Smooth Neural Point Processes via B-Splines

2026-07-23 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A novel neural Temporal Point Process (TPP) model is proposed, which directly parametrizes the Conditional Intensity Function (CIF) as a non-negative combination of B-spline basis functions. A neural network predicts the coefficients for these B-splines. This formulation overcomes limitations of existing neural TPPs, which often model the compensator, impose architectural constraints, and suffer from computationally expensive sequential NLL evaluation during training. The new model enables exact evaluation of the negative log-likelihood (NLL), preserves full flexibility in the neural architecture, and allows for efficient parallelization during training. It also naturally supports CIF smoothness regularization through the integrated squared second derivative. Experiments on both synthetic and real-world datasets demonstrate improved computational efficiency and predictive accuracy compared to reference neural TPP baselines.

Key takeaway

If you are developing or deploying Temporal Point Process (TPP) models for event sequence prediction, you should consider this B-spline-based approach. It offers significant advantages in computational efficiency and predictive accuracy over traditional neural TPPs, especially due to its parallel training capability and direct Conditional Intensity Function (CIF) parametrization. This can streamline your model development and improve real-world performance.

Key insights

A novel neural TPP model uses B-splines for direct CIF parametrization, enabling parallel training and improved accuracy.

Principles

• Direct CIF parametrization enhances TPP modeling.
• B-splines enable exact NLL and smoothness regularization.
• Parallel training improves computational efficiency.

Method

Parametrize the CIF as a non-negative combination of B-spline basis functions, with coefficients predicted by a neural network, allowing parallel NLL evaluation.

In practice

• Apply B-spline CIFs for TPPs requiring exact NLL.
• Use this model for parallelized TPP training.
• Integrate smoothness regularization for TPP CIFs.

Topics

• Temporal Point Processes
• Neural Networks
• B-splines
• Conditional Intensity Function
• Maximum Likelihood Estimation
• Parallel Training

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

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.