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 nature of these empirical mechanisms hinders estimation in the multivariate setting. Spatiotemporal applications alleviate this by allowing relationships to depend only on relative distances in real Euclidean space; we employ this framework as a vessel for embedding arbitrary event types in a new latent space. We demonstrate that learning the embedding alongside a point process model is resilient to ambiguities in the relationships among event types by performing synthetic experiments on short records as well as an investigation into options markets and pathogens.