Smooth Neural Point Processes via B-Splines

2026-07-24 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, medium

Summary

A novel neural Temporal Point Process (TPP) model, "Smooth Neural Point Processes via B-splines," directly parametrizes the Conditional Intensity Function (CIF) using a non-negative combination of B-spline basis functions. This approach, where a neural network predicts the B-spline coefficients, overcomes limitations of prior neural TPPs. Unlike methods relying on numerical integration or compensator modeling with architectural constraints, this new model enables exact and efficient Negative Log-Likelihood (NLL) evaluation without numerical integration. It preserves full flexibility in neural architecture, allows efficient parallelization during training, and naturally supports CIF smoothness regularization through an integrated squared second derivative penalty. Experiments on both synthetic and real-world datasets demonstrate improved computational efficiency and predictive accuracy compared to the Omi et al. (2019) neural TPP baseline. The model also extends to multivariate TPPs.

Key takeaway

For Machine Learning Engineers developing Temporal Point Process models, this B-spline based CIF parametrization offers a superior approach. You can achieve exact Negative Log-Likelihood evaluation and parallelized training, significantly improving computational efficiency over prior methods. This allows for more flexible neural architectures without monotonicity constraints. Consider implementing this technique to enhance model accuracy and training speed for event sequence prediction tasks, especially in data-intensive environments.

Key insights

Directly modeling CIF with B-splines enables efficient, flexible, and smooth neural TPPs.

Principles

• B-splines ensure non-negativity and closed-form integrals.
• Smoothness regularization prevents overfitting.
• Local support of B-splines improves efficiency.

Method

The model parametrizes the CIF as a non-negative B-spline combination, with coefficients predicted by a neural network. NLL includes a roughness penalty for smoothness.

In practice

• Use B-splines for exact NLL in TPPs.
• Apply roughness penalty for CIF smoothness.
• Parallelize TPP training with B-spline CIFs.

Topics

• Temporal Point Processes
• B-splines
• Conditional Intensity Function
• Neural Networks
• Maximum Likelihood Estimation
• Smoothness Regularization

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.