Kolmogorov Structure Function - The MDL Variant and Probability Models

The MDL Variant and Probability Models

The MDL function: The length of the minimal two-part code for x consisting of the model cost K(P) and the length of, in the model class of computable probability mass functions of given maximal Kolmogorov complexity, the complexity of P upper bounded by, is given by the MDL function or constrained MDL estimator:

$\lambda'_{x}(\alpha) = \min_{P} \{\Lambda(P): P(x)> 0,\; K(P) \leq \alpha\},$

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

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