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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2023
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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 |
collection | PubMed |
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. |
format | Online Article Text |
id | pubmed-9955902 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT kozyrevsergei learningbypopulationgeneticsandmatrixriccatiequation |