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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.
Truncated normals with fixed support form an exponential family. Nielsen [3] reported closed-form formula for calculating the Kullback-Leibler divergence and the Bhattacharyya distance between two truncated normal distributions with the support of the first distribution nested into the support of the second distribution.
The only divergence for probabilities over a finite alphabet that is both an f-divergence and a Bregman divergence is the Kullback–Leibler divergence. [8] The squared Euclidean divergence is a Bregman divergence (corresponding to the function x 2 {\displaystyle x^{2}} ) but not an f -divergence.
It is useful to think of each feature (column vector) in the features matrix W as a document archetype comprising a set of words where each word's cell value defines the word's rank in the feature: The higher a word's cell value the higher the word's rank in the feature.
where is the Kullback–Leibler divergence, and is the outer product distribution which assigns probability () to each (,).. 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 (and hence observing tells you nothing about ).
The KLRS algorithm was designed to create a flexible policy that matches class percentages in the buffer to a target distribution while employing Reservoir Sampling techniques. This is achieved by minimizing the Kullback-Leibler (KL) divergence between the current buffer distribution and the desired target distribution.
The Rényi divergence is indeed a divergence, meaning simply that (‖) is greater than or equal to zero, and zero only when P = Q. For any fixed distributions P and Q , the Rényi divergence is nondecreasing as a function of its order α , and it is continuous on the set of α for which it is finite, [ 13 ] or for the sake of brevity, the ...
In probability theory, particularly information theory, the conditional mutual information [1] [2] is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.