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--- data_mining:hmm [2014/11/22 03:13] – [Parameter] phreazer
+++ data_mining:hmm [2014/12/17 01:22] – [Forward-Backward Algorithmus] phreazer
@@ Line 29: / Line 29: @@
 $T(i,j) = P(Z_{k+1}=j|z_k=i)$ ($i,j \in \{i,\dots,m\}$)
-Emission probabilities
+T ist die Transition Matrix (Übergangswkt.)
+Emission probabilities:
 $\varepsilon_i(x) = p(x|Z_k=i)$ für $i\in \{i,\dots,m\} x \in X$
@@ Line 39: / Line 41: @@
 pmf
-Initial distribution: $\pi(i) = P(Z_i=i), \in \{i,\dots,m\}$
+Initial distribution:
+$\pi(i) = P(Z_i=i), \in \{i,\dots,m\}$
 Joint Distribution:
-$p(x_1,...,x_n,z_1,...z_n) = \pi(z_1) \varepsilon_z_1(x_1) \prod_{k=2}^n T(z_{k-1},z_k) \varepsilon_z_k(x_k)$
+$p(x_1,\dots,x_n,z_1,\dots,z_n) = \pi(z_1) \varepsilon_{z_1}(x_1) \prod_{k=2}^n T(z_{k-1},z_k) \varepsilon_{z_k}(x_k)$
+===== Forward-Backward Algorithmus =====
+===== Beispiel =====