Rabiner to Charniak

Formally we can regard a Charniak model as a tuple of N M, and single , 3-dimensional matrix C, with dimensions N by N by M, where C_ijk is the conditional probability that the system makes a transition to state j and generates the kth symbol given that it is in state i. Clearly we can generate a Charniak style model from a balls amd urns model by setting C such that .

Graphically, this amounts to doing the following at each state:

1.

Count the symbols with a non-zero probability of being generated.

2.

Duplicate each exit arc such that there is one arc going to the target state for each of the possible symbols. Annotate the new exit arcs with their symbols.

3.

Form the probabilities of the new exit arcs, by multiplying the generation probabilties at the state by the probability of the original exit arc

Table 10.2 and figure 10.2 were generated by this procedure.