Randomness conservation inequalities; information and independence in mathematical theories
Information and Control
Elements of information theory
Elements of information theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Applying MDL to learn best model granularity
Artificial Intelligence
The minimum description length principle in coding and modeling
IEEE Transactions on Information Theory
Minimum description length induction, Bayesianism, and Kolmogorov complexity
IEEE Transactions on Information Theory
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While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing the information in the data, for example, a finite set where the data sample typically came from. The statistical theory based on such relations between individual objects can be called algorithmic statistics, in contrast to ordinary statistical theory that deals with relations between probabilistic ensembles. We develop a new algorithmic theory of typical statistic, sufficient statistic, and minimal sufficient statistic.