Publication

A Finite-Sample Strong Converse for Binary Hypothesis Testing via (Reverse) Rényi Divergence

2026

Abstract

This work investigates binary hypothesis testing between H0 ∼ P0 and H1 ∼ P1 in the finite-sample regime under asymmetric error constraints. By employing the "reverse" Rényi divergence, we derive novel non-asymptotic bounds on the Type II error probability which naturally establish a strong converse result. Furthermore, when the Type I error is constrained to decay exponentially with a rate c, we show that the Type II error converges to 1 exponentially fast if c exceeds the Kullback-Leibler divergence D(P1||P0), and vanishes exponentially fast if c is smaller. Finally, we present numerical examples demonstrating that the proposed converse bounds strictly improve upon existing finite-sample results in the literature.

Official source

https://infoscience.epfl.ch/entities/publication/205aa7bc-e5f4-4aa9-8aa6-8a29f93dcefe

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/205aa7bc-e5f4-4aa9-8aa6-8a29f93dcefe

About this result

Related concepts (32)

Kullback–Leibler divergence

In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q. A simple interpretation of the KL divergence of P from Q is the expected excess surprise from using Q as a model when the actual distribution is P.

Exponential distribution

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.

Rényi entropy

In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is important in ecology and statistics as index of diversity.

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