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The KLD is more or less a measure of how much information is lost when an approximation is used to replace an actual probability distribution.

How you calculate it depends on whether you are considering discrete or continuous values for the distribution.

If you have discrete values,

KLD = Σ P(i) log [P(i)/Q(i)] (summing over the values of i)

where P(i) is the "true" distribution and Q(i) a corresponding approximation.

If you have a continuous function for the probability, i.e. the variable can assume any value over a certain range (usually with different probability density for different values since uniform probability is a pretty boring problem)

KLD = ∫ p(x)log[p(x)/q(x)] dx (integrated from -∞ to +∞)

where p(x) is the true function of the probability - the "density" of P, and q(x) is the approximated function of the probability - the "density" of Q.

Note that these formulas only hold for a single variable. More complex formulas are required to calculate the KLD for multi-variable distributions.

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