Instead, we employ an exponential decay strategy where we update the current mixture distribution by linearly interpolating it with the posterior topic distribution given the current word.
applying Bayes' rule, the probability of topic t generating the current word w is given by: To achieve the exponential decay, we update the topic distribution after each word according to P i+1 (t) = (1 -) P i (t) + P(t | w i ), where is the adaptation rate.