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Addressing Mark Imbalance in Integration-free Marked Temporal Point Processes
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Proposes thresholding on mark probability normalized by prior, predicting mark first then time, and a neural MTPP model (IFNMTPP) that directly models the unified survival-type integral Γ*(m,t) to avoid numerical improper integration.
Problem
Next-event prediction in marked temporal point processes degrades for rare marks when the mark distribution is highly imbalanced; existing MTPP models predict time first and rely on numerical improper integration for mark probabilities and expected times.
Approach
Predict the mark first using thresholded mark probabilities normalized by mark priors, then sample time from p*(t|m) via inverse transform sampling using a neural model of the integral Γ*(m,t) = ∫_t^∞ p*(m,τ)dτ, whose monotone non-negative network with gradient -p*(m,t) yields both p*(m) and the CDF without numerical integration.
Key results
- On Retweet, the proposed model reaches rare-mark macro-F1 of 0.2010 versus 0.0000-0.0252 for FullyNN, THP, AttNHP and Marked-LNM... (SAHP 0.0266)
- Thresholding improves rare-mark macro-F1 over no-thresholding on Retweet (0.2010 vs 0.0333) and USearthquake (0.0339 vs 0.0121) for the proposed model.
- Proposed model achieves lowest MMAE on Retweet (2515.1), SO (0.5212) and USearthquake (0.6856) among compared MTPP models, outperforming Marked-LNM on time prediction in most datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add thresholding to mark prediction (ablation) | IFNMTPP · Retweet rare marks | macro-F1: 0.0333 -> 0.2010 | Helped |
| add thresholding to mark prediction (ablation) | IFNMTPP · StackOverflow rare marks | macro-F1: 0.1065 -> 0.1476 | Helped |
| add thresholding to mark prediction (ablation) | IFNMTPP · Taobao rare marks | macro-F1: 0.3759 -> 0.3987 | Helped |
| add thresholding to mark prediction (ablation) | IFNMTPP · USearthquake rare marks | macro-F1: 0.0121 -> 0.0339 | Helped |
| predict the mark before time rather than time before mark (ablation) | IFNMTPP · Retweet rare marks | macro-F1: 0.2000 -> 0.2010 | Helped |
| predict the mark before time rather than time before mark (ablation) | IFNMTPP · StackOverflow rare marks | macro-F1: 0.1023 -> 0.1476 | Helped |
| predict the mark before time rather than time before mark (ablation) | IFNMTPP · Taobao rare marks | macro-F1: 0.3054 -> 0.3987 | Helped |
| predict the mark before time rather than time before mark (ablation) | IFNMTPP · USearthquake rare marks | macro-F1: 0.0298 -> 0.0339 | Helped |
| add thresholding to time-first mark prediction (ablation) | time-mark baseline · Retweet M | macro-F1: 0.4252 -> 0.4741 | Helped |
| add thresholding to time-first mark prediction (ablation) | time-mark baseline · StackOverflow M | macro-F1: 0.0906 -> 0.1431 | Helped |
| add thresholding to time-first mark prediction (ablation) | time-mark baseline · Taobao M | macro-F1: 0.3135 -> 0.3289 | Helped |
| add thresholding to time-first mark prediction (ablation) | time-mark baseline · USearthquake M | macro-F1: 0.1066 -> 0.1214 | Helped |
Surprising findings
- Predicting time first and then mark with thresholding (time-mark-with-thresholding) gave lower rare-mark performance than the proposed mark-first ordering on all datasets.
- Resampling baselines (oversampling and undersampling) produced much higher time MMAE on SO, Taobao and USearthquake than the proposed model.
Limitations
- Only the mark-first ordering and thresholding were evaluated; resampling and cost-sensitive approaches were not studied in this setting.
- Domain-knowledge incorporation into thresholding (e.g., importance of rare marks) is not explored.
- Tanh activation makes the implemented model only approximately satisfy the monotone-integral assumption.
Experimental setup
Datasets: Retweet StackOverflow Taobao USearthquake five synthetic datasets (Hawkes_1, Hawkes_2, Poisson, self-correct, stationary renewal)
Benchmarks: Retweet StackOverflow Taobao USearthquake
Metrics: macro-F1 micro-F1 MMAE Spearman coefficient L1 distance
Baselines: FullyNN THP SAHP AttNHP Marked-LNM oversampling undersampling ours-w/o-thresholding time-mark-with-thresholding time-mark-w/o-thresholding
Builds on: Hawkes process FullyNN Marked-LNM SAHP
Closest papers by meaning
- Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations (ICLR 2024 · similarity 0.86)
- Decomposable Transformer Point Processes (NeurIPS 2024 · similarity 0.86)
- EasyTPP: Towards Open Benchmarking Temporal Point Processes (ICLR 2024 · similarity 0.86)
- Deep Continuous-Time State-Space Models for Marked Event Sequences (NeurIPS 2025 · similarity 0.85)
- Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes (NeurIPS 2026 · similarity 0.85)
- Interacting Diffusion Processes for Event Sequence Forecasting (ICML 2024 · similarity 0.84)
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