Kolmogorov Structure Function - The MDL Variant

The MDL Variant

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 length of the index of x in S, in the model class of sets of given maximal Kolmogorov complexity, the complexity of S upper bounded by, is given by the MDL function or constrained MDL estimator:

\lambda_{x}(\alpha) = \min_{S} \{\Lambda(S): S \ni x,\; K(S) \leq \alpha\},

where is the total length of two-part code of x with help of model S.

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