通过B样条实现平滑神经点过程
Smooth Neural Point Processes via B-Splines
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中文总结 AI 辅助
研究提出一种神经TPP模型，直接将CIF参数化为B样条基函数组合，由神经网络预测系数。此模型能精确评估NLL，保持架构灵活，支持并行训练与平滑正则化，实验显示相比基线提高了计算效率和预测准确性。
中文摘要 AI 辅助
时间点过程（TPP）为连续时间中的事件序列建模提供了通用且灵活的框架。神经网络已成功用于以高表达性和数据驱动的方式对TPP进行建模。神经TPP通常通过最大似然估计（MLE）进行训练，通过最小化负对数似然（NLL），这取决于条件强度函数（CIF）及其随时间的积分补偿器。最近的神经TPP方法能够在无需数值积分的情况下精确评估NLL。然而，这些方法通常对补偿器而非CIF直接建模，对神经网络架构施加约束，且训练时计算成本高。在这项工作中，我们提出了一种新颖的神经TPP模型，将CIF直接参数化为B样条基函数的非负组合，其系数由神经网络预测。该公式能够精确评估NLL，保持神经架构的完全灵活性，允许训练期间高效并行化，并通过积分平方二阶导数自然支持CIF平滑正则化。在合成和真实世界数据集上的实验表明，与参考神经TPP基线相比，计算效率和预测准确性有所提高。
英文摘要
Temporal point processes (TPPs) provide a general and flexible framework for modeling sequences of events in continuous time. Neural networks have been successfully employed to model TPPs in a highly expressive and data-driven way. Neural TPPs are typically trained via Maximum Likelihood Estimation (MLE) by minimizing the negative log-likelihood (NLL), which depends on both the conditional intensity function (CIF) and its integral over time, the compensator. Recent neural TPP approaches enable exact evaluation of the NLL without numerical integration. However, these methods typically model the compensator rather than the CIF directly, impose constraints on the neural network architecture, and are computationally expensive during training, as event contributions to the NLL are evaluated sequentially rather than in parallel. In this work, we propose a novel neural TPP model that directly parametrizes the CIF as a non-negative combination of B-spline basis functions, whose coefficients are predicted by a neural network. This formulation enables exact evaluation of the NLL, preserves full flexibility in the neural architecture, allows efficient parallelization during training, and naturally supports CIF smoothness regularization through the integrated squared second derivative. Experiments on both synthetic and real-world datasets show improved computational efficiency and predictive accuracy compared to the reference neural TPP baseline.
发表机构
- Politecnico di Milano（米兰理工大学）
- University College London（伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。
