Frank Nielsen generalizes Bhattacharyya and Chernoff Bayes-error bounds via power means
FrnkNlsn · x · 2026-09-03
Frank Nielsen's arXiv paper studies closed-form upper bounds on Bayes error in Bayesian classification, which is usually intractable to compute exactly.
- Expresses Bayes risk via total variation distance and extends the Bhattacharyya and Chernoff upper-bound mechanisms using generalized weighted (quasi-arithmetic) means
- Introduces a Bhattacharyya similarity α-coefficient tying together α-divergences, Chernoff information, and Tsallis/Rényi/Hellinger/chi-squared divergences; the coefficient is a weighted geometric mean, extended to power means
- Derives new bounds for univariate Cauchy and multivariate t-distributions, shown experimentally to be tighter
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