About: Kullback–Leibler divergence

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Measurement of how one probability distribution is different from a second, reference probability distribution

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  • mesura de com una distribució de probabilitat és diferent d'una segona distribució de probabilitat de referència (ca)
  • measurement of how one probability distribution is different from a second, reference probability distribution (en)
  • míra používaná v matematické statistice pro stanovení, jak se jedna distribuční funkce (P) odlišuje od jiné (Q) (cs)
  • Maß für die Unterschiedlichkeit zweier Wahrscheinlichkeitsverteilungen (de)
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  • Let be a set endowed with an appropriate -field , and two probability measures and , which formulate two probability spaces and , with . Let be a real-valued integrable random variable on . Then the following equality holds Further, the supremum on the right-hand side is attained if and only if it holds almost surely with respect to probability measure , where denotes the Radon-Nikodym derivative of with respect to . (en)
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  • For a short proof assuming integrability of with respect to , let have -density , i.e. Then Therefore, where the last inequality follows from , for which equality occurs if and only if . The conclusion follows. (en)
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  • Proof (en)
  • [Proof] (en)
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  • Kullback–Leibler divergence (en)
  • تباعد كولباك - ليبلير (ar)
  • Kullbackova–Leiblerova divergence (cs)
  • Kullback-Leibler-Divergenz (de)
  • Divergencia de Kullback-Leibler (es)
  • Divergenza di Kullback-Leibler (it)
  • Divergence de Kullback-Leibler (fr)
  • カルバック・ライブラー情報量 (ja)
  • 쿨백-라이블러 발산 (ko)
  • Dywergencja Kullbacka-Leiblera (pl)
  • Divergência de Kullback-leibler (pt)
  • Расстояние Кульбака — Лейблера (ru)
  • Розходження Кульбака — Лейблера (uk)
  • 相对熵 (zh)
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