。我们为这两个估计器提供了理论上的学习保证，然后在一系列来自金融、预测性维护和食品供应链管理的模拟和真实世界数据集上展示了我们模型的性能。