Nonsymmetrical distance between probability distributions, entropy and the theorem of pythagoras
Nonsymmetrical distance between probability distributions, entropy and the theorem of pythagoras
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概率分布、熵和毕达哥拉斯定理之间的非对称距离
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发表时间：
1968
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影响因子：
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通讯作者：
N. Chentsov
中科院分区：
文献类型：
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作者：
N. Chentsov
用于区分概率分布Q对P的Kullback-Leibler信息I[Q β p β]被认为是“点”Q和P之间距离平方的一半的非对称模拟。对于n维“平面”，我们取指数族。我们将证明一个非对称的类似定理的毕达哥拉斯在制定：“平方长度的斜线等于总和的平方长度的垂直和投影的斜线，”也是一个类似的余弦定理等。
The Kullback-Leibler information I[Q¦p¦ for discrimination in favor of the probability distribution Q against P is considered as a nonsymmetrical analog of one half of the square of the distance between the “points” Q and P. For the n-dimensional “planes” we take the exponential families. We shall prove a nonsymmetrical analogue of the theorem of Pythagoras in the formulation: “The squared length of an oblique line equals the sum of the squared lengths of the perpendicular and the projection of the oblique line,” and also an analog of the cosine theorem and the like.