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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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Detalles Bibliográficos
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
Descripción
Sumario: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.