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Learning by Population Genetics and Matrix Riccati Equation

A model of learning as a generalization of the Eigen’s quasispecies model in population genetics is introduced. Eigen’s model is considered as a matrix Riccati equation. The error catastrophe in the Eigen’s model (when the purifying selection becomes ineffective) is discussed as the divergence of th...

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Autor principal: Kozyrev, Sergei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955902/
https://www.ncbi.nlm.nih.gov/pubmed/36832714
http://dx.doi.org/10.3390/e25020348
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author Kozyrev, Sergei
author_facet Kozyrev, Sergei
author_sort Kozyrev, Sergei
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description A model of learning as a generalization of the Eigen’s quasispecies model in population genetics is introduced. Eigen’s model is considered as a matrix Riccati equation. The error catastrophe in the Eigen’s model (when the purifying selection becomes ineffective) is discussed as the divergence of the Perron–Frobenius eigenvalue of the Riccati model in the limit of large matrices. A known estimate for the Perron–Frobenius eigenvalue provides an explanation for observed patterns of genomic evolution. We propose to consider the error catastrophe in Eigen’s model as an analog of overfitting in learning theory; this gives a criterion for the presence of overfitting in learning.
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spelling pubmed-99559022023-02-25 Learning by Population Genetics and Matrix Riccati Equation Kozyrev, Sergei Entropy (Basel) Article A model of learning as a generalization of the Eigen’s quasispecies model in population genetics is introduced. Eigen’s model is considered as a matrix Riccati equation. The error catastrophe in the Eigen’s model (when the purifying selection becomes ineffective) is discussed as the divergence of the Perron–Frobenius eigenvalue of the Riccati model in the limit of large matrices. A known estimate for the Perron–Frobenius eigenvalue provides an explanation for observed patterns of genomic evolution. We propose to consider the error catastrophe in Eigen’s model as an analog of overfitting in learning theory; this gives a criterion for the presence of overfitting in learning. MDPI 2023-02-14 /pmc/articles/PMC9955902/ /pubmed/36832714 http://dx.doi.org/10.3390/e25020348 Text en © 2023 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kozyrev, Sergei
Learning by Population Genetics and Matrix Riccati Equation
title Learning by Population Genetics and Matrix Riccati Equation
title_full Learning by Population Genetics and Matrix Riccati Equation
title_fullStr Learning by Population Genetics and Matrix Riccati Equation
title_full_unstemmed Learning by Population Genetics and Matrix Riccati Equation
title_short Learning by Population Genetics and Matrix Riccati Equation
title_sort learning by population genetics and matrix riccati equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955902/
https://www.ncbi.nlm.nih.gov/pubmed/36832714
http://dx.doi.org/10.3390/e25020348
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