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Divergence (statistics) : ウィキペディア英語版
Divergence (statistics)

In statistics and information geometry, divergence or a contrast function is a function which establishes the "distance" of one probability distribution to the other on a statistical manifold. The divergence is a weaker notion than that of the distance, in particular the divergence need not be symmetric (that is, in general the divergence from ''p'' to ''q'' is not equal to the divergence from ''q'' to ''p''), and need not satisfy the triangle inequality.
== Definition ==
Suppose ''S'' is a space of all probability distributions with common support. Then a divergence on ''S'' is a function satisfying
# ''D''(''p'' || ''q'') ≥ 0 for all ''p'', ''q'' ∈ ''S'',
# ''D''(''p'' || ''q'') = 0 if and only if ''p'' = ''q'',
The dual divergence ''D
*'' is defined as
:
D^
*(p \parallel q) = D(q \parallel p).


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