Research map / Probabilistic and scientific modeling / Causal discovery
Cumulants of Hawkes Processes are Robust to Observation Noise
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use cumulant-based estimator (NPHC) instead of maximum-likelihood under random translation noise | Multivariate Hawkes process causal structure learning · Synthetic 10-dim MHP with Gaussian translations | L2,2 norm and Precision@10 | Helped |
| Random translation noise (increasing noise variance) | Maximum-likelihood estimators (ADM4, Desync-MLE) · Synthetic 10-dim MHP | L2,2 norm of estimated excitation matrix | Hurt |
| Wiener-Hopf (WH) estimator under increasing noise | WH method · Synthetic 10-dim MHP | Precision and norm | Mixed |
| Random translation noise on real data | ADM4 on Bund Futures · Bund Futures (Eurex) | excitation matrix norm | Hurt |
| Cumulant-based estimators (NPHC, WH) used under random translation on real data | NPHC and WH on Bund Futures · Bund Futures (Eurex) | stability of estimates vs noise-free estimate | No clear effect |
| Cumulant estimators' sensitivity to noise scale (integrated covariance and skewness) | Integrated cumulant estimators · Synthetic 10-dim MHP | average L2-distance to ground-truth cumulants | No clear effect |
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