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We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights.
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[author] Dasgupta, SanjoyS. and Schulman, Leonard J.L. J. (2007). A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians. Journal of Machine Learning Research 8 203-226
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Brubaker, S. C
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Chaudhuri, K
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[author] Kannan, RavindranR., Salmasian, HadiH. and Vempala, SantoshS. (2008). The Spectral Method for General Mixture Models. SIAM Journal on Computing 38 1141-1156
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Belkin, M
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Kalai, A. T
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Moitra, A
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[author] Wang, ZhaoranZ., Gu, QuanquanQ., Ning, YangY. and Liu, HanH. (2015). High Dimensional EM Algorithm: Statistical Optimization and Asymptotic Normality. In Advances in Neural Information Processing Systems 28 2521–2529
2015
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2015
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2016
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2016
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[author] Nguyen, XuanLongX. (2013). Convergence of latent mixing measures in finite and infinite mixture models. The Annals of Statistics 370–400
2013
Cited alongside, same era.
Hardt, M
2015
Cited alongside, same era.
[author] Cai, TonyT., Ma, JingJ. and Zhang, LinjunL. CHIME: Clustering of High-dimensional Gaussian Mixtures with EM Algorithm and its Optimality. The Annals of Statistics To appear
Cited in the paper.
Cited in the paper.
[author] Vershynin, RomanR. High-Dimensional Probability: An introduction with Applications in Data Science
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[author] Balakrishnan, SivaramanS., Wainwright, Martin J.M. J. and Yu, BinB. (2017). Statistical guarantees for the EM algorithm: From population to sample-based analysis. The Annals of Statistics 77–120
2017
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Daskalakis, C
2017
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[author] Yan, BoweiB., Yin, MingzhangM. and Sarkar, PurnamritaP. (2017). Convergence of Gradient EM on Multi-component Mixture of Gaussians. In Advances in Neural Information Processing Systems 30
2017
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[author] Heinrich, PhilippeP. and Kahn, JonasJ. (2018). Strong Identifiability and Optimal Minimax Rates for Finite Mixture Estimation. The Annals of Statistics 2844–2870
2018
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