Concentrated or non-concentrated discrete distributions are almost independent
2007 (English)Manuscript (preprint) (Other academic)
The task of approximating a simultaneous distribution with a product of distributions in a single variable is important in the theory and applications of classification and learning, probabilistic reasoning, and random algmithms. The evaluation of the goodness of this approximation by statistical independence amounts to bounding uniformly upwards the difference between a joint distribution and the product of the distributions (marginals). In this paper we develop a bound that uses information about the most probable state to find a sharp estimate, which is often as sharp as possible. We also examine the extreme cases of concentration and non-conccntmtion, respectively, of the approximated distribution.
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IdentifiersURN: urn:nbn:se:liu:diva-13105OAI: oai:DiVA.org:liu-13105DiVA: diva2:17843