EM's role is to induce a probability distribution over candidates to maximize the likelihood of the (p, k) pairs observed in our training set: We can rewrite Pr(p, k) so that it uses a hidden candidate (or antecedent) variable c that influences the observed p and k: To improve our ability to generalize to future cases, we use a naïve Bayes assumption to state that the choices of pronoun and context are conditionally independent, given an antecedent.
once we select the word the pronoun represents, the pronoun and its context are no longer coupled: We can split each candidate c into its lexical component l and its jump value j.