方法对比

	Kullback-Leibler 散度	Hellinger距离
领域	决策	决策
方法族	MCDM	MCDM
起源年份	1951	1909
提出者	Solomon Kullback and Richard Leibler	Ernst Hellinger
类型	Asymmetric probability distribution dissimilarity	Symmetric metric for probability distributions
开创性文献	Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22(1), 79-86.	Hellinger, E. (1909). Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die Reine und Angewandte Mathematik, 136, 210-271.
别名	KL divergence, relative entropy, information divergence	Bhattacharyya distance, Hellinger metric
相关	2	2
摘要	Kullback-Leibler divergence, also called relative entropy or information divergence, measures the asymmetric difference between two probability distributions. Introduced by Solomon Kullback and Richard Leibler in 1951, this information-theoretic measure quantifies how one probability distribution diverges from a reference distribution, ranging from 0 (identical distributions) to infinity. It is foundational in information theory, machine learning, and decision-making with probabilistic frameworks.	Hellinger distance is a symmetric, bounded metric that measures the difference between two probability distributions. Rooted in the work of Ernst Hellinger (1909) and later formalized in statistical divergence by Anil Bhattacharyya (1946), this distance ranges from 0 (identical distributions) to 1. It is a true metric satisfying all mathematical distance properties and is particularly well-suited for comparing probability distributions in a symmetric, numerically stable manner.