To describe the MMI training procedure, we need the appropriate forms of eqns. 1.39 and 1.40.
First consider the clamped case. Since we are working in the sentence level, we form an HMM, (by interconnecting the HMMs of speech units) which represents a class l of sentences to which the current observation sequence belongs. Then starting from eqn. 1.39 ,
where the second line follows from eqn.1.3.
For the free case, we have only one HMM, which represents the whole language. Therefore summing up over all the alternative classes will be equivalent to summing up over the whole set of states. Thus the eqn. 1.40, takes following form,
Now the MMI procedure will be as follows.