Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the state-space point process (S2P2) model, a novel and performant model that leverages techniques derived for modern deep state-space models (SSMs) to overcome limitations of existing MTPP models, while simultaneously imbuing strong inductive biases for continuous-time event sequences that other discrete sequence models (i.e., RNNs, transformers) do not capture. Inspired by the classical linear Hawkes processes, we propose an architecture that interleaves stochastic jump differential equations with nonlinearities to create a highly expressive intensity-based MTPP model, without the need for restrictive parametric assumptions for the intensity. Our approach enables efficient training and inference with a parallel scan, bringing linear complexity and sublinear scaling while retaining expressivity to MTPPs. Empirically, S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets, delivering an average improvement of 33% over the best existing approaches.

翻译：标记时间点过程（MTPPs）用于建模在非规则时间间隔发生的事件序列，在医疗保健、金融和社交网络等领域具有广泛的应用。我们提出了状态空间点过程（S2P2）模型，这是一种新颖且高性能的模型，它利用为现代深度状态空间模型（SSMs）开发的技术来克服现有MTPP模型的局限性，同时为连续时间事件序列注入了其他离散序列模型（即RNN、Transformer）所不具备的强大归纳偏置。受经典线性霍克斯过程的启发，我们提出了一种将随机跳跃微分方程与非线性层交错结合的架构，从而创建了一个高度表达性的基于强度的MTPP模型，无需对强度函数施加限制性的参数假设。我们的方法通过并行扫描实现了高效的训练和推理，在保持对MTPPs表达力的同时，带来了线性复杂度和亚线性扩展能力。实证结果表明，S2P2在八个真实世界数据集上实现了最先进的预测似然，相比现有最佳方法平均提升了33%。