# Moment-Based Variational Inference for Markov Jump Processes

## TL;DR

This paper introduces a flexible moment-based variational inference framework for approximate smoothing in latent Markov jump processes, enabling efficient inference and parameter estimation in complex stochastic models.

## Contribution

It presents a novel variational inference method that partitions transitions to express divergence in terms of moments, applicable to common jump processes and extended to parameter inference.

## Key findings

- Effective approximation of smoothing in Markov jump processes.
- Extension to parameter inference demonstrated on multiple examples.
- Flexible framework adaptable to various jump process classes.

## Abstract

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.