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Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations
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Proposes Dec-ODE, a marked temporal point process model that decouples per-event influence trajectories evolved by neural ODEs, enabling parallel computation of intensity, survival and mark probabilities.
Problem
Marked temporal point process modeling is typically done with entangled hidden states; individual event influences are not interpretable, and integrals (density, survival, expectations) need costly sequential or sampling-based computation.
Approach
Each event's hidden state is propagated independently by a shared neural ODE from its occurrence time; the ground intensity is a linear (softplus-summed) combination of per-event influence functions, and the compensator and survival are obtained by integrating the ODE jointly, so all inference quantities come from one parallel solve.
Key results
- Dec-ODE achieves best RMSE on MOOC (0.467), Reddit (0.934), Retweet (0.985) and MIMIC-II (0.810) in the reported table, and is comparable or better on most metrics across five datasets.
- Parallel decoupled computation reduces training time per iteration to 0.20-0.47 of sequential computation (e.g., Reddit 15.5 vs 78.7 sec/iter).
- On the simulated Hawkes process, Dec-ODE gets NLL 0.2739 vs ANHP 0.2807 and THP 3.0121.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · MOOC | RMSE: 0.470 -> 0.467 | Helped |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · MOOC | ACC: 32.30 -> 42.08 | Helped |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · Reddit | RMSE: 0.953 -> 0.934 | Helped |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · Reddit | ACC: 63.45 -> 62.32 | Hurt |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · Retweet | RMSE: 0.990 -> 0.985 | Helped |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · Retweet | NLL: -3.134 -> -2.897 | Hurt |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · MIMIC-II | RMSE: 0.859 -> 0.810 | Helped |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · MIMIC-II | ACC: 85.98 -> 85.06 | Hurt |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · StackOverflow | RMSE: 1.017 -> 1.018 | Hurt |
| Use decoupled event influences with neural ODE dynamics | Dec-ODE · StackOverflow | ACC: 56.80 -> 55.58 | Hurt |
| Replace linear Φλ with non-linear Φλ (softplus after summing influences) (ablation) | Dec-ODE · StackOverflow | NLL: 0.9948 -> 0.8987 | Helped |
| Replace linear Φλ with non-linear Φλ (softplus after summing influences) (ablation) | Dec-ODE · MIMIC-II | NLL: 0.2451 -> 0.2183 | Helped |
Surprising findings
- Dec-ODE was not uniformly best: ANHP achieved better NLL on several datasets (e.g., Reddit, Retweet, MIMIC-II), with Dec-ODE's NLL worse than ANHP's in most cases.
- The non-linear variant with softplus after summation improved NLL on StackOverflow, MIMIC-II and Retweet but was much worse on Reddit (18.26 vs 0.52).
Limitations
- Linear influence functions only allow excitatory effects; non-negativity constraint restricts modeling of inhibitory effects.
- Thinning-based baselines required extensive hyperparameter tuning; hyperparameters were not fully searched per dataset.
- Dec-ODE does not model inter-event dependencies, so it may miss contextual relations between events.
Experimental setup
Datasets: Reddit StackOverflow MIMIC-II MOOC Retweet Hawkes simulation (tick library)
Benchmarks: MOOC Reddit Retweet MIMIC-II StackOverflow simulated Hawkes process
Metrics: RMSE ACC NLL training time per iteration memory
Baselines: RMTPP THP IFL ANHP
Builds on: Neural ODE Hawkes process Intensity-Free Learning Transformer Hawkes Process Attentive Neural Hawkes Process
Closest papers by meaning
- Deep Continuous-Time State-Space Models for Marked Event Sequences (NeurIPS 2025 · similarity 0.89)
- Interacting Diffusion Processes for Event Sequence Forecasting (ICML 2024 · similarity 0.88)
- EasyTPP: Towards Open Benchmarking Temporal Point Processes (ICLR 2024 · similarity 0.87)
- Neural Jump-Diffusion Temporal Point Processes (ICML 2024 · similarity 0.87)
- Addressing Mark Imbalance in Integration-free Marked Temporal Point Processes (NeurIPS 2025 · similarity 0.86)
- Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes (NeurIPS 2026 · similarity 0.86)
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