What do you mean by total correlation?
The total correlation is the amount of information shared among the variables in the set.
Is mutual information a distance?
Mutual information is an absolute measure of information common to both sources. For independent sources, it converges towards zero. However, mutual information by itself would not be a suitable measure, because it is not a distance and it is not bounded.
How is mutual information related to correlation coefficient?
This is more in line with the intuition behind the above plots – at higher values of the correlation coefficient, the mutual information between the random variables increases significantly. Mutual information is a fundamental and interesting way of thinking about how two random variables are related.
How to calculate mi with a correlation coefficient?
If follows a bivariate Gaussian distribution, with mean vector , unit variance for both variables and a correlation coefficient , we write the pdf as: To calculate the MI we need the following results, shown without proof:
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.
What is mutual information between two random variables?
The Mutual Information between 2 random variables is the amount of information that one gains about a random variable by observing the value of the other. It is linked to the entropy – a key concept in Information Theory (which can be thought of as how surprised we are on average when observing a random variable – as discussed in a previous post).