From Jumps to Signatures: a Generative Method for Temporal Point Processes

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

Summary

The paper "From Jumps to Signatures: a Generative Method for Temporal Point Processes" introduces a novel approach to address limitations in applying rough path signatures to Temporal Point Processes (TPPs) and the absence of global sequence-level loss in neural TPP models. It proposes the `interarrival embedding`, a stable, injective lift that extends signature methods from continuous paths to discrete event sequences. This theoretical contribution underpins `sigTPP`, the first signature-based generative model for TPPs, which is trained using a path-level loss on complete trajectories. Furthermore, the research derives three new distributional discrepancies, offering mathematically justified tools for evaluating generative TPP models. Across synthetic and real-world datasets, `sigTPP` achieved the best average rank based on eight complementary metrics, outperformed or was within a standard error of the strongest baseline in 64% of dataset-metric pairs, and improved against every baseline by at least 19% on average.

Key takeaway

For Machine Learning Engineers developing generative models for Temporal Point Processes, `sigTPP` presents a significant advancement. This model, which utilizes interarrival embeddings and a path-level loss, offers superior performance in generating realistic event sequences compared to existing baselines. You should consider integrating `sigTPP` into your toolkit for tasks requiring high-fidelity TPP generation and utilize the proposed distributional discrepancies for more rigorous model evaluation.

Key insights

`sigTPP` is the first signature-based generative model for Temporal Point Processes, using interarrival embeddings and path-level loss for improved sequence generation.

Principles

• Interarrival embedding extends signatures to discrete event sequences.
• Path-level loss improves generative TPP model training.
• Distributional discrepancies are vital for TPP model evaluation.

Method

The method involves an `interarrival embedding` to transform jump paths into continuous paths, allowing signature methods for TPPs. `sigTPP` is then trained with a path-level loss on full trajectories, addressing global sequence generation.

In practice

• Apply `sigTPP` for generative event sequence modeling.
• Use interarrival embeddings for discrete signature methods.
• Employ new distributional discrepancies for TPP evaluation.

Topics

• Temporal Point Processes
• Generative Models
• Rough Path Signatures
• Interarrival Embedding
• Distributional Discrepancy
• Event Sequence Modeling

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.