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不规则采样时间序列中学习计数过程的个体特异性强度。我们提出了一种新颖的建模方法，其中强度是受控微分方程的解。我们首先基于神经受控微分方程设计了一个神经估计器。其次，我们证明在足够的正则性条件下，我们的模型可以在签名空间中线性化，从而产生一种基于签名的估计器，我们称之为CoxSig。我们为两种估计器提供了理论学习保证，随后在来自金融、预测性维护和食品供应链管理的大量模拟和真实数据集上展示了我们模型的性能。