stateDiagram-v2 direction LR state "JuliaCon\nonline" as online state "JuliaCon\nin Europe" as europe state "JuliaCon\noverseas" as overseas online --> overseas: 1 overseas --> online: 1 overseas --> europe: 2 europe --> overseas: 1 overseas --> overseas: 3 online --> online: 2
Main algorithms
Given an HMM, one may want to:
- Observation likelihood \(\mathbb{P}_\theta(Y_{1:T})\) \(\implies\) Forward
- Most likely states \(\underset{X_{1:T}}{\max} \mathbb{P}_\theta(X_{1:T} | Y_{1:T})\) \(\implies\) Viterbi
- Best parameters \(\underset{\theta}{\max} \mathbb{P}_\theta(Y_{1:T})\) \(\implies\) Baum-Welch
See the tutorial by Rabiner (1989) for details.