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From Typical Sequences to Typical Genotypes

Omri Tal, Tat Dat Tran, Jacobus Portegies
doi: https://doi.org/10.1101/079491
Omri Tal
Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany Inselstrasse 22, D-04103 Leipzig
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  • For correspondence: Omri.Tal@mis.mpg.de
Tat Dat Tran
Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany Inselstrasse 22, D-04103 Leipzig
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Jacobus Portegies
Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany Inselstrasse 22, D-04103 Leipzig
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Abstract

We demonstrate an application of a core notion of information theory, that of typical sequences and their related properties, to analysis of population genetic data. Based on the asymptotic equipartition property (AEP) for non-stationary discrete-time sources producing independent symbols, we introduce the concepts of typical genotypes and population entropy rate and cross entropy rate. We analyze three perspectives on typical genotypes: a set perspective on the interplay of typical sets of genotypes from two populations, a geometric perspective on their structure in high dimensional space, and a statistical learning perspective on the prospects of constructing typical-set based classifiers. In particular, we show that such classifiers have a surprising resilience to noise originating from small population samples, and highlight the potential for further links between inference and communication.

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Posted October 13, 2016.
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From Typical Sequences to Typical Genotypes
Omri Tal, Tat Dat Tran, Jacobus Portegies
bioRxiv 079491; doi: https://doi.org/10.1101/079491
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From Typical Sequences to Typical Genotypes
Omri Tal, Tat Dat Tran, Jacobus Portegies
bioRxiv 079491; doi: https://doi.org/10.1101/079491

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