On the Identifiability of Parameters in the Population Stratification Problem: A Worst-Case Analysis

Behrooz Tahmasebi, Abolfazl S. Motahari, Mohammad Ali Maddah-Ali

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In the problem of population stratification, each data instance is generated based on a finite mixture model with K mixture components and L observed variables. Each variable takes its value in a finite state space with cardinality M. The variables are drawn independently in each mixture component. In this paper, we study the problem of the identifiability of parameters in this model, i.e. interpolation of the parameters of a mixture model from its mixture distribution. First we define the notion of informative variables. Then, we prove that the parameters of the problem are identifiable in the worst-case regime, if and only if the number of informative variables is greater than or equal to 2K - 1. As a result, in the worst-case analysis of the identifiability problem of finite mixture models, the number of required informative variables is Θ(K) and it is independent of the state space size.

Original languageEnglish (US)
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1051-1055
Number of pages5
ISBN (Print)9781538647806
DOIs
StatePublished - Aug 15 2018
Externally publishedYes
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: Jun 17 2018Jun 22 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-June
ISSN (Print)2157-8095

Other

Other2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/TerritoryUnited States
CityVail
Period6/17/186/22/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

Keywords

  • Identifiability
  • Population genetics
  • Population stratification

Fingerprint

Dive into the research topics of 'On the Identifiability of Parameters in the Population Stratification Problem: A Worst-Case Analysis'. Together they form a unique fingerprint.

Cite this