Volume 26, 2022
|Page(s)||208 - 242|
|Published online||20 May 2022|
Asymptotic Analysis of a Matrix Latent Decomposition Model
1 ARAMIS Project Team, Inria, Paris 75013, France
2 ARAMIS Lab, Brain and Spine Institute, ICM, INSERM UMR 1127, CNRS UMR 7225, Sorbonne Universite, Hopital de la Pitie-Salpetriere, Paris 75013, France
3 CMAP, Ecole polytechnique, Palaiseau 91120, France
4 Centre de Recherche des Cordeliers, Universite de Paris, INSERM UMR 1138, Sorbonne Universite, Paris 75006, France
5 HEKA Project Team, Inria, Paris 75006, France
* Corresponding author: firstname.lastname@example.org
Accepted: 7 April 2022
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.
Mathematics Subject Classification: 62F12 / 62H21
Key words: Hierarchical model / matrix data sets / low rank / stiefel manifold / identifiability / strong consistency / asymptotic normality
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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