From typical sequences to typical genotypes. (21st April 2017) - Tal, Omri; Tran, Tat Dat; Portegies, Jacobus
Abstract: We demonstrate an application of a core notion of information theory, typical sequences and their related properties, to analysis of population genetic data. Based on the asymptotic equipartition property (AEP) for nonstationary discrete-time sources producing independent symbols, we introduce the concepts of typical genotypes and population entropy 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. Abstract : Highlights: We demonstrate deep links between a core information-theoretic concept and features of genetic data. Long stretches of population variants may be captured as typical sequences of a nonstationary source. We introduce the concepts of typical genotypes, population entropy rate and mutual typicality. We derive the asymptotic properties of mutually typical genotypes. We develop a simple ancestry inference scheme and analyze resilience to noise from small samples.