Better Approximate Inference for Partial Likelihood Models with a Latent Structure
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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.
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