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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.
Jackknife (statistics) – redirects to Resampling (statistics) Jackson network; Jackson's theorem (queueing theory) Jadad scale; James–Stein estimator; Jarque–Bera test; Jeffreys prior; Jensen's inequality; Jensen–Shannon divergence; JMulTi – software; Johansen test; Johnson SU distribution; Joint probability distribution; Jonckheere's ...
In probability theory, an -divergence is a certain type of function (‖) that measures the difference between two probability distributions and . Many common divergences, such as KL-divergence , Hellinger distance , and total variation distance , are special cases of f {\displaystyle f} -divergence.
In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.
The only divergence on that is both a Bregman divergence and an f-divergence is the Kullback–Leibler divergence. [ 6 ] If n ≥ 3 {\displaystyle n\geq 3} , then any Bregman divergence on Γ n {\displaystyle \Gamma _{n}} that satisfies the data processing inequality must be the Kullback–Leibler divergence.
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.
The divergence from Randomness Model is based on the Bernoulli model and its limiting forms, the hypergeometric distribution, Bose-Einstein statistics and its limiting forms, the compound of the binomial distribution with the beta distribution, and the fat-tailed distribution. Divergence from randomness model shows a unifying framework that has ...
Quantum Jensen–Shannon divergence for = (,) and two density matrices is a symmetric function, everywhere defined, bounded and equal to zero only if two density matrices are the same. It is a square of a metric for pure states , [ 13 ] and it was recently shown that this metric property holds for mixed states as well.