Contents
What is self and mutual information?
(Mutual) information is the average statistical dependence between two sets of variables, such as the inputs and the outputs of a channel. The (self)-information contained in a single system state is simply the negative logarithm of its probability of occurrence.
What are the properties of mutual information?
Properties of Mutual information Mutual information of a channel is symmetric. Mutual information is non-negative. Mutual information can be expressed in terms of entropy of the channel output. Mutual information of a channel is related to the joint entropy of the channel input and the channel output.
Why mutual information is nonnegative?
Mutual information is nonnegative, i.e. I(X;Y ) ≥ 0. Equivalently, H(X|Y ) ≤ H(X). Hence conditioning one random variable on another can only decrease entropy. Equality holds if and only if the random variables are independent.
Which is the best definition of mutual information?
All Information is Mutual. Theorem: Proofs: These are all simple variants of the definition, the calculation in the second bullet above and the material in the previous lecture. For example, One might read , the Mutual Information as:
How is mutual information used in signal processing?
Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric [17] is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images.
How is the expected value of self-information expressed?
Information content is expressed in a unit of information, as explained below. The expected value of self-information is information theoretic entropy, the average amount of information an observer would expect to gain about a system when sampling the random variable.
Is there a minus sign when there is no mutual information?
In the setting of the previous lecture, given two jointly distributed Finite Random Variables and their Mutual Informationis defined as follows: There is no minus sign! If and are Independent since There is no Mutual Information, Example 2 from the previous section.