用分段线性插值提升时间点过程建模效率与精度
Efficient Temporal Point Processes via Monotone Alternating Splines
- 引入单调交替样条，分离插值与外推能力
- 在真实和合成数据上显著优于现有方法
- 适合需要高效建模复杂时间动态的研究者
时间点过程（TPPs）在多个领域有广泛应用。相较于建模条件强度，建模累积条件强度函数（CCIF）可提升计算效率并消除数值近似误差。然而，当前的CCIF参数化普遍依赖单调神经网络（MNNs），我们发现其存在三大结构性瓶颈——凸性限制、饱和极限以及不满足CCIF建模要求，从根本上制约了对复杂时间动态的表达能力。为此，本文提出一种新框架：单调交替样条（MAS）。通过区分插值与外推组件，MAS提供灵活高效的CCIF建模方案。理论上，其插值部分具有强拟合精度，外推部分支持鲁棒泛化，有效缩小了MNNs的不可约近似差距。大量实验表明，MAS在合成与真实世界数据集上均取得更优性能。
原文摘要 · Abstract (English)
Temporal point processes (TPPs) have widespread applications across various domains. Compared to modeling the conditional intensity of a TPP, modeling its cumulative conditional intensity function (CCIF) improves computational efficiency and eliminates numerical approximation errors. However, current CCIF parameterizations uniformly rely on Monotone Neural Networks (MNNs), which we identify as suffering from three structural deadlocks--convexity restrictions, saturation limits, and violations of CCIF modeling requirements--that fundamentally restrict their representational capacity for complex temporal dynamics. To resolve these bottlenecks, this paper proposes a novel framework called Monotone Alternating Splines (MAS). By leveraging distinct interpolation and extrapolation components, MAS provides a flexible and efficient framework for modeling CCIFs. Theoretically, MAS's interpolation provides strong fitting accuracy, while its extrapolation supports robust generalization, reducing the irreducible approximation gaps of MNNs. Extensive experiments show that MAS achieves superior performance on both synthetic and real-world datasets.
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