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The mutual information of two multivariate normal distribution is a special case of the Kullback–Leibler divergence in which is the full dimensional multivariate distribution and is the product of the and dimensional marginal distributions and , such that + =.
The circle on the left (red and violet) is the individual entropy H(X), with the red being the conditional entropy H(X|Y). The circle on the right (blue and violet) is H(Y), with the blue being H(Y|X). The violet is the mutual information I(X;Y). In information theory, joint entropy is a measure of the uncertainty associated with a set of ...
For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" [15] and Watkinson et al. applied it to genetic expression. [16] For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression. [17] [14] It can be zero, positive, or negative. [13]
A python package for computing all multivariate interaction or mutual informations, conditional mutual information, joint entropies, total correlations, information distance in a dataset of n variables is available .
In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence [1]), denoted (), is a type of statistical distance: a measure of how much a model probability distribution Q is different from a true probability distribution P.
Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy (a measure of average surprisal) of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just ...
is the maximum entropy distribution among all continuous distributions supported in [0,∞) that have a specified mean of 1/λ. In the case of distributions supported on [0,∞), the maximum entropy distribution depends on relationships between the first and second moments.
It is a multivariate generalization of the beta distribution, [1] hence its alternative name of multivariate beta distribution (MBD). [2] Dirichlet distributions are commonly used as prior distributions in Bayesian statistics , and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial ...