When we which to refer to a cluster of a word w in general we will use the notation W. The ACM estimates the probability of w i given the two preceeding words w i-2 and w i-1 as the product of the following two probabilities: (1) The probability of the predicted cluster PW i given the preceding conditional clusters CW i-2 and CW i-1 , P(PW i |CW i-2 CW i-1 ), and (2) The probability of the word given its cluster PW i and the preceding conditional clusters CW i-2 and CW i-1 , P(w i |CW i-2 CW i-1 PW i ).
the ACM can be parameterized by The ACM consists of two sub-models: (1) the cluster sub-model P(PW i |CW i-2 CW i-1 ), and (2) the word sub-model P(w i |CW i-2 CW i-1 PW i ).