Research map / Probabilistic and scientific modeling / Variational and generative sampling
Hawkes Processes with Stochastic Excitations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Model contagion levels Y as a stochastic process (GBM or exponential Langevin SDE) instead of constant or iid Gamma | Hawkes process intensity · synthetic simulated event data (ground truth GBM vs iid Gamma) | qualitative reproduction of ground-truth stylized facts | Helped |
| Learn contagion levels Y as iid Gamma rather than GBM when ground truth is GBM (ablation) | Stochastic Hawkes with iid Gamma levels · synthetic data with GBM ground truth | qualitative reproduction of ground-truth dynamics | Hurt |
| Use GBM rather than iid Gamma as the contagion model when ground truth is iid Gamma (ablation) | Stochastic Hawkes with GBM levels · synthetic data with iid Gamma ground truth | qualitative recovery of ground-truth properties | Helped |
| Sampling algorithm for stochastic Hawkes replaces naive Ogata thinning | Simulation of event sequences · general | computational complexity in number of events n | Helped |
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