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Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes

NeurIPS 2026 · Time series › Causal and generative time series · approach: Generative temporal point processes · 0 citations (OpenAlex)

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Proposes the hyper Hawkes process (HHP), a Hawkes-style MTPP with a latent linear recurrence whose time-varying diagonalizable dynamics are predicted by a GRU hypernetwork, achieving strong likelihood and time/mark prediction on seven benchmarks while enabling per-event attribution via particle and leave-one-out influence measures.

Problem

Classical Hawkes processes are interpretable but inexpressive, while neural MTPPs are accurate but opaque; the paper seeks an MTPP that is both highly predictive and allows event-level attribution of predictions.

Approach

Lift the Hawkes linear recurrence into a latent space and let a GRU hypernetwork predict piecewise-constant, per-event eigen-decomposed dynamics (V_i, D_i) from the history, keeping the recurrence linear (conditionally) so that each past event's contribution (particle) can be tracked and attributed.

Key results

• HHP obtains the best average rank on the composite metric (2.6), with the best next-event time RMSE rank (1.4) and best mark accuracy rank (1.7) across seven datasets.
• HHP's per-event log-likelihood is second only to S2P2 on average (rank 2.0 vs 1.9), using on average 54% fewer parameters than S2P2.
• Ablation HHP-static (no hypernetwork) still outperforms several baselines, suggesting the latent-dimension decoupling from marks is a major factor.

Surprising findings

• Even with static, non-history-dependent dynamics (HHP-static), the model outperforms several neural baselines, suggesting the Hawkes inductive bias and latent decoupling matter more than hypernetwork dynamics alone.
• Attribution analysis shows the model can use both trigger events jointly for a response, so causal separation is not guaranteed.

Limitations

• Interpretability is a description of the model's solution strategy, not causal relationships; the model is predictive not explanatory.
• Sequential GRU hypernetwork is the main training throughput bottleneck.
• Attribution can assign credit jointly to multiple trigger events, so causal separation is not guaranteed.

Experimental setup

Datasets: Amazon Retweet Taxi Taobao StackOverflow Last.fm MIMIC-II

Benchmarks: Amazon Retweet Taxi Taobao StackOverflow Last.fm MIMIC-II

Metrics: per-event log-likelihood RMSE mark accuracy PCE ECE composite rank

Baselines: RMTPP NHP SAHP THP IFTPP AttNHP S2P2

Builds on: Hawkes process linear Hawkes process S2P2 DFBETA/DFFIT

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