Difficulties in understanding mutual information concept

1. Can mutual information be negative in information theory?
2. How do you evaluate mutual information?
3. How do you interpret mutual information values?
4. What is the significance of mutual information in information theory?
5. Why mutual information is better than correlation?
6. Can conditional mutual information be negative?

Can mutual information be negative in information theory?

Note that the mutual information is symmetric in the arguments. That is, I(X;Y ) = I(Y ;X). Mutual information is also non-negative, as we will show in a minute.

How do you evaluate mutual information?

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))

How do you interpret mutual information values?

High mutual information indicates a large reduction in uncertainty; low mutual information indicates a small reduction; and zero mutual information between two random variables means the variables are independent.

What is the significance of mutual information in information theory?

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.

Why mutual information is better than correlation?

The main difference is that correlation is a measure of linear dependence, whereas mutual information measures general dependence (including non-linear relations). Therefore, mutual information detects dependencies that do not only depend on the covariance.

Can conditional mutual information be negative?

Because the conditional mutual information can be greater than or less than its unconditional counterpart, the interaction information can be positive, negative, or zero, which makes it hard to interpret.