compute PPMI(digital, result) using data in below table

Question

cherry strawberry digital information
computer
2
0
1670
3325
data
08
1683
3982
result
9
1
85
378
count(context)
4997
5673
473
ple
442
60
5
5
512

sugar
25
19
4
13
61
count(w)
486
80
3447
7703
11716

Answer 1

To compute PPMI (Pointwise Mutual Information) for the words digital and result, we need to calculate the following:

PPMI(digital, result) = max(log2(P(digital, result) / (P(digital) * P(result))), 0)

First, we need to find the probabilities P(digital), P(result), and P(digital, result) using the provided data:

P(digital) = count(digital) / sum(count(w)) = 3447 / 22732 ≈ 0.1516

P(result) = count(result) / sum(count(w)) = 7703 / 22732 ≈ 0.3389

P(digital, result) = count(digital, result) / sum(count(w)) = 85 / 22732 ≈ 0.0037

Now, we can compute PPMI(digital, result):

PPMI(digital, result) = max(log2(P(digital, result) / (P(digital) * P(result))), 0)
= max(log2(0.0037 / (0.1516 * 0.3389)), 0)
= max(log2(0.0037 / 0.0514), 0)
= max(log2(0.072), 0)
= max(-3.845, 0)
= 0

Therefore, PPMI(digital, result) = 0.