CUED Publications database

A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration

Kontoyiannis, I and Sezer, AD (2003) A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration. In: Stochastic Inequalities and Applications. Progress in Probability, 56 . Springer, pp. 23-32.

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Abstract

Let A be finite set equipped with a probability distribution P, and let M be a “mass” function on A. A characterization is given for the most efficient way in which A n can be covered using spheres of a fixed radius. A covering is a subset C n of A n with the property that most of the elements of A n are within some fixed distance from at least one element of C n , and “most of the elements” means a set whose probability is exponentially close to one (with respect to the product distribution P n ). An efficient covering is one with small mass M n (C n ). With different choices for the geometry on A, this characterization gives various corollaries as special cases, including Marton’s error-exponents theorem in lossy data compression, Hoeffding’s optimal hypothesis testing exponents, and a new sharp converse to some measure concentration inequalities on discrete spaces.

Item Type: Book Section
Uncontrolled Keywords: math.PR math.PR math.OC
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 13 Oct 2020 03:20
DOI: 10.1007/978-3-0348-8069-5_3