Estimation of Entropy Rate of a Finite Markov Process in a Biological System

• Activity Number: 262
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Brian Vegetabile* and Hal Stern
• Companies: University of California at Irvine and University of California at Irvine
• Keywords: Predictability ; Entropy ; Entropy Rate ; Markov Process ; Complexity ; Behavior

Abstract

Entropy rate is a concept from information theory that measures the predictability of a stochastic process. Entropy rate has been previously used by Amigo et al. (2004), Song et al. (2010), and McInerney et al. (2013), among others as a measure of the predictability of human processes, utilizing a measure called the Lempel-Ziv (1976) complexity of a finite sequence as an estimate of the true entropy rate. We provide an alternative approach to the estimation of the entropy rate and compare it with estimates obtained by the Lempel-Ziv complexity. Simulations are provided for low, medium, and high entropy rate examples of an eight-state stochastic process, highlighting that performance of the estimators is a function of chain length. The method is applied to a dataset collected as part of a project to characterize the predictability of an interaction between a mother and child based upon tagged video data.