New Spline Method Boosts Temporal Point Process Efficiency

Temporal Point Processes (TPPs) are widely used across various fields, but accurately modeling their conditional intensity can be computationally intensive and prone to numerical errors. A common approach is to model the cumulative conditional intensity function (CCIF), which improves efficiency. However, current CCIF parameterizations, primarily Monotone Neural Networks (MNNs), suffer from structural limitations like convexity restrictions, saturation, and violations of CCIF requirements, which hinder their ability to capture complex temporal dynamics. To address these issues, this paper proposes Monotone Alternating Splines (MAS). MAS offers a flexible and efficient framework for CCIF modeling by leveraging distinct interpolation and extrapolation components. Theoretically, MAS's interpolation ensures high fitting accuracy, while its extrapolation supports robust generalization, effectively reducing the irreducible approximation gaps found in MNNs. Extensive experiments on both synthetic and real-world datasets demonstrate that MAS consistently achieves superior performance, making it a more powerful tool for analyzing and predicting event sequences.