Baum-Welch Algorithm
Baum-Welch is the EM specialization for HMM parameter learning: the E step uses forward-backward to compute expected hidden-state occupancies, and the M step updates transition and emission probabilities.
Purpose
To learn HMM parameters from observation sequences without labeled hidden states.
Mechanism
E step: forward α and backward β compute γ_t(i)=P(q_t=i|O,λ) and ξ_t(i,j)=P(q_t=i,q_{t+1}=j|O,λ). M step: re-estimate transition and emission probabilities from γ/ξ. Iterate until convergence.
Use cases
- HMM training
- Speech models
- Biological sequences