# Baum-Welch algorithm

(45 minutes to learn)

## Summary

The Baum-Welch algorithm is an algorithm for maximum likelihood learning in hidden Markov models (HMMs). It is a special case of expectation-maximization (EM), and alternates between inferring the posterior marginals and maximizing the expected log-likelihood given those posterior marginals.

## Context

This concept has the prerequisites:

- hidden Markov models (Baum-Welch is an algorithm for learning HMM parameters.)
- Expectation-Maximization algorithm (Baum-Welch is a special case of EM.)
- forward-backward algorithm (The forward-backward algorithm is used to compute the E step.)

## Goals

- Derive the Baum-Welch algorithm as a special case of EM.

## Core resources (read/watch one of the following)

## -Paid-

→ Pattern Recognition and Machine Learning

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

Location:
Section 13.2.1, pages 615-618

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Sections 17.5-17.5.2, pages 617-620

## See also

-No Additional Notes-