Type
ArticleAuthors
Moshkov, Mikhail
KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Date
2022-01-12Submitted Date
2021-10-20Permanent link to this record
http://hdl.handle.net/10754/674972
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Show full item recordAbstract
In 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.Citation
Moshkov, M. (2022). On the Depth of Decision Trees with Hypotheses. Entropy, 24(1), 116. doi:10.3390/e24010116Sponsors
Research 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.Publisher
MDPI AGJournal
EntropyAdditional Links
https://www.mdpi.com/1099-4300/24/1/116ae974a485f413a2113503eed53cd6c53
10.3390/e24010116
Scopus Count
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