What is the meaning of Mutual Information beyond the numerical calculation?

1. What is the meaning of mutual information?
2. How is mutual information calculated?
3. What does mutual information score mean?
4. What does it mean when mutual information is 0?

What is the meaning of mutual information?

Mutual information is a quantity that measures a relationship between two random variables that are sampled simultaneously. In particular, it measures how much information is communicated, on average, in one random variable about another.

How is mutual information calculated?

The mutual information can also be calculated as the KL divergence between the joint probability distribution and the product of the marginal probabilities for each variable. — Page 57, Pattern Recognition and Machine Learning, 2006. This can be stated formally as follows: I(X ; Y) = KL(p(X, Y) || p(X) * p(Y))

What does mutual information score mean?

The Mutual Information score expresses the extent to which observed frequency of co-occurrence differs from what we would expect (statistically speaking). In statistically pure terms this is a measure of the strength of association between words x and y.

What does it mean when mutual information is 0?

If the mutual information is zero, that means that the two random variables are independent.