When is KL divergence symmetric? Cauchy distributions get a closed-form formula

FrnkNlsn · x · 2026-09-07

Frank Nielsen discusses when KL divergence is symmetric for parametric models: in exponential families only for same-covariance normal families, while location-scale Cauchy densities also have finite, symmetric KL.

The linked paper (arXiv:1905.10965) derives a closed-form expression for the KL divergence between Cauchy distributions via a novel definite integral, proving it is always finite and symmetric.

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