The application of algorithmic information theory to noisy patterned strings

Devine, Sean

doi:10.1002/cplx.20152

Cited by 7 publications

(15 citation statements)

References 22 publications

(23 reference statements)

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“…With an interventionist calculus such as the one performed on the time series above, one may rule out some but not all cases, but more importantly, the perturbation analysis offers the means to start constructing a model explaining the system and data rather than merely describing it in terms of simpler correlations. In our approach to integrated information, the idea is to identify the set of most likely generating candidates able to produce certain observed behaviour even if such behaviour may not carry any statistical regularity and for all purposes appear statistically random [9]. Strictly speaking, computational mechanics [4,3], is a framework that bridges statistical inference and stochastic modelling that suggests a model based on an automaton called an -machine.…”

Section: Causal Perturbation Analysismentioning

confidence: 99%

Estimations of Integrated Information Based on Algorithmic Complexity and Dynamic Querying

Hernández-Espinosa

Zenil

Kiani

et al. 2021

Handbook of Unconventional Computing

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Information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of information generated by a system beyond the information generated by its elements. Yet, this intriguing notion comes with the price of being prohibitively expensive to calculate, since the calculations require an exponential number of sub-divisions of a system. Here we introduce a novel framework to connect algorithmic randomness and integrated information, and a numerical method for estimating integrated information using a perturbation test rooted in algorithmic information dynamics. This method quantifies the change in program size of a system, when subjected to a perturbation. The intuition behind is that if an object is random then random perturbations have little to no effect to what happens when a shorter program but when an objects has the ability to move in both directions (towards or away from randomness) it will be shown to be better integrated as a measure of sophistication telling apart randomness and simplicity from structure. We show that an object with a high integrated information value is also more compressible, and is therefore more sensitive to perturbations. We find that such a perturbation test quantifying compression sensitivity, provides a system with a means to extract explanations-causal accounts-of its own behaviour. Our technique can reduce the number of calculations to arrive to some bounds or estimations, as the algorithmic perturbation test guides an efficient search for estimating integrated information. Our work sets the stage for a systematic exploration of connections between algorithmic complexity and integrated information at the level of both theory and practice.

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Section: Causal Perturbation Analysismentioning

confidence: 99%

Estimations of Integrated Information Based on Algorithmic Complexity and Dynamic Querying

Hernández-Espinosa

Zenil

Kiani

et al. 2021

Handbook of Unconventional Computing

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“…Indeed, for a typical outcome representing an equilibrium configuration, allowing for computational overheads, the algorithmic measure returns the same value as the Shannon entropy or, allowing for units, the Boltzmann and Gibbs entropies. Indeed, the Shannon entropy can be considered as a special case of the algorithmic entropy for a typical or random string [10,11]. The similarity with the Shannon entropy can be seen in relationships like H(x, y) derived from the algorithm that calculates both strings x and y.…”

Section: A Algorithmic Information Theorymentioning

confidence: 99%

An Algorithmic Information Theory Challenge to Intelligent Design

Devine¹

2014

Zygon

Self Cite

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Abstract.William Dembski claims to have established a decision process to determine when highly unlikely events observed in the natural world are due to Intelligent Design. This article argues that, as no implementable randomness test is superior to a universal Martin-Löf test, this test should be used to replace Dembski's decision process. Furthermore, Dembski's decision process is flawed, as natural explanations are eliminated before chance. Dembski also introduces a fourth law of thermodynamics, his "law of conservation of information," to argue that information cannot increase by natural processes. However, this article, using algorithmic information theory, shows that this law is no more than the second law of thermodynamics. The article concludes that any discussions on the possibilities of design interventions in nature should be articulated in terms of the algorithmic information theory approach to randomness and its robust decision process.

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“…Let the common instruction string be represented by 'CI' [27] and, given the common instructions or common subroutines, the physically significant entropy will be denoted by the conditional algorithmic entropy H algo (x|CI). In what follows unless specifically stated otherwise, H algo (x) can be used to represent H algo (x|CI).…”

Section: Entropy Relative To the Common Frameworkmentioning

confidence: 99%

“…Devine [27] has shown that where pattern in a noisy sequence is recognized there is an implicit reference to a set containing all similar strings exhibiting the pattern. As this set will be recursively enumerable (i.e.…”

Section: Provisional Entropymentioning

confidence: 99%

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The Insights of Algorithmic Entropy

Devine

2009

Entropy

Self Cite

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Abstract:The algorithmic entropy of a system, the length of the shortest algorithm that specifies the system's exact state adds some missing pieces to the entropy jigsaw. Because the approach embodies the traditional entropies as a special case, problematic issues such as the coarse graining framework of the Gibbs' entropy manifest themselves in a different and more manageable form, appearing as the description of the system and the choice of the universal computing machine. The provisional algorithmic entropy combines the best information about the state of the system together with any underlying uncertainty; the latter represents the Shannon entropy. The algorithmic approach also specifies structure that the traditional entropies take as given. Furthermore, algorithmic entropy provides insights into how a system can maintain itself off equilibrium, leading to Ashby's law of requisite variety. This review shows how the algorithmic approach can provide insights into real world systems, by outlining recent work on how replicating structures that generate order can evolve to maintain a system far from equilibrium.

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The application of algorithmic information theory to noisy patterned strings

Cited by 7 publications

References 22 publications

Estimations of Integrated Information Based on Algorithmic Complexity and Dynamic Querying

Estimations of Integrated Information Based on Algorithmic Complexity and Dynamic Querying

An Algorithmic Information Theory Challenge to Intelligent Design

The Insights of Algorithmic Entropy

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