We investigate Strong Data-Processing Inequality (SDPI) constants for R\'enyi Divergences on finite spaces. We study their dependence on the R\'enyi order $\alpha$, proving that they are non-decreasing and that their scaling by $(\alpha-1)$ is convex for $\alpha\geq1$. We also identify several support restrictions on t...
Adrien Vandenbroucque, A. Esposito, Michael C. Gastpar· 1 citation· ⚡1
The main converse recovers the phase transition of the optimal Type II error under the exponentially decaying Type I error constraint $\varepsilon_n=e^{-nr}$.
Roberto Bruno, Adrien Vandenbroucque, A. Esposito· 0 citations
We investigate composite binary hypothesis testing in the finite sample regime under asymmetric error constraints. Using R\'enyi divergences, we derive explicit achievability and converse bounds for the optimal Type II error. When the Type I error is constrained to decay exponentially with sample size, the bounds ident...
The results show that sharp converses for minimax quantiles require adapting the information measure to the recovery resolution, whether exact or approximate, and to the tail behaviour of the likelihood ratio.
A. Esposito· 0 citations
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