Kullback Leibler Distance (KL)

LA home
 KL Distance
The Kullback Leibler distance (KL-distance, KL-divergence) is a natural distance function from a "true" probability distribution, p, to a "target" probability distribution, q. It can be interpreted as the expected extra message-length per datum due to using a code based on the wrong (target) distribution compared to using a code based on the true distribution.
For discrete (not necessarily finite) probability distributions, p={p1, ..., pn} and q={q1, ..., qn}, the KL-distance is defined to be
KL(p, q) = Σi pi . log2( pi / qi )
For continuous probability densities, the sum is replaced by an integral.
Note that
KL(p, p) = 0
KL(p, q) ≥ 0
and that the KL-distance is not, in general, symmetric.
However, a symmetric distance can be made, e.g.,
KL(p, q) + KL(q, p)
(sometimes divided by two).
www #ad:

↑ © L. Allison, www.allisons.org/ll/   (or as otherwise indicated).
Created with "vi (Linux)",  charset=iso-8859-1,   fetched Wednesday, 08-Feb-2023 08:01:50 UTC.

Free: Linux, Ubuntu operating-sys, OpenOffice office-suite, The GIMP ~photoshop, Firefox web-browser, FlashBlock flash on/off.