  Temporal Point Processes (TPP) with partial likelihoods involving a latent
structure often entail an intractable marginalization, thus making inference
hard. We propose a novel approach to Maximum Likelihood Estimation (MLE)
involving approximate inference over the latent variables by minimizing a tight
upper bound on the approximation gap. Given a discrete latent variable $Z$, the
proposed approximation reduces inference complexity from $O(|Z|^c)$ to
$O(|Z|)$. We use convex conjugates to determine this upper bound in a closed
form and show that its addition to the optimization objective results in
improved results for models assuming proportional hazards as in Survival
Analysis.
