Proposing Jeffreys-Fisher-Rao Center: Fast Proxy for Symmetrized KL Divergence Centroids
FrnkNlsn · x · 2026-08-02
To address the lack of closed-form solutions for Jeffreys centroids (symmetrized KL divergence centroids), this paper proposes the Jeffreys-Fisher-Rao center as a fast proxy. Defined as the Fisher-Rao midpoint of sided KL centroids, the method admits a generic formula for uni-parameter exponential family distributions and closed-form formulas for categorical and normal distributions. Furthermore, the paper introduces an inductive center approach by generalizing the principle of Gauss arithmetic-geometric double sequence means to further approximate the centroids.
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