Why some families of probability distributions are practically efficient: A symmetry-based explanation

© Springer International Publishing Switzerland 2016. Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem o...

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Main Authors: Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, Songsak Sriboonchitta
Format: Book Series
Published: 2018
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Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952685290&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55598
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-555982018-09-05T02:58:20Z Why some families of probability distributions are practically efficient: A symmetry-based explanation Vladik Kreinovich Olga Kosheleva Hung T. Nguyen Songsak Sriboonchitta Computer Science © Springer International Publishing Switzerland 2016. Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate constraints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries—shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity x— then the resulting optimal families of probability distributions indeed include most of the empirically successful families. Thus, we get a symmetry-based explanation for their empirical success. 2018-09-05T02:58:20Z 2018-09-05T02:58:20Z 2016-01-01 Book Series 1860949X 2-s2.0-84952685290 10.1007/978-3-319-27284-9_8 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952685290&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/55598
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Computer Science
spellingShingle Computer Science
Vladik Kreinovich
Olga Kosheleva
Hung T. Nguyen
Songsak Sriboonchitta
Why some families of probability distributions are practically efficient: A symmetry-based explanation
description © Springer International Publishing Switzerland 2016. Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate constraints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries—shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity x— then the resulting optimal families of probability distributions indeed include most of the empirically successful families. Thus, we get a symmetry-based explanation for their empirical success.
format Book Series
author Vladik Kreinovich
Olga Kosheleva
Hung T. Nguyen
Songsak Sriboonchitta
author_facet Vladik Kreinovich
Olga Kosheleva
Hung T. Nguyen
Songsak Sriboonchitta
author_sort Vladik Kreinovich
title Why some families of probability distributions are practically efficient: A symmetry-based explanation
title_short Why some families of probability distributions are practically efficient: A symmetry-based explanation
title_full Why some families of probability distributions are practically efficient: A symmetry-based explanation
title_fullStr Why some families of probability distributions are practically efficient: A symmetry-based explanation
title_full_unstemmed Why some families of probability distributions are practically efficient: A symmetry-based explanation
title_sort why some families of probability distributions are practically efficient: a symmetry-based explanation
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952685290&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55598
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