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Fundamental Limits of Population Stratification From an Information Theoretic View

Tahmasebi, Behrooz | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51252 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Maddah-Ali, Mohammad Ali; Motahari, Abolfazl
  7. Abstract:
  8. This thesis consists of two parts. For the first, we study the identifiability of finite mixtures of finite product measures. This class of mixture models has a large number of applications in real-world data modeling. An important example is the population genetic application of them in modeling of mixed population datasets. The identifiability means that the mapping between the class parameters and the mixture distributions is one to one. In this manuscript, we define some separability metrics inspired by methods used in clustering mixture models and study the fundamental trade off between identifiability and the number of separable variables of the mixture model. For the second part of this thesis, we consider the Genome Wide Association Studies (GWAS) problem. The problem is that given a genomic data set of individuals and their observed characteristics (phenotypes), is it possible to detect the genomic locations which are correlated to the phenotype or not? The problem is very important in biology and medicine. In this thesis, we propose an abstract model to study the problem in a mathematical way. We show that there is a threshold effect for reliable learning of the genomic locations by ,introducing an achievable scheme and relying on an appropriate
    converse argument
  9. Keywords:
  10. Genome-Wide Asocciation Studies (GWAS) ; Information Theory ; Statistical Model ; Finite Mixture Models ; Statistical Models Identifiability

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