Publication

Contraction of Rényi Divergences for Discrete Channels: Properties and Applications

2026

Abstract

This work explores properties of Strong Data-Processing constants for Rényi Divergences. Parallels are made with the well-studied φ-Divergences, and it is shown that the order α of Rényi Divergences dictates whether certain properties of the contraction of φ-Divergences are mirrored or not. In particular, we demonstrate that when α > 1, the contraction properties can deviate quite strikingly from those of φ-Divergences. We also uncover specific characteristics of contraction for the ∞-Rényi Divergence and relate it to ε-Local Differential Privacy. The results are then applied to bound the speed of convergence of Markov chains, where we argue that the contraction of Rényi Divergences offers a new perspective on the contraction of Lα-norms commonly studied in the literature.

Official source

https://infoscience.epfl.ch/entities/publication/0c6705d3-025e-4a48-b3ba-c3bb276a4026

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0c6705d3-025e-4a48-b3ba-c3bb276a4026

About this result

Related concepts (31)

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.

F-divergence

In probability theory, an -divergence is a function that measures the difference between two probability distributions and . Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of -divergence. These divergences were introduced by Alfréd Rényi in the same paper where he introduced the well-known Rényi entropy. He proved that these divergences decrease in Markov processes.

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.

Related publications (8)

Contraction of Rényi Divergences for Discrete Channels: Properties and Applications

Chat with Graph Search

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

Robust estimation of a Markov chain transition matrix from multiple sample paths

What One Cannot, Two Can: Two-Layer Transformers Provably Represent Induction Heads on Any-Order Markov Chains