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Is mutual information a correlation?
So, what is the difference between Mutual Information and correlation? The main difference is that correlation is a measure of linear dependence, whereas mutual information measures general dependence (including non-linear relations).
What does mutual information tell us?
Mutual information is one of many quantities that measures how much one random variables tells us about another. It is a dimensionless quantity with (generally) units of bits, and can be thought of as the reduction in uncertainty about one random variable given knowledge of another.
What’s the difference between a correlation and mutual information?
Correlation is a linear distance between two random variables. You can have a mutual information between any two probabilities defined for a set of symbols, while you cannot have a correlation between symbols that cannot naturally be mapped into a R^N space.
How is mutual information written in mathemafrica?
To calculate the MI we need the following results, shown without proof: This means that our mutual information can be written as: We can see from the previous line that mutual information can be thought of as a function of correlation. Importantly, it can be thought of as a non-linear function of correlation.
What is mutual information between X and Y?
The mutual information between random variables X and Y is defined as: Where is the joint and and are the marginal distributions of the random variables in question. is the Kullback-Liebner divergence between (in this case bivariate) probability distributions.
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).