Influence of Explanatory Variable Distributions on the Behavior of the Impurity Measures Used in Classification Tree Learning.
| Title: | Influence of Explanatory Variable Distributions on the Behavior of the Impurity Measures Used in Classification Tree Learning. |
|---|---|
| Authors: | Gajowniczek, Krzysztof1 (AUTHOR) krzysztof_gajowniczek@sggw.edu.pl, Dudziński, Marcin1 (AUTHOR) |
| Source: | Entropy. Dec2024, Vol. 26 Issue 12, p1020. 35p. |
| Subject Terms: | *BETA distribution, *INTERACTIVE learning, *DISTRIBUTION (Probability theory), *MACHINE learning, *VALUES (Ethics), *LOGISTIC regression analysis |
| Abstract: | The primary objective of our study is to analyze how the nature of explanatory variables influences the values and behavior of impurity measures, including the Shannon, Rényi, Tsallis, Sharma–Mittal, Sharma–Taneja, and Kapur entropies. Our analysis aims to use these measures in the interactive learning of decision trees, particularly in the tie-breaking situations where an expert needs to make a decision. We simulate the values of explanatory variables from various probability distributions in order to consider a wide range of variability and properties. These probability distributions include the normal, Cauchy, uniform, exponential, and two beta distributions. This research assumes that the values of the binary responses are generated from the logistic regression model. All of the six mentioned probability distributions of the explanatory variables are presented in the same graphical format. The first two graphs depict histograms of the explanatory variables values and their corresponding probabilities generated by a particular model. The remaining graphs present distinct impurity measures with different parameters. In order to examine and discuss the behavior of the obtained results, we conduct a sensitivity analysis of the algorithms with regard to the entropy parameter values. We also demonstrate how certain explanatory variables affect the process of interactive tree learning. [ABSTRACT FROM AUTHOR] |
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| Items | – Name: Title Label: Title Group: Ti Data: Influence of Explanatory Variable Distributions on the Behavior of the Impurity Measures Used in Classification Tree Learning. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gajowniczek%2C+Krzysztof%22">Gajowniczek, Krzysztof</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> krzysztof_gajowniczek@sggw.edu.pl</i><br /><searchLink fieldCode="AR" term="%22Dudziński%2C+Marcin%22">Dudziński, Marcin</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Entropy%22">Entropy</searchLink>. Dec2024, Vol. 26 Issue 12, p1020. 35p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22BETA+distribution%22">BETA distribution</searchLink><br />*<searchLink fieldCode="DE" term="%22INTERACTIVE+learning%22">INTERACTIVE learning</searchLink><br />*<searchLink fieldCode="DE" term="%22DISTRIBUTION+%28Probability+theory%29%22">DISTRIBUTION (Probability theory)</searchLink><br />*<searchLink fieldCode="DE" term="%22MACHINE+learning%22">MACHINE learning</searchLink><br />*<searchLink fieldCode="DE" term="%22VALUES+%28Ethics%29%22">VALUES (Ethics)</searchLink><br />*<searchLink fieldCode="DE" term="%22LOGISTIC+regression+analysis%22">LOGISTIC regression analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The primary objective of our study is to analyze how the nature of explanatory variables influences the values and behavior of impurity measures, including the Shannon, Rényi, Tsallis, Sharma–Mittal, Sharma–Taneja, and Kapur entropies. Our analysis aims to use these measures in the interactive learning of decision trees, particularly in the tie-breaking situations where an expert needs to make a decision. We simulate the values of explanatory variables from various probability distributions in order to consider a wide range of variability and properties. These probability distributions include the normal, Cauchy, uniform, exponential, and two beta distributions. This research assumes that the values of the binary responses are generated from the logistic regression model. All of the six mentioned probability distributions of the explanatory variables are presented in the same graphical format. The first two graphs depict histograms of the explanatory variables values and their corresponding probabilities generated by a particular model. The remaining graphs present distinct impurity measures with different parameters. In order to examine and discuss the behavior of the obtained results, we conduct a sensitivity analysis of the algorithms with regard to the entropy parameter values. We also demonstrate how certain explanatory variables affect the process of interactive tree learning. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Entropy is the property of MDPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3390/e26121020 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 1020 Subjects: – SubjectFull: BETA distribution Type: general – SubjectFull: INTERACTIVE learning Type: general – SubjectFull: DISTRIBUTION (Probability theory) Type: general – SubjectFull: MACHINE learning Type: general – SubjectFull: VALUES (Ethics) Type: general – SubjectFull: LOGISTIC regression analysis Type: general Titles: – TitleFull: Influence of Explanatory Variable Distributions on the Behavior of the Impurity Measures Used in Classification Tree Learning. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gajowniczek, Krzysztof – PersonEntity: Name: NameFull: Dudziński, Marcin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 10994300 Numbering: – Type: volume Value: 26 – Type: issue Value: 12 Titles: – TitleFull: Entropy Type: main |
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