Moment-Based Variational Inference for Markov Jump Processes
This work addresses inference challenges for Markov jump processes, which are common in applications, but appears incremental as it builds on existing variational methods with a specific partitioning approach.
The authors tackled the problem of approximate smoothing for latent Markov jump processes by proposing a moment-based variational inference framework, which partitions transitions into classes to express the Kullback-Leibler divergence in terms of moment functions, and demonstrated it on examples.
We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to parameter inference and demonstrate the method on several examples.