# Kolmogorov structure function

**Kolmogorov structure configuration**

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

14 Related Articles

### 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.

### Acoustic Doppler current profiler

**ADCPacoustic Doppler current profilersAcoustic Doppler Current Profilers (ADCPs)**

A typical approach is to fit the along beam velocity to the Kolmogorov structure configuration and thereby estimate the dissipation rate.