# HMM inference as belief propagation

## Summary

The forward-backward algorithm for computing posterior marginals in an HMM can be viewed as a special case of sum-product belief propagation. Similarly, the Viterbi algorithm for computing the most likely state sequence can be viewed as a special case of max-product belief propagation.

## Context

This concept has the prerequisites:

## 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)

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 13.2.3, pages 625-627

## See also

- Following on this result, the Baum-Welch algorithm for learning HMM parameters can be seen as a [speical case](baum_welch_as_em) of [Expectation-Maximization](expectation_maximization) .
- Kalman smoothing can be seen as a [speical case](kalman_as_bp) of the forward-backward algorithm, hence a special case of BP.