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Deep Representation Learning for Forecasting Recursive and Multi-Relational Events in Temporal Networks
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Proposes RRHyperTPP, a temporal point process model over multi-relational recursive hyperedges that uses a dynamic node encoder, hyperedge link-prediction decoder, and noise contrastive estimation to forecast interaction type and time.
Problem
Forecasting higher-order interaction events that are multi-relational and recursive (hyperedges containing other hyperedges) in temporal networks, where exact maximum likelihood for TPP over exponentially many hyperedges is intractable.
Approach
Models recursive multi-relational hyperedges as TPP event types with intensity parameterized by dynamic node embeddings (interaction update plus temporal drift) and attention-based hyperedge link prediction, trained with noise contrastive estimation instead of negative-sampling likelihood approximation.
Key results
- RRHyperTPP-f reaches 93.4% AUC on Enron versus 87.6% for HGDHE and 85.8% for TGN on interaction type prediction.
- RRHyperTPP-f shows an average 8.2% AUC gain over the negative-sampling variant RRHyperTPP-N, but a 15.3% higher MAE on average.
- On depth-two ICEWS datasets, RRHyperTPP-f achieves 58.9% AUC on ICEWS-India and 60.5% on ICEWS-Nigeria.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RRHyperTPP-j instead of TGN for interaction-type prediction | RRHyperTPP-j · Enron, Twitter, Boston, Obama, Pope, Cannes | AUC (%): +2.9%, +2.3%, and +2.2% for RRHyperTPP-j, RRHyperTPP-f, and RRHyperTPP-o, respectively | Helped |
| Use RRHyperTPP-f instead of HGDHE | RRHyperTPP-f · Enron, Twitter, Boston, Obama, Pope, Cannes | AUC (%): 13.6% | Helped |
| Train with noise-contrastive loss instead of negative-sampling approximate NLL | RRHyperTPP · Enron, Twitter, Boston, Obama, Pope, Cannes | AUC (%): 8.2% | Helped |
| Train with noise-contrastive loss instead of negative-sampling approximate NLL | RRHyperTPP · Enron, Twitter, Boston, Obama, Pope, Cannes | MAE: 15.3% | Hurt |
| Add the Node Update stage (ablation) | RRHyperTPP · Enron | loss: 5.1% | Helped |
| Add the Node Update stage (ablation) | RRHyperTPP · Twitter, Boston, Obama, Pope | loss: 1.88%, 1.02%, 4.37%, and 6.19% | Helped |
| Add the Drift stage (ablation) | RRHyperTPP · Enron | loss: 4.9% | Helped |
| Add the Drift stage (ablation) | RRHyperTPP · Twitter, Boston, Obama, Pope, Cannes | loss: 6.41%, 1.44%, 10.49%, 22.22%, and 3.59% | Helped |
| Use recursive multi-relational hyperedge prediction instead of flattened HyperTPP hyperedges (ablation) | RRHyperTPP · Enron | loss: 4.8% | Helped |
| Use recursive multi-relational hyperedge prediction instead of HyperTPP (ablation) | RRHyperTPP · Twitter, Boston, Obama, Pope, Cannes | loss: 0.67%, 1.31%, 1.51%, 3.35%, and 1.64% | Helped |
| Add supervised noise-contrastive loss with α=1 instead of α=0 (ablation) | RRHyperTPP-f · Interaction-type prediction | AUC (%): 1.7% | Helped |
| Increase supervised noise-contrastive loss weight from α=1 to α=2 (ablation) | RRHyperTPP-f · Cannes | AUC (%) | Hurt |
Surprising findings
- No single drift variant (time projection, Fourier embedding, Neural ODE) dominates across all tasks and datasets, despite the expectation that Neural ODEs should perform best.
- The noise-contrastive training improves type-prediction AUC but worsens time-prediction MAE relative to the negative-sampling variant.
Limitations
- Time prediction is worse than the negative-sampling baseline (higher MAE), so the trade-off is unresolved.
- Noise generation strategy is heuristic and the authors note it needs improvement.
- Depth-two datasets are only ICEWS and performance on them is modest (around 59-61% AUC).
Experimental setup
Datasets: Enron Twitter Boston Obama Pope Cannes ICEWS-India ICEWS-Nigeria
Benchmarks: Enron Twitter Boston Obama Pope Cannes ICEWS-India ICEWS-Nigeria
Metrics: AUC MAE
Baselines: TGN HGDHE RRHyperTPP-N HyperTPP-j/f/o
Builds on: HGDHE JODIE Neural ODE Fourier time features transformer multi-head attention
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