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Asymptotic Analysis of a Matrix Latent Decomposition Model

Abstract : Matrix data sets arise in network analysis for medical applications, where each network belongs to a subject and represents a measurable phenotype. These large dimensional data are often modeled using lower-dimensional latent variables, which explain most of the observed variability and can be used for predictive purposes. In this paper, we provide asymptotic convergence guarantees for the estimation of a hierarchical statistical model for matrix data sets. It captures the variability of matrices by modeling a truncation of their eigendecomposition. We show that this model is identifiable, and that consistent Maximum A Posteriori (MAP) estimation can be performed to estimate the distribution of eigenvalues and eigenvectors. The MAP estimator is shown to be asymptotically normal for a restricted version of the model.
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https://hal.archives-ouvertes.fr/hal-03674722
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Submitted on : Friday, May 20, 2022 - 10:35:13 PM
Last modification on : Saturday, June 25, 2022 - 3:44:07 AM

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Clément Mantoux, Stanley Durrleman, Stéphanie Allassonnière. Asymptotic Analysis of a Matrix Latent Decomposition Model. ESAIM: Probability and Statistics, EDP Sciences, 2022, 26, pp.208-242. ⟨10.1051/ps/2022004⟩. ⟨hal-03674722⟩

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