Estimation of Overfitting Degree of Algebraic Machine Learning in Boolean Algebra
The paper presents an estimation of overfitting probability for VKF-method of algebraic machine learning in the simplest case of Boolean algebra without counter-examples. The model uses the Vapnik—Chervonenkis proposal to minimize the empirical risk. Asymptotically the probability of overfitting err...
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| Published in | Automatic documentation and mathematical linguistics Vol. 56; no. 3; pp. 160 - 162 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.06.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1055 1934-8371 |
| DOI | 10.3103/S0005105522030098 |
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| Abstract | The paper presents an estimation of overfitting probability for VKF-method of algebraic machine learning in the simplest case of Boolean algebra without counter-examples. The model uses the Vapnik—Chervonenkis proposal to minimize the empirical risk. Asymptotically the probability of overfitting errors for a fixed fraction of test examples tends to zero faster than exponentially decrease if the description length and the number of requested hypotheses go to infinity. |
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| AbstractList | The paper presents an estimation of overfitting probability for VKF-method of algebraic machine learning in the simplest case of Boolean algebra without counter-examples. The model uses the Vapnik—Chervonenkis proposal to minimize the empirical risk. Asymptotically the probability of overfitting errors for a fixed fraction of test examples tends to zero faster than exponentially decrease if the description length and the number of requested hypotheses go to infinity. |
| Author | Vinogradov, D. |
| Author_xml | – sequence: 1 givenname: D. surname: Vinogradov fullname: Vinogradov, D. email: vinogradov.d.w@gmail.com organization: Federal Research Center Computer Science and Control, Russian Academy of Sciences |
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| Cites_doi | 10.3103/S0005105518010090 10.1063/1.3062516 |
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| Copyright | Allerton Press, Inc. 2022. ISSN 0005-1055, Automatic Documentation and Mathematical Linguistics, 2022, Vol. 56, No. 3, pp. 160–162. © Allerton Press, Inc., 2022. Russian Text © The Author(s), 2022, published in Nauchno-Tekhnicheskaya Informatsiya, Seriya 2: Informatsionnye Protsessy i Sistemy, 2022, No. 6, pp. 17–19. |
| Copyright_xml | – notice: Allerton Press, Inc. 2022. ISSN 0005-1055, Automatic Documentation and Mathematical Linguistics, 2022, Vol. 56, No. 3, pp. 160–162. © Allerton Press, Inc., 2022. Russian Text © The Author(s), 2022, published in Nauchno-Tekhnicheskaya Informatsiya, Seriya 2: Informatsionnye Protsessy i Sistemy, 2022, No. 6, pp. 17–19. |
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| Keywords | overfitting empirical risk Boolean algebra VKF-method |
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| References | Vorontsov (CR4) 2004 CR2 CR5 Anshakov (CR7) 2009 Vinogradov (CR1) 2018; 934 Feller (CR6) 1958 Vinogradov (CR3) 2018; 52 7110_CR5 W. Feller (7110_CR6) 1958 D.V. Vinogradov (7110_CR1) 2018; 934 D.V. Vinogradov (7110_CR3) 2018; 52 7110_CR2 K.V. Vorontsov (7110_CR4) 2004 (7110_CR7) 2009 |
| References_xml | – volume: 52 start-page: 35 year: 2018 end-page: 37 ident: CR3 article-title: The rate of convergence to the limit of the probability of encountering an accidental similarity in the presence of counter examples publication-title: Autom. Doc. Math. Linguist. doi: 10.3103/S0005105518010090 – year: 1958 ident: CR6 doi: 10.1063/1.3062516 – ident: CR5 – ident: CR2 – year: 2004 ident: CR4 publication-title: Combinatorial approach to estimation of quality of learnable algorithms, (Mathematical Questions of Cybernetics) – volume: 934 start-page: 46 year: 2018 end-page: 59 ident: CR1 article-title: Machine learning based on similarity operation publication-title: Commun. Comput. Inf. Sci. – year: 2009 ident: CR7 publication-title: (JSM Method of Automated Hypothesis Generation: Logical and Epistemological Foundations) – volume: 52 start-page: 35 year: 2018 ident: 7110_CR3 publication-title: Autom. Doc. Math. Linguist. doi: 10.3103/S0005105518010090 – ident: 7110_CR5 – volume-title: DSM-metod avtomaticheskogo porozhdeniya gipotez: logicheskie i epistemologicheskie osnovaniya (JSM Method of Automated Hypothesis Generation: Logical and Epistemological Foundations) year: 2009 ident: 7110_CR7 – volume: 934 start-page: 46 year: 2018 ident: 7110_CR1 publication-title: Commun. Comput. Inf. Sci. – volume-title: An Introduction to Probability Theory and Its Applications year: 1958 ident: 7110_CR6 doi: 10.1063/1.3062516 – ident: 7110_CR2 – volume-title: Combinatorial approach to estimation of quality of learnable algorithms, Matematicheskie voprosy kibernetiki (Mathematical Questions of Cybernetics) year: 2004 ident: 7110_CR4 |
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| SubjectTerms | Boolean algebra Computer Science Fractions Information Storage and Retrieval Intelligent Systems Machine learning |
| Title | Estimation of Overfitting Degree of Algebraic Machine Learning in Boolean Algebra |
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