Automatic Stochastic Network Language Model Acquisition using an Ergodic HMM

A Mealy-type Ergodic discrete-density HMM is considered to be a stochastic network language model. This HMM has parameters $\lambda = ( \Pi,A,B )$.

$\Pi = { \pi_N (i); \ \ i=1,..,N }$, is the initial state probability distribution.

$A = { a_N (i,j); \ \ i=1,..,N; j=1,..,N }$, is the state transition probability distribution between state $i$ and state $j$.

$B = { b_N (i,j,w); \ \ i=1,..,N; j=1,..,N; w=1,..,V }$, is the word $w$'s output word probability belonging somewhere between state $i$ and state $j$.
In these equations, $N$ is the number of states and $V$ is the vocabulary size.