Information and estimation in Fokker-Planck channels
Information Theory
2017-02-14 v1 math.IT
Statistics Theory
Statistics Theory
Abstract
We study the relationship between information- and estimation-theoretic quantities in time-evolving systems. We focus on the Fokker-Planck channel defined by a general stochastic differential equation, and show that the time derivatives of entropy, KL divergence, and mutual information are characterized by estimation-theoretic quantities involving an appropriate generalization of the Fisher information. Our results vastly extend De Bruijn's identity and the classical I-MMSE relation.
Keywords
Cite
@article{arxiv.1702.03656,
title = {Information and estimation in Fokker-Planck channels},
author = {Andre Wibisono and Varun Jog and Po-Ling Loh},
journal= {arXiv preprint arXiv:1702.03656},
year = {2017}
}