# Variational Approximations between Mean Field Theory and the Junction Tree Algorithm

arXiv: https://arxiv.org/abs/1301.3901 · HTML: https://mlsanity.com/paper/1301.3901/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

## Built on by (most cited first, 2 of 2)

- [CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver](https://mlsanity.com/paper/2403.03391/) (2024)
- [Realising Active Inference in Variational Message Passing: the Outcome-blind Certainty Seeker](https://mlsanity.com/paper/2104.11798/) (2021)

## Abstract (arXiv)

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generalized mean field equations to optimize the cluster potentials. We show that the method bridges the gap between the standard mean field approximation and the exact junction tree algorithm. In addition, we address the problem of how to choose the graphical structure of the approximating distribution. From the generalised mean field equations we derive rules to simplify the structure of the approximating distribution in advance without affecting the quality of the approximation. We also show how the method fits into some other variational approximations that are currently popular.