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Journal Articles ESAIM: Probability and Statistics Year : 2022

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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Dates and versions

hal-03674722 , version 1 (20-05-2022)

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