compute PPMI(digital, result) using data in below table
cherry strawberry digital information
computer data result ple sugar count(w)
cherry 2 8 9 442 25 486 strawberry 0 0 1 60 19 80 digital 1670 1683 85 5 4 3447 information 3325 3982 378 5 13 7703 count(context) 4997 5673 473 512 61 11716
To compute PPMI (Positive Pointwise Mutual Information) between "digital" and "result", we need to calculate the following formula:
PPMI(digital, result) = max{log2(P(digital, result) / (P(digital) * P(result))), 0}
Where:
- P(digital, result) is the probability of both "digital" and "result" occurring together, which can be calculated as count("digital", "result") / count(context).
- P(digital) is the probability of "digital" occurring, which can be calculated as count("digital") / count(context).
- P(result) is the probability of "result" occurring, which can be calculated as count("result") / count(context).
From the given data, we can extract the following information:
- count("digital", "result") = 85
- count("digital") = 3447
- count("result") = 473
- count(context) = 11716
Let's calculate the probabilities:
P(digital, result) = 85 / 11716 = 0.0072581
P(digital) = 3447 / 11716 = 0.2941368
P(result) = 473 / 11716 = 0.0403853
Now, let's calculate PPMI(digital, result):
PPMI(digital, result) = max{log2(0.0072581 / (0.2941368 * 0.0403853)), 0} = max{-9.71696, 0} = 0
Therefore, PPMI(digital, result) is 0.