Particle variational message passing
Graphical inference using empirical distribution estimates
July 25, 2014 — April 30, 2025
Empirical CDFs: Can they be used to approximate belief propagation updates, or any other kind of variational message passing algorithm?
We could use several variational methods that can be understood as using empirical CDFs for message passing; one candidate is Stein variational gradient descent message passing, which constructs the ensemble by solving an optimisation problem. Another might be Ensemble Kalman filtering, which uses a stochastic perturbation of a fixed population to find the posterior. That would be Gaussian Ensemble Belief Propagation.
This page is about the particle filter analogue, which would use an importance sampling-like update. How does that work? TBD
1 Basic
- TBC.
2 Expectation
The Expectation form reputedly has advantages (Lienart, Teh, and Doucet 2015). TBC.
3 Stein variational gradient descent
Define a kernel over factors and Stein Variational Gradient Descent decomposes into local messages. Discovered simultaneously in 2018 by Wang, Zeng, and Liu (2018) and Zhuo et al. (2018), and elaborated/expanded/varied in subsequent works. (Pavlasek et al. 2024; Zhou and Qiu 2023).
I just met Joshua Mah who introduced me to Stein Variational Belief Propagation for Multi-Robot Coordination (Pavlasek et al. 2024) but I have not digested it fully yet. TBC