Smooth Neural Point Processes via B-Splines

2026-07-23

AI Summary

This work addresses key limitations of existing neural temporal point process models, which often suffer from low training efficiency due to sequential event processing and difficulty in directly modeling smooth conditional intensity functions. The authors propose a novel approach that, for the first time, employs B-spline basis functions to directly parameterize the conditional intensity, with non-negative combination coefficients predicted by an arbitrary neural network. This formulation enables exact maximum likelihood estimation, supports highly efficient parallel training, and incorporates natural smoothness regularization through integration of second-order derivatives. Experimental results demonstrate that the proposed model significantly outperforms current baselines on both synthetic and real-world datasets, achieving simultaneous improvements in predictive accuracy and training efficiency.

Abstract

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.

Problem

• Temporal Point Processes
• Neural Networks
• Conditional Intensity Function
• Maximum Likelihood Estimation
• Computational Efficiency

Innovation

• B-splines
• neural point processes
• conditional intensity function
• exact likelihood evaluation
• smoothness regularization