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.

从静态变量和不规则采样的时间序列中学习个体特定强度的计数过程的任务。我们引入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控制微分方程来设计一个神经估计器。然后，在足够的正则条件下，我们展示了我们的模型可以在特征空间中线性化，得到一种基于特征的估计器，称为CoxSig。我们对这两个估计器提供了理论上的学习保证，然后展示了我们模型在金融、预测性维护和食品供应链管理等各种模拟和真实世界数据集上的性能。

控制潜在状态的动态存活分析