KL divergence and its missing support case

Read the equation

For normalized distributions, the sum p log(p/q) measures relative entropy in nats with the file’s natural logarithm. A term with positive p and zero q should make the divergence infinite. The code skips such terms when q is below its cutoff, so it can return a finite value where the mathematical divergence is infinite and can lose its usual nonnegativity guarantee after truncation.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

		if p > EPSILON_PHI && p < 1.0-EPSILON_PHI {
			h -= p * math.Log2(p)
		}
	}
	return h
}

// KLDivergence computes D_KL(P||Q) = Σ p(x) log(p(x)/q(x))
func KLDivergence(p, q []float64) float64 {
	if len(p) != len(q) {
		return math.Inf(1)
	}

	kl := 0.0
	for i := range p {
		if p[i] > EPSILON_PHI && q[i] > EPSILON_PHI {
			kl += p[i] * math.Log(p[i]/q[i])
		}

KLDivergence computes D_KL(P||Q) = Σ p(x) log(p(x)/q(x))

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