In order to penalize low-frequency observations with artificially high scores, we used the simple discounting method described by Pantel and Ravichandran (2004) resulting in the following modification of Equation 3: Thus, if two argument positions are rarely observed as coreferent, the value x x+1 will be small, reducing the PMI score.
the denominator in Equation 2is computed with a similar discount factor: if either of the argument positions is rarely observed as coreferent with other argument positions, the value min(x 1 ,x 2 ) min(x 1 ,x 2 )+1 will be small, making the denominator of Equation (2) large, reducing the PMI score.