Efficient Temporal Point Processes via Monotone Alternating Splines

2026-07-02

AI Summary

Existing approaches to modeling cumulative conditional intensity functions using monotonic neural networks are hindered by convexity constraints, saturation bottlenecks, and structural limitations, impeding their ability to capture complex temporal dynamics effectively. This work proposes the Monotonic Alternating Splines (MAS) framework, which decouples interpolation and extrapolation components to enable flexible monotonic function approximation. By doing so, MAS maintains high fitting accuracy while significantly enhancing generalization capabilities. The method overcomes the structural constraints inherent in conventional monotonic neural networks and theoretically eliminates irreducible approximation error. Empirical evaluations demonstrate that MAS consistently outperforms state-of-the-art methods on both synthetic and real-world datasets, achieving superior performance with remarkable efficiency and accuracy.

Abstract

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.

Problem

• Temporal Point Processes
• Cumulative Conditional Intensity Function
• Monotone Neural Networks
• Representational Capacity
• Modeling Limitations

Innovation

• Monotone Alternating Splines
• Temporal Point Processes
• Cumulative Conditional Intensity Function
• Monotone Neural Networks
• Interpolation and Extrapolation