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A Data-Driven Bound on Covariance Matrices for Avoiding Degeneracy in Multivariate Gaussian Mixtures

Christophe Biernacki 1, 2 Gwénaelle Castellan 2 
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : Unbounded likelihood for multivariate Gaussian mixture is an important theoretical and practical problem. Using the weak information that the latent sample size of each component has to be greater than the space dimension, we derive a simple strategy relying on non-asymptotic stochastic lower bounds for monitoring singular values of the covariance matrix of each component. Maximizing the likelihood under this data-driven constraint is proved to give consistent estimates in the univariate situation, consistency for the multivariate case being still to establish. This strategy is implemented in an EM algorithm and its excellent performance is assessed through simulated data.
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Submitted on : Wednesday, December 31, 2014 - 10:23:07 AM
Last modification on : Wednesday, March 23, 2022 - 3:51:06 PM
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  • HAL Id : hal-01099080, version 1



Christophe Biernacki, Gwénaelle Castellan. A Data-Driven Bound on Covariance Matrices for Avoiding Degeneracy in Multivariate Gaussian Mixtures. 46° Journées de Statistique, Jun 2014, Rennes, France. ⟨hal-01099080⟩



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