# Kolmogorov structure function

Kolmogorov structure configuration
In 1973 Kolmogorov proposed a non-probabilistic approach to statistics and model selection.wikipedia
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### Kolmogorov complexity

algorithmic complexity theoryalgorithm complexity theoryalgorithmic entropy
Consider model classes consisting of models of given maximal Kolmogorov complexity.
Kolmogorov structure function

### Sufficient statistic

sufficient statisticssufficientsufficiency
The main properties of an algorithmic sufficient statistic are the following: If S is an algorithmic sufficient statistic for x, then
The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic.

### Andrey Kolmogorov

KolmogorovA. N. KolmogorovA.N. Kolmogorov
The structure function was originally proposed by Kolmogorov in 1973 at a Soviet Information Theory symposium in Tallinn, but these results were not published p. 182.
Kolmogorov structure function

### Minimum description length

MDLminimum description length principle
The Minimum description length (MDL) function: The length of the minimal two-part code for x consisting of the model cost K(S) and the The mathematics developed above were taken as the foundation of MDL by its inventor Jorma Rissanen.
In the last mentioned reference Rissanen bases the mathematical underpinning of MDL on the Kolmogorov structure function.

### Stochastic

stochastic musicstochasticsstochasticity
The structure function determines all stochastic properties of the individual data string: for every constrained model class it determines the individual best-fitting model in the class irrespective of whether the true model is in the model class considered or not.

### Algorithmic information theory

Algorithmic complexityalgorithmic informationdecorrelation
The Kolmogorov structure function is used in the algorithmic information theory, also known as the theory of Kolmogorov complexity, for describing the structure of a string by use of models of increasing complexity.

### String (computer science)

stringstringscharacter string
The Kolmogorov structure function is used in the algorithmic information theory, also known as the theory of Kolmogorov complexity, for describing the structure of a string by use of models of increasing complexity.

### Mathematical model

modelmathematical modelingmathematical models
The Kolmogorov structure function is used in the algorithmic information theory, also known as the theory of Kolmogorov complexity, for describing the structure of a string by use of models of increasing complexity.

### Jorma Rissanen

Rissanen, Jorma
The mathematics developed above were taken as the foundation of MDL by its inventor Jorma Rissanen.

### Maximum likelihood estimation

maximum likelihoodmaximum likelihood estimatormaximum likelihood estimate
For every complexity level \alpha the function is the Kolmogorov complexity version of the maximum likelihood (ML).

### Rate–distortion theory

rate-distortionrate distortionArimoto-Blahut method
It turns out that the approach can be extended to a theory of rate distortion of individual finite sequences

### Noise reduction

denoisingaudio noise reductionimage denoising
and denoising of individual finite sequences using Kolmogorov complexity.