Similarly, all the above concepts have their pointwise counterparts, obtained by dropping the expectation operator.
the pointwise interaction information is defined as PInt(x 1 , x 2 , y) = PMI(y; x 1 , x 2 ) − PMI(y; x 1 ) − PMI(y; x 2 ) = log P (x 1 )P (x 2 )P (y)P (x 1 ,x 2 ,y) P (x 1 ,x 2 )P (x 1 ,y)P (x 2 ,y) .