I have a dataset consisting 5000 sentences. I need to calculate PMI between 3-gram and 5-grams in this dataset.
For example:
The 5-gram is: $x_1$$x_2$$x_3$$x_4$$x_5$
And the 3-gram is: $x_2$$x_3$$x_4$
How can I calculate PMI($x_2$$x_3$$x_4$, $x_1$$x_2$$x_3$$x_4$$x_5$) in this dataset? What is the exact formula?
As far as I know, in order to calculate PMI(y,z), it is needed to keep track of these counts in the dataset:
Count(y,z) --> The number of co-occurrences of y and z
Count(i,z) --> The number of occurrences of z
Count(y,i) --> The number of occurrences of y
N --> The sample size
The final formula is:
$PMI(y,z) = \frac{Count(y,z)*N}{Count(i,z)*Count(y,i)}$$PMI(y,z) = \frac{Count(y,z)N}{Count(i,z)Count(y,i)}$
In the context of my problem, these counts are listed as below:
$Count_1$($x_2$$x_3$$x_4$, $x_1$$x_2$$x_3$$x_4$$x_5$) : All occurrences of exact 5-gram " $x_1$$x_2$$x_3$$x_4$$x_5$ "
$Count_2$(i, $x_1$$x_2$$x_3$$x_4$$x_5$) : All occurrences of exact 5-gram "$x_1$$x_2$$x_3$$x_4$$x_5$ " !!!!!
$Count_3$($x_2$$x_3$$x_4$, i) : All occurences of 5-grams in the form of " _ $x_2$$x_3$$x_4$ _ ", that is the first and last words are subsituted with all the possible words in the dataset.
$N$ : All the 3-grams. !!!!!
My problem is with $Count_2$ and $N$. As you see, $Count_2$ is equal to $Count_1$. Is it sensible? And I'm not sure about the way I have counted $N$.
