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

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

doi:10.1109/ISIT.2018.8437716

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 proceeding › Conference contribution

3 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 language	English (US)
Title of host publication	2018 IEEE International Symposium on Information Theory, ISIT 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1051-1055
Number of pages	5
ISBN (Print)	9781538647806
DOIs	https://doi.org/10.1109/ISIT.2018.8437716
State	Published - Aug 15 2018
Externally published	Yes
Event	2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: Jun 17 2018 → Jun 22 2018

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2018-June
ISSN (Print)	2157-8095

Other

Other	2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/Territory	United States
City	Vail
Period	6/17/18 → 6/22/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

Keywords

Identifiability
Population genetics
Population stratification

Publisher link

10.1109/ISIT.2018.8437716

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Tahmasebi, B., Motahari, A. S., & Maddah-Ali, M. A. (2018). On the Identifiability of Parameters in the Population Stratification Problem: A Worst-Case Analysis. In 2018 IEEE International Symposium on Information Theory, ISIT 2018 (pp. 1051-1055). Article 8437716 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2018.8437716

On the Identifiability of Parameters in the Population Stratification Problem: A Worst-Case Analysis. / Tahmasebi, Behrooz; Motahari, Abolfazl S.; Maddah-Ali, Mohammad Ali.
2018 IEEE International Symposium on Information Theory, ISIT 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1051-1055 8437716 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Tahmasebi, B, Motahari, AS & Maddah-Ali, MA 2018, On the Identifiability of Parameters in the Population Stratification Problem: A Worst-Case Analysis. in 2018 IEEE International Symposium on Information Theory, ISIT 2018., 8437716, IEEE International Symposium on Information Theory - Proceedings, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 1051-1055, 2018 IEEE International Symposium on Information Theory, ISIT 2018, Vail, United States, 6/17/18. https://doi.org/10.1109/ISIT.2018.8437716

Tahmasebi B, Motahari AS, Maddah-Ali MA. On the Identifiability of Parameters in the Population Stratification Problem: A Worst-Case Analysis. In 2018 IEEE International Symposium on Information Theory, ISIT 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1051-1055. 8437716. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2018.8437716

Tahmasebi, Behrooz ; Motahari, Abolfazl S. ; Maddah-Ali, Mohammad Ali. / On the Identifiability of Parameters in the Population Stratification Problem : A Worst-Case Analysis. 2018 IEEE International Symposium on Information Theory, ISIT 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1051-1055 (IEEE International Symposium on Information Theory - Proceedings).

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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.",

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

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