8)
compute PPMI(digital, result) using data in below table
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 every column of the last row says that count(context)
= 4997
count(w) = 11716
To compute PPMI(digital, result), we first need to calculate the joint probability of the two words occurring together.
P(digital, result) = count(digital, result) / count(w)
count(digital, result) = 85
P(digital, result) = 85 / 11716 ≈ 0.00725
Next, we calculate the individual probabilities of each word occurring independently.
P(digital) = count(digital) / count(w)
count(digital) = 473
P(digital) = 473 / 11716 ≈ 0.04039
P(result) = count(result) / count(w)
count(result) = 9
P(result) = 9 / 11716 ≈ 0.00077
Finally, we calculate PPMI(digital, result) using the formula:
PPMI(digital, result) = max(log(P(digital, result) / (P(digital) * P(result))), 0)
PPMI(digital, result) = max(log(0.00725 / (0.04039 * 0.00077)), 0)
PPMI(digital, result) = max(log(232.3), 0)
PPMI(digital, result) ≈ max(5.449, 0)
PPMI(digital, result) = 5.449
Therefore, PPMI(digital, result) is approximately 5.449.