jensenShannonDivergence

Computes the Jensen-Shannon divergence between a and b, which is the sum (ai * log(2 * ai / (ai + bi)) + bi * log(2 * bi / (ai + bi))) / 2. The base of logarithm is 2. The ranges are assumed to contain elements in [0, 1]. Usually the ranges are normalized probability distributions, but this is not required or checked by jensenShannonDivergence. If the inputs are normalized, the result is bounded within [0, 1]. The three-parameter version stops evaluations as soon as the intermediate result is greater than or equal to limit.

  1. CommonType!(ElementType!Range1, ElementType!Range2) jensenShannonDivergence(Range1 a, Range2 b)
    jensenShannonDivergence
    (
    Range1
    Range2
    )
    (
    Range1 a
    ,
    Range2 b
    )
    if (
    isInputRange!Range1 &&
    &&
    )
  2. CommonType!(ElementType!Range1, ElementType!Range2) jensenShannonDivergence(Range1 a, Range2 b, F limit)

Examples

import std.math.operations : isClose;

double[] p = [ 0.0, 0, 0, 1 ];
assert(jensenShannonDivergence(p, p) == 0);
double[] p1 = [ 0.25, 0.25, 0.25, 0.25 ];
assert(jensenShannonDivergence(p1, p1) == 0);
assert(isClose(jensenShannonDivergence(p1, p), 0.548795, 1e-5));
double[] p2 = [ 0.2, 0.2, 0.2, 0.4 ];
assert(isClose(jensenShannonDivergence(p1, p2), 0.0186218, 1e-5));
assert(isClose(jensenShannonDivergence(p2, p1), 0.0186218, 1e-5));
assert(isClose(jensenShannonDivergence(p2, p1, 0.005), 0.00602366, 1e-5));

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