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dc.contributor.authorMoshkov, Mikhail
dc.date.accessioned2022-01-17T06:46:32Z
dc.date.available2022-01-17T06:46:32Z
dc.date.issued2022-01-12
dc.date.submitted2021-10-20
dc.identifier.citationMoshkov, M. (2022). On the Depth of Decision Trees with Hypotheses. Entropy, 24(1), 116. doi:10.3390/e24010116
dc.identifier.issn1099-4300
dc.identifier.doi10.3390/e24010116
dc.identifier.urihttp://hdl.handle.net/10754/674972
dc.description.abstractIn this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system and study three functions of the Shannon type, which characterize the dependence in the worst case of the minimum depth of a decision tree solving a problem on the number of attributes in the problem description. The considered three functions correspond to (i) decision trees using attributes, (ii) decision trees using hypotheses (an analog of equivalence queries from exact learning), and (iii) decision trees using both attributes and hypotheses. The first function has two possible types of behavior: logarithmic and linear (this result follows from more general results published by the author earlier). The second and the third functions have three possible types of behavior: constant, logarithmic, and linear (these results were published by the author earlier without proofs that are given in the present paper). Based on the obtained results, we divided the set of all infinite binary information systems into four complexity classes. In each class, the type of behavior for each of the considered three functions does not change.
dc.description.sponsorshipResearch reported in this publication was supported by King Abdullah University of Science and Technology (KAUST). The author is greatly indebted to the anonymous reviewers for their useful comments and suggestions.
dc.publisherMDPI AG
dc.relation.urlhttps://www.mdpi.com/1099-4300/24/1/116
dc.rightsThis is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleOn the Depth of Decision Trees with Hypotheses
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.identifier.journalEntropy
dc.eprint.versionPublisher's Version/PDF
dc.identifier.volume24
dc.identifier.issue1
dc.identifier.pages116
kaust.personMoshkov, Mikhail
dc.date.accepted2022-01-10
refterms.dateFOA2022-01-17T06:48:31Z


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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Except where otherwise noted, this item's license is described as This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.