Kirchhoff's diffraction formula

In information theory, the information projection or I-projection of a probability distribution q onto a set of distributions P is

$p^{*}=\underset{p\in P}{\arg \min }{\mathrm{D}}_{\mathrm{K}\mathrm{L}}(p||q)$

where $D_{\mathrm{K}\mathrm{L}}$ is the Kullback–Leibler divergence from p to q. Viewing the Kullback–Leibler divergence as a measure of distance, the I-projection $p^{*}$ is the "closest" distribution to q of all the distributions in P.

See also

• Sanov's theorem