# structured mean field

## Summary

The naive mean field approximation assumes a fully factorized approximating distribution, which can be inaccurate if variables are tightly coupled. Structured mean field instead assumes the distribution factorizes into a product of tractable distributions, such as trees or chains.

## Context

This concept has the prerequisites:

- mean field approximation
- inference in MRFs (Structured mean field is a graphical model inference algorithm.)
- sum-product on trees (Structured mean field uses exact inference algorithms for graphical models, most commonly sum-product.)

## Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Graphical models, exponential families, and variational inference (2008)

An in-depth review of exact and approximate inference methods for graphical models.

Location:
Section 5.5, pages 142-147

## -Paid-

→ Probabilistic Graphical Models: Principles and Techniques

A very comprehensive textbook for a graduate-level course on probabilistic AI.

Location:
Section 11.5.2, pages 456-468

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 21.4, pages 739-742

Additional dependencies:

- hidden Markov models

## See also

-No Additional Notes-