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MiS Preprint
66/2016
From Typical Sequences to Typical Genotypes
Omri Tal, Tat Dat Tran and Jacobus Willem Portegies
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 discretetime 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.
