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  1. Journal of Systems Science and Complexity
  2. Journal of Systems Science and Complexity : Volume 25
  3. Journal of Systems Science and Complexity : Volume 25, Issue 1, February 2012
  4. Predictive models and generative complexity
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Journal of Systems Science and Complexity : Volume 30
Journal of Systems Science and Complexity : Volume 29
Journal of Systems Science and Complexity : Volume 28
Journal of Systems Science and Complexity : Volume 27
Journal of Systems Science and Complexity : Volume 26
Journal of Systems Science and Complexity : Volume 25
Journal of Systems Science and Complexity : Volume 25, Issue 6, December 2012
Journal of Systems Science and Complexity : Volume 25, Issue 5, October 2012
Journal of Systems Science and Complexity : Volume 25, Issue 4, August 2012
Journal of Systems Science and Complexity : Volume 25, Issue 3, June 2012
Journal of Systems Science and Complexity : Volume 25, Issue 2, April 2012
Journal of Systems Science and Complexity : Volume 25, Issue 1, February 2012
On control of strong consensus for networked agents with noisy observations
On formability of linear continuous-time multi-agent systems
Predictive models and generative complexity
Sensor selection for random field estimation in wireless sensor networks
Stabilization of switched linear systems with constrained inputs
Synchronized path following control of multiple homogenous underactuated AUVs
H $_{∞}$ filtering for continuous-time systems with pointwise time-varying delay
L $^{∞}$-estimates of mixed finite element methods for general nonlinear optimal control problems
An interval method for studying the relationship between the Australian dollar exchange rate and the gold price
Analysis of a continuous time SM[K]/PH[K]/1/FCFS queue: Age process, sojourn times, and queue lengths
Structural decomposition analysis on China’s energy intensity change for 1987–2005
The compound binomial model with a constant dividend barrier and periodically paid dividends
Complete monotonicity of the probability of ruin and de Finetti’s dividend problem
A MacWilliams type identity on Lee weight for linear codes over $$\mathbb{F}_2 + u\mathbb{F}_2^*$$
Error reduction, convergence and optimality of an adaptive mixed finite element method
Journal of Systems Science and Complexity : Volume 24
Journal of Systems Science and Complexity : Volume 23
Journal of Systems Science and Complexity : Volume 22
Journal of Systems Science and Complexity : Volume 21
Journal of Systems Science and Complexity : Volume 20
Journal of Systems Science and Complexity : Volume 19

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Predictive models and generative complexity

Content Provider SpringerLink
Author Löhr, Wolfgang
Copyright Year 2012
Abstract The causal states of computational mechanics define the minimal sufficient memory for a given discrete stationary stochastic process. Their entropy is an important complexity measure called statistical complexity (or true measure complexity). They induce the ɛ-machine, which is a hidden Markov model (HMM) generating the process. But it is not the minimal one, although generative HMMs also have a natural predictive interpretation. This paper gives a mathematical proof of the idea that the ɛ-machine is the minimal HMM with an additional (partial) determinism condition. Minimal internal state entropy of a generative HMM is in analogy to statistical complexity called generative complexity. This paper also shows that generative complexity depends on the process in a nice way. It is, as a function of the process, lower semi-continuous (w.r.t. weak-* topology), concave, and behaves nice under ergodic decomposition of the process.
Starting Page 30
Ending Page 45
Page Count 16
File Format PDF
ISSN 10096124
Journal Journal of Systems Science and Complexity
Volume Number 25
Issue Number 1
e-ISSN 15597067
Language English
Publisher Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Publisher Date 2012-02-03
Publisher Place Beijing
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Causal states complexity ɛ-machine generative complexity HMM partially deterministic HMM predictive model statistical Systems Theory, Control Statistics Statistical Physics, Dynamical Systems and Complexity Operations Research/Decision Theory Mathematics of Computing
Content Type Text
Resource Type Article
Subject Information Systems
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