Jensen–Shannon divergence

upshard

\mathrm{JSD}(P \parallel Q) = \tfrac{1}{2} D_{\mathrm{KL}}(P \parallel M) + \tfrac{1}{2} D_{\mathrm{KL}}(Q \parallel M)

A symmetric, always-finite cousin of the KL divergence, built by comparing both distributions against their average. Its square root is a true distance, which KL divergence never is.

Symbols

$M$: The mixture, equal to half of P plus half of Q.
$P$: The first distribution.
$Q$: The second distribution.

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Jensen–Shannon divergence

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