Why is mutual information symmetric but conditional entropy isn't?

1. Is conditional mutual information symmetric?
2. Why is mutual information symmetric?
3. When mutual information is equal to entropy?
4. What is conditional entropy in information theory?

Is conditional mutual information symmetric?

Mutual information is symmetricI(X;Y)=I(Y;X)\ . This follows directly from the definition, Eq.

Why is mutual information symmetric?

The mutual information (MI) between two random variables captures how much information entropy is obtained about one random variable by observing the other. Since that definition does not specify which is the observed random variable, we might suspect this is a symmetric quantity.

When mutual information is equal to entropy?

They only do if they are constant.. Indeed if they are fully identical, their mutual information will be equal to the entropy of any of the two: I(X,X)=H(X). This entropy is only zero in case of constant data, otherwise it may have other values.

What is conditional entropy in information theory?

In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known.