We quantify the selectional preference for a relative r to instantiate a relation R of a target t as the probability Pr(r | t, R), estimated as follows.
by the definition of conditional probability: We care only about the relative probability of different r for fixed t and R, so we rewrite it as: We use the chain rule: and notice that t is held constant: We estimate the second factor as follows: We calculate the denominator freq(t) as the number of N-grams in the Google N-gram corpus that contain t, and the numerator freq(t, r) as the number of N-grams containing both t and r. To estimate the factor Pr(R | r, t) directly from a corpus of text labeled with grammatical relations, it would be trivial to count how often a word r bears relation R to target word t. the results would be limited to the words in the corpus, and many relation frequencies would be estimated sparsely or missing altogether; t or r might not even occur.