Kullback-Leibler divergence
kullback_leibler_divergence(x, y)Numeric vectors representing probabilities
The Kullback-Leibler divergence between x and y. We
adopt the following conventions if elements of x or y are
zero: \(0 \log (0 / y_i) = 0\), \(0 \log (0 / 0) = 0\), and
\(x_i \log (x_i / 0) = \infty\). As a result, if elements of x are
zero, they do not contribute to the sum. If elements of y are zero
where x is nonzero, the result will be Inf. If either
x or y sum to zero, we are not able to compute the
proportions, and we return NaN.
Kullback-Leibler divergence is a non-symmetric measure of difference between two probability vectors. In general, KL(x, y) is not equal to KL(y, x).
Because this measure is defined for probabilities, the vectors x and y are normalized in the function so they sum to 1.