Population Level Analysis of Convergence of the EM Algorithm for Overspecified Mixtures

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dc.contributor.authorPak, Artur
dc.date.accessioned2025-05-20T05:20:23Z
dc.date.available2025-05-20T05:20:23Z
dc.date.issued2025
dc.description.abstractThis thesis analyzes the convergence properties of the Expectation-Maximization (EM) algorithm when applied to an overspecified Gaussian Mixture Model (GMM). Specifically, it examines the case where a two-component balanced GMM is fitted to data generated from a single Gaussian distribution. A population-level analysis establishes an upper bound of Õ(1/t^2 ) on the Kullback-Leibler (KL) divergence between the learned and true distributions, where t is number of steps of EM algorithm. These theoretical findings are further validated through empirical experiments. This thesis contributes to a broader collaborative study (see Acknowledgments) titled Convergence of the EM Algorithm in KL Distance for Overspecified Gaussian Mixtures.
dc.identifier.citationPak, Artur. (2025). Population Level Analysis of Convergence of the EM Algorithm for Overspecified Mixtures. Nazarbayev University School of Sciences and Humanities.
dc.identifier.urihttps://nur.nu.edu.kz/handle/123456789/8542
dc.language.isoen
dc.publisherNazarbayev University School of Sciences and Humanities
dc.rightsAttribution 3.0 United Statesen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/us/
dc.subjectType of access: Open access
dc.subjectEM algorithm
dc.subjectKL divegence
dc.subjectExpectation-Maximization
dc.subjectKullback-Leibler
dc.subjectGMM
dc.subjectGaussian Mixture Model
dc.subjectOverspecified models
dc.titlePopulation Level Analysis of Convergence of the EM Algorithm for Overspecified Mixtures
dc.typeMaster`s thesis

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This thesis analyzes the convergence properties of the Expectation-Maximization (EM) algorithm when applied to an overspecified Gaussian Mixture Model (GMM). Specifically, it examines the case where a two-component balanced GMM is fitted to data generated from a single Gaussian distribution. A population-level analysis establishes an upper bound of Õ(1/t^2 ) on the Kullback-Leibler (KL) divergence between the learned and true distributions, where t is number of steps of EM algorithm. These theoretical findings are further validated through empirical experiments. This thesis contributes to a broader collaborative study (see Acknowledgments) titled Convergence of the EM Algorithm in KL Distance for Overspecified Gaussian Mixtures.
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02. Master's Thesis