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How to calculate mutual information between two variables?
Definition The mutual information between two discreet random variables X,Y jointly distributed according to p(x,y) is given by I(X;Y) = X x,y p(x,y)log p(x,y) p(x)p(y) (24) = H(X)−H(X|Y) = H(Y)−H(Y|X) = H(X)+H(Y)−H(X,Y). (25) 4
How is mutual information measured in probability theory?
In probability theoryand information theory, the mutual information(MI) of two random variablesis a measure of the mutual dependencebetween the two variables. More specifically, it quantifies the “amount of information” (in unitssuch as shannons, commonly called bits) obtained about one random variable through observing the other random variable.
How does mutual information quantize the amount of information?
More specifically, it quantifies the ” amount of information ” (in units such as shannons ( bits ), nats or hartleys) obtained about one random variable through observing the other random variable.
When is mutual information equal to the marginal distribution?
If their joint distribution is and the marginal distributions are and , the mutual information is defined as Notice, as per property of the Kullback–Leibler divergence, that is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when and are independent.
How is mutual information used in feature selection?
A common feature selection method is to compute as the expected mutual information (MI) of term and class . MI measures how much information the presence/absence of a term contributes to making the correct classification decision on .
How does mutual information work in a class?
Mutual information measures how much information – in the information-theoretic sense – a term contains about the class. If a term’s distribution is the same in the class as it is in the collection as a whole, then .
Which is a measure of conditional mutual information?
The conditional mutual information is a measure of how much uncertainty is shared byXandY, but not byZ. 4.3 Properties