Properties of the statistical complexity functional and partially deterministic HMMs
type: Item
instance of: scholarly article
title: Properties of the statistical complexity functional and partially deterministic HMMs
zbMATH Open document ID: 1179.82099
author: Wolfgang Löhr
published in: Entropy
publication date: 2010-01-29T00:00:00Z
review text: Summary: Statistical complexity is a measure of complexity of discrete-time stationary stochastic processes, which has many applications. We investigate its more abstract properties as a non-linear function of the space of processes and show its close relation to the Knight's prediction process. We prove lower semi-continuity, concavity, and a formula for the ergodic decomposition of statistical complexity. On the way, we show that the discrete version of the prediction process has a continuous Markov transition. We also prove that, given the past output of a partially deterministic hidden Markov model (HMM), the uncertainty of the internal state is constant over time and knowledge of the internal state gives no additional information on the future output. Using this fact, we show that the causal state distribution is the unique stationary representation on prediction space that may have finite entropy.
Mathematics Subject Classification ID: 82C31
zbMATH DE Number: 5664166
zbMATH Keywords: statistical complexity
zbMATH Keywords: lower semi-continuity
zbMATH Keywords: ergodic decomposition
zbMATH Keywords: concavity
zbMATH Keywords: prediction process
zbMATH Keywords: partially deterministic hidden Markov models (HMMs)
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e110300385
OpenAlex ID: W2046755574
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DOI: 10.3390/E110300385
description: scientific article; zbMATH DE number 5664166