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| | In [[information theory]], the '''information projection''' or '''I-projection''' of a [[probability distribution]] ''q'' onto a set of distributions ''P'' is |
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| | :<math>p^* = \underset{p \in P}{\arg\min} \operatorname{D}_{\mathrm{KL}}(p||q)</math> |
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| | where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]] from ''p'' to ''q''. Viewing the Kullback–Leibler divergence as a measure of distance, the I-projection <math>p^*</math> is the "closest" distribution to ''q'' of all the distributions in ''P''. |
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| | ==See also== |
| | *[[Sanov's theorem]] |
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| | {{noreferences|date=October 2011}} |
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| | [[Category:Information theory]] |
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| | {{probability-stub}} |
Revision as of 18:45, 1 February 2014
In information theory, the information projection or I-projection of a probability distribution q onto a set of distributions P is
where is the Kullback–Leibler divergence from p to q. Viewing the Kullback–Leibler divergence as a measure of distance, the I-projection is the "closest" distribution to q of all the distributions in P.
See also
Template:Noreferences
Template:Probability-stub