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Books > Computing & IT > General theory of computing > Data structures
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Algorithmic Statistics (Hardcover, 2020 ed.)
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Algorithmic Statistics (Hardcover, 2020 ed.)
Series: Monographs in Computer Science
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Whereas 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 (or probability distribution)
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 classical statistical theory
that deals with relations between probabilistic ensembles.
"Algorithmic Statistics" develops the algorithmic theory of
statistics, sufficient statistics, and minimal sufficient
statistics. This theory is based on two-part codes consisting of
the code for the statistic (the model summarizing the regularity,
the meaningful information, in the data) and the model-to-data
code. In contrast to the situation in probabilistic statistical
theory, the algorithmic relation of (minimal) sufficiency is an
absolute relation between the individual model and the individual
data sample. The book distinguishes implicit and explicit
descriptions of the models and gives characterizations of
algorithmic (Kolmogorov) minimal sufficient statistic for all data
samples for both description modes - in the explicit mode under
some constraints. It also strengthens and elaborates upon earlier
results on the 'Kolmogorov structure function' and 'absolutely
non-stochastic objects' - those rare objects for which the simplest
models that summarize their relevant information (minimal
sufficient statistics) are at least as complex as the objects
themselves.
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