  The publication time of a document carries a relevant information about its
semantic content. The Dirichlet-Hawkes process has been proposed to jointly
model textual information and publication dynamics. 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 current form does not allow for complex
publication dynamics. In particular, inferred topics are independent from each
other --a publication about finance is assumed to have no influence on
publications about politics, for instance.
  In this work, we develop the Multivariate Powered Dirichlet-Hawkes Process
(MPDHP), that alleviates this assumption. Publications about various 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.
