Multivariate Powered Dirichlet-Hawkes Process

Gaël Poux-Médard, Julien Velcin, Sabine Loudcher

Abstract:

The publication time of a document carries a relevant in- formation about its semantic content. The Dirichlet-Hawkes process has been proposed to jointly model textual information and publication dy- namics. This approach has been used with success in several recent works, and extended to tackle specific challenging problems –typically for short texts or entangled publication dynamics. However, the prior in its cur- rent form does not allow for complex publication dynamics. In particular, inferred topics are independent from each other –a publication about fi- nance is assumed to have no influence on publications about politics, for instance.
In this work, we develop the Multivariate Powered Dirichlet-Hawkes Pro- cess (MPDHP), that alleviates this assumption. Publications about var- ious topics can now influence each other. We detail and overcome the technical challenges that arise from considering interacting topics. We conduct a systematic evaluation of MPDHP on a range of synthetic datasets to define its application domain and limitations. Finally, we develop a use case of the MPDHP on Reddit data. At the end of this article, the interested reader will know how and when to use MPDHP, and when not to.