# Moment-Based Variational Inference for Markov Jump Processes

arXiv: https://arxiv.org/abs/1905.05451 · HTML: https://mlsanity.com/paper/1905.05451/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2019.

## Built on by (most cited first, 7 of 7)

- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [Variational Inference for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2109.14492/) (2021)
- [Moment-Based Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/2103.00988/) (2021)
- [Entropic Matching for Expectation Propagation of Markov Jump Processes](https://mlsanity.com/paper/2309.15604/) (2023)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)
- [Scan-Parallel Variational Inference for event-driven Latent Jump Models](https://mlsanity.com/paper/2610.12986/) (2026)

## Abstract (arXiv)

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.