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Kolmogorov structure function

In 1973, Andrey Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let each datum be a finite binary string and a model be a finite set of binary strings. Consider model classes consisting of models of given maximal Kolmogorov complexity. The Kolmogorov structure function of an individual data string expresses the…

Products, Contemporary definition & The MDL variant

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Contemporary definition

VitányiSufficient statisticMinimal sufficient statistic
3 related topics

The MDL variant

MDLJorma Rissanen
2 related topics

Extension to rate distortion and denoising

Rate distortionDenoising
2 related topics

Kolmogorov's definition

Kolmogorov
1 related topics

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Kolmogorov's definition

Contemporary definition

The MDL variant

Probability models

Extension to rate distortion and denoising

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Kolmogorov structure function

Nodes26
Edges25
Triples8
Avg. degree1.92
Density0.076923
Components1

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Kolmogorov structure function

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related to Contemporary definition · 8
Kolmogorov structure function → Clearly, Cover, It, Kolmogorov, The Kolmogorov, Thomas, Vereshchagin, Vitányi

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Important terminology

displaystyle kolmogorov function model complexity log alpha string structure probability individual data properties mdl leq set sufficient algorithmic models level

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Kolmogorov structure functionrelated to Contemporary definitionIt0.60section
Kolmogorov structure functionrelated to Contemporary definitionCover0.60section
Kolmogorov structure functionrelated to Contemporary definitionThomas0.60section
Kolmogorov structure functionrelated to Contemporary definitionVereshchagin0.60section
Kolmogorov structure functionrelated to Contemporary definitionVitányi0.60section
Kolmogorov structure functionrelated to Contemporary definitionThe Kolmogorov0.60section
Kolmogorov structure functionrelated to Contemporary definitionKolmogorov0.60section
Kolmogorov structure functionrelated to Contemporary definitionClearly0.60section

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