Estimation of an Entropy-based Functional

Entropy

关键词: entropy;    differential entropy;    Shannon entropy;    entropy estimation;    nonlinear functional;    signal processing;   

DOI  :  10.3390/e12030338

来源: mdpi

【 摘 要 】

Given a function f from [0, 1] to the real line, we consider the (nonlinear) functional h obtained by evaluating the continuous entropy of the “density function” of f. Motivated by an application in signal processing, we wish to estimate h(f). Our main tool is a decomposition of h into two terms, which each have favorable scaling properties. We show that, if functions f and g satisfy a regularity condition, then the smallness of ∥f −g∥_∞ and ∥f′ − g′∥_∞, along with some basic control on derivatives of f and g, is sufficient to imply that h(f) and h(g) are close.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.