In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D KL ( P ∥ Q ) {\displaystyle...
72 KB (12,414 words) - 08:24, 15 September 2024
as information radius (IRad) or total divergence to the average. It is based on the Kullback–Leibler divergence, with some notable (and useful) differences...
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called Kullback–Leibler divergence), which is central to information theory. There are numerous other specific divergences and classes of divergences, notably...
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George Washington University. The Kullback–Leibler divergence is named after Kullback and Richard Leibler. Kullback was born to Jewish parents in Brooklyn...
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The only divergence on Γ n {\displaystyle \Gamma _{n}} that is both a Bregman divergence and an f-divergence is the Kullback–Leibler divergence. If n ≥...
26 KB (4,434 words) - 13:48, 23 June 2024
(X)=k+\ln \theta +\ln \Gamma (k)+(1-k)\psi (k).} The Kullback–Leibler divergence (KL-divergence), of Gamma(αp, βp) ("true" distribution) from Gamma(αq...
60 KB (8,717 words) - 19:52, 20 August 2024
Maximum likelihood estimation (section Relation to minimizing Kullback–Leibler divergence and cross entropy)
Q_{\hat {\theta }}} ) that has a minimal distance, in terms of Kullback–Leibler divergence, to the real probability distribution from which our data were...
66 KB (9,623 words) - 15:33, 31 August 2024
Rényi entropy (redirect from Renyi divergence)
defined a spectrum of divergence measures generalising the Kullback–Leibler divergence. The Rényi divergence of order α or alpha-divergence of a distribution...
21 KB (3,449 words) - 05:51, 15 May 2024
of ln(xk) equal to ln(λk) − γ {\displaystyle \gamma } . The Kullback–Leibler divergence between two Weibulll distributions is given by D KL ( W e i b...
38 KB (5,764 words) - 06:49, 10 September 2024
dimensionality of the vector space, and the result has units of nats. The Kullback–Leibler divergence from N 1 ( μ 1 , Σ 1 ) {\displaystyle {\mathcal {N}}_{1}({\boldsymbol...
65 KB (9,519 words) - 19:30, 12 August 2024
=e^{1-\lambda x}\}=e^{1-\lambda x}\end{aligned}}} The directed Kullback–Leibler divergence in nats of e λ {\displaystyle e^{\lambda }} ("approximating"...
42 KB (6,567 words) - 10:39, 19 June 2024
P_{Y})} where D K L {\displaystyle D_{\mathrm {KL} }} is the Kullback–Leibler divergence, and P X ⊗ P Y {\displaystyle P_{X}\otimes P_{Y}} is the outer...
57 KB (8,727 words) - 05:28, 26 August 2024
the Kullback-Leibler divergence between Cauchy distributions". arXiv:1905.10965 [cs.IT]. Nielsen, Frank; Okamura, Kazuki (2023). "On f-Divergences Between...
45 KB (6,843 words) - 22:08, 3 August 2024
Divergence (statistics), a measure of dissimilarity between probability measures Bregman divergence f-divergence Jensen–Shannon divergence Kullback–Leibler...
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normal distributions as special cases. Kullback-Leibler divergence (KLD) is a method using for compute the divergence or similarity between two probability...
24 KB (2,749 words) - 18:09, 18 September 2024
at the National Security Agency, he and Solomon Kullback formulated the Kullback–Leibler divergence, a measure of similarity between probability distributions...
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points in the low-dimensional map, and it minimizes the Kullback–Leibler divergence (KL divergence) between the two distributions with respect to the locations...
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has a well-specified asymptotic distribution. The Kullback–Leibler divergence (or information divergence, information gain, or relative entropy) is a way...
56 KB (7,327 words) - 14:50, 8 September 2024
In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate...
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of the relative entropy (i.e., the Kullback–Leibler divergence); specifically, it is the Hessian of the divergence. Alternately, it can be understood...
26 KB (4,698 words) - 14:56, 24 July 2024
functions of two generalized gamma distributions, then their Kullback-Leibler divergence is given by D K L ( f 1 ∥ f 2 ) = ∫ 0 ∞ f 1 ( x ; a 1 , d 1 ...
8 KB (1,208 words) - 04:44, 26 May 2024
} The G-test statistic is proportional to the Kullback–Leibler divergence of the theoretical distribution from the empirical distribution:...
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fit to the distribution) because the ELBO includes a Kullback-Leibler divergence (KL divergence) term which decreases the ELBO due to an internal part...
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needs to know two terms: the "reconstruction error", and the Kullback–Leibler divergence (KL-D). Both terms are derived from the free energy expression...
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variation distance (or statistical distance) in terms of the Kullback–Leibler divergence. The inequality is tight up to constant factors. Pinsker's inequality...
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be formulated using the Kullback–Leibler divergence D K L ( p ∥ q ) {\displaystyle D_{\mathrm {KL} }(p\parallel q)} , divergence of p {\displaystyle p}...
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(X|Y)=\mathrm {H} (X,Y)-\mathrm {H} (Y).\,} The Kullback–Leibler divergence (or information divergence, information gain, or relative entropy) is a way...
12 KB (2,183 words) - 12:22, 14 August 2024
density functions of two Gompertz distributions, then their Kullback-Leibler divergence is given by D K L ( f 1 ∥ f 2 ) = ∫ 0 ∞ f 1 ( x ; b 1 , η 1 )...
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that the Kullback–Leibler divergence is non-negative. Another inequality concerning the Kullback–Leibler divergence is known as Kullback's inequality...
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theory and machine learning, information gain is a synonym for Kullback–Leibler divergence; the amount of information gained about a random variable or...
21 KB (3,001 words) - 17:14, 10 September 2024