Latent Embeddings of Point Process Excitations

When specific events seem to spur others in their wake, marked Hawkes processes enable us to reckon with their statistics. The underdetermined empirical nature of these event-triggering mechanisms hinders estimation in the multivariate setting. Spatiotemporal applications alleviate this obstacle by allowing relationships to depend only on relative distances in real Euclidean space; we employ the framework as a vessel for embedding arbitrary event types in a new latent space. By performing synthetic experiments on short records as well as an investigation into options markets and pathogens, we demonstrate that learning the embedding alongside a point process model uncovers the coherent, rather than spurious, interactions.