Next Article in Journal
Maximum Entropy Production vs. Kolmogorov-Sinai Entropy in a Constrained ASEP Model
Next Article in Special Issue
Matrix Algebraic Properties of the Fisher Information Matrix of Stationary Processes
Previous Article in Journal
Prediction Method for Image Coding Quality Based on Differential Information Entropy
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(2), 1002-1036; doi:10.3390/e16021002

Learning from Complex Systems: On the Roles of Entropy and Fisher Information in Pairwise Isotropic Gaussian Markov Random Fields

Computing Department, Federal University of São Carlos, Rod. Washington Luiz, km 235, São Carlos, SP, Brazil
Received: 4 December 2013 / Accepted: 30 January 2014 / Published: 18 February 2014
(This article belongs to the Special Issue Information Geometry)
View Full-Text   |   Download PDF [6192 KB, uploaded 24 February 2015]   |  

Abstract

Markov random field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In this paper, our goal is to enlighten the connection between Fisher information, Shannon entropy, information geometry and the behavior of complex systems modeled by isotropic pairwise Gaussian Markov random fields. We propose analytical expressions to compute local and global versions of these measures using Besag’s pseudo-likelihood function, characterizing the system’s behavior through its Fisher curve , a parametric trajectory across the information space that provides a geometric representation for the study of complex systems in which temperature deviates from infinity. Computational experiments show how the proposed tools can be useful in extracting relevant information from complex patterns. The obtained results quantify and support our main conclusion, which is: in terms of information, moving towards higher entropy states (A –> B) is different from moving towards lower entropy states (B –> A), since the Fisher curves are not the same, given a natural orientation (the direction of time).
Keywords: Markov random fields; information theory; Fisher information; entropy; maximum pseudo-likelihood estimation Markov random fields; information theory; Fisher information; entropy; maximum pseudo-likelihood estimation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Levada, A. Learning from Complex Systems: On the Roles of Entropy and Fisher Information in Pairwise Isotropic Gaussian Markov Random Fields. Entropy 2014, 16, 1002-1036.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top