This is an old revision of the document!
Hidden Markov Model
$Z_1, \dots, Z_n \in \{1,\dots,m\}$ diskrete Zufallsvariablen (Hidden/Latent Variables)
$X_1, \dots, X_n \in X$ diskret, real, real^d Beobachtete Zufallsvariablen (observed variables)
$D=(x_1,\dots,x_n)$
Trelis-Diagramm
Z_1 ⇒ Z_2 ⇒ … ⇒ Z_n
X_1
Joint distribution (multidimensionale Wahrscheinlichkeitsverteilung): $p(x_1,\dots,x_n,Z1,\dots,Z_n) = p(z_1)p(x_1|z_1) \pro_{k=2}^n p(z_k|z_{k-1})p(x_k|z_k)$