# Expectation propagation for continuous time stochastic processes

arXiv: https://arxiv.org/abs/1512.06098 · HTML: https://mlsanity.com/paper/1512.06098/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2015.

## Built on by (most cited first, 4 of 4)

- [Variational Gaussian Process Diffusion Processes](https://mlsanity.com/paper/2306.02066/) (2023)
- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [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)

## Abstract (arXiv)

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference. We then show how the approximation can be extended to a wide class of discrete-state Markov jump pro- cesses by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.