Exponential mask PMI (ExpPMI)
This is our first new proposed score. PMI treats every position in a binary way: it’s either in the context of q or not. With a window size of say 50, a token which appears three words from a query q and a token which appears 45 words from a query q are treated the same. We thought it might be useful to consider a measure which distinguishes positions in the context based on the number of words away that position is from an occurrence of q. We did this by weighting the positions in the context by some weight between 0 and 1. Our weighting is based on an exponential decay (which has some nice properties especially when we extend to the case of logical queries).