Kullback Leibler Distance (KL)

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 KL Distance
The Kullback Leibler distance (KL-distance) 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.
KL(p, p) = 0
KL(p, q) ≥ 0
Note that the KL-distance is not, in general, symmetric.
Coding Ockham's Razor, L. Allison, Springer

A Practical Introduction to Denotational Semantics, L. Allison, CUP

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© L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated),
Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University,
was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.)
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