用B样条直接建模事件强度,提升神经点过程的训练效率与精度。
Smooth Neural Point Processes via B-Splines

- 以B样条基函数组合直接参数化条件强度函数
- 训练速度提升,预测准确率优于基准模型
- 支持平滑正则化,适合需要连续时间建模的场景
时间点过程(TPPs)为连续时间事件序列建模提供了通用且灵活的框架。神经网络被成功用于以高度表达性和数据驱动的方式建模TPPs。典型的神经TPP通过最大似然估计(MLE)训练,最小化负对数似然(NLL),其依赖于条件强度函数(CIF)及其在时间上的积分(补偿器)。近期方法可精确计算NLL,无需数值积分,但通常建模补偿器而非直接建模CIF,对神经网络架构有约束,且训练时事件贡献需串行计算,效率较低。本文提出一种新神经TPP模型,直接将CIF表示为非负B样条基函数的组合,其系数由神经网络预测。该形式支持精确计算NLL,保留神经网络架构灵活性,可高效并行训练,并通过积分平方二阶导数自然实现CIF平滑正则化。在合成与真实数据集上的实验表明,相比基准神经TPP模型,本方法在计算效率和预测精度上均有提升。
原文摘要 · Abstract (English)
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.
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