The HMM finds (probabilistic) categories Y for both the current word x i and the context word x i−1 , and models the probability that one category follows the other: P (Y i |Y i−1 ).
the HMM is our most extreme smoothing model, as it aggregates information over the greatest number of examples: for a given consecutive pair of words x i−1 , x i in the test set, it aggregates over all pairs of consecutive words x i−1 , x i where x i−1 is similar to x i−1 and x i is similar to x i .