Journal
ENTROPY
Volume 25, Issue 2, Pages -Publisher
MDPI
DOI: 10.3390/e25020348
Keywords
learning theory; statistical mechanics; evolution theory
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A learning model is introduced as a generalization of Eigen's quasispecies model in population genetics. The error catastrophe in Eigen's model is discussed as the divergence of the Perron-Frobenius eigenvalue of the Riccati model in the limit of large matrices. The analogy between the error catastrophe and overfitting in learning theory is proposed, providing a criterion for detecting overfitting.
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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