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Continuous-Time Graph Representation with Sequential Survival Process
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Proposes GraS^2P, a continuous-time latent distance model whose likelihood uses a sequential survival process to capture intermittent link persistence and absence, with piecewise-linear node trajectories.
Problem
Continuous-time dynamic network representation learning typically treats links as instantaneous events or uses binary cross-entropy, failing to model links that persist for durations and then disappear and reappear.
Approach
A Sequential Survival process (alternating survival functions for link and non-link states) defines the likelihood of interval networks; the hazard rate is exp(beta(s) + s*squared latent distance), with node positions following piecewise-linear velocity trajectories and a Gaussian prior on velocities.
Key results
- Network reconstruction on Synthetic-alpha: GraS^2P ROC 0.845 vs 0.749 for best baseline PiVeM.
- Future link prediction on Synthetic-alpha: GraS^2P ROC 0.902 vs 0.784 for HTNE.
- On Infectious and Contacts future link prediction, LDM beats GraS^2P (e.g., Contacts ROC 0.821 vs 0.793) and on Facebook future link prediction GraS^2P (0.705) trails LDM (0.781).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GraS²P instead of the strongest baseline | Network completion · Contacts | AUC-ROC: $.584\pm.004$ -> $.680\pm.013$ | Helped |
| Use GraS²P instead of the strongest baseline | Network completion · NeurIPS | AUC-ROC: $.748\pm.010$ -> $.735\pm.029$ | Hurt |
| Use GraS²P instead of the strongest baseline | Network reconstruction · Contacts | AUC-ROC: $.593\pm.004$ -> $.825\pm.008$ | Helped |
| Use GraS²P instead of the strongest baseline | Network reconstruction · NeurIPS | AUC-ROC: $.760\pm.007$ -> $.889\pm.013$ | Helped |
| Use GraS²P instead of the strongest baseline | Future link prediction · Synthetic-α | AUC-ROC: $.784\pm.013$ -> $.902\pm.011$ | Helped |
| Use GraS²P instead of the strongest baseline | Future link prediction · Synthetic-β | AUC-ROC: $.894\pm.005$ -> $.880\pm.012$ | Hurt |
| Use GraS²P instead of the strongest baseline | Future link prediction · Contacts | AUC-ROC: $.821\pm.004$ -> $.793\pm.013$ | Hurt |
| Use GraS²P instead of the strongest baseline | Future link prediction · HyperText | AUC-ROC: $.663\pm.004$ -> $.654\pm.005$ | Hurt |
| Use GraS²P instead of the strongest baseline | Future link prediction · Infectious | AUC-ROC: $.958\pm.004$ -> $.943\pm.017$ | Hurt |
| Use GraS²P instead of the strongest baseline | Future link prediction · Facebook | AUC-ROC: $.781\pm.007$ -> $.705\pm.009$ | Hurt |
| Use GraS²P instead of the strongest baseline | Future link prediction · NeurIPS | AUC-ROC: $.695\pm.012$ -> $.820\pm.008$ | Helped |
| Increase embedding dimension | GraS²P · Synthetic-α | performance | Helped |
Surprising findings
- Static LDM outperforms GraS^2P on several future link prediction tasks (Contacts, HyperText, Infectious, Facebook), which the authors attribute to global information from aggregated links.
- PiVeM outperforms GraS^2P on NeurIPS network reconstruction and completion-related comparisons in some cases.
Limitations
- Piecewise linear trajectories restrict node motion; periodic structures are not captured.
- Performance on future link prediction for Synthetic-beta and some real datasets is not optimal relative to baselines.
- Extension to weighted, signed, and large-scale networks is left to future work.
Experimental setup
Datasets: Facebook NeurIPS Contacts HyperText Infectious Synthetic-alpha Synthetic-beta
Benchmarks: Facebook NeurIPS Contacts HyperText Infectious Synthetic-alpha Synthetic-beta
Metrics: AUC-ROC AUC-PR
Baselines: LDM Node2Vec CTDNE HTNE M2DNE PiVeM
Builds on: latent distance model PiVeM Hawkes process (HTNE) Node2Vec
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