矩阵潜在分解模型的渐近分析

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Esaim-Probability and Statistics Pub Date : 2022-04-13 DOI:10.1051/ps/2022004
Clément Mantoux, S. Durrleman, S. Allassonnière
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引用次数: 1

摘要

矩阵数据集出现在医疗应用的网络分析中,其中每个网络属于一个主题并代表可测量的表型。这些大维度的数据通常使用低维度的潜在变量进行建模,这些潜在变量解释了大多数观察到的变异性,并可用于预测目的。本文给出了矩阵数据集的层次统计模型估计的渐近收敛保证。它通过对矩阵特征分解的截断建模来捕获矩阵的可变性。我们证明了该模型是可识别的,并且可以进行一致的最大后验估计(MAP)来估计特征值和特征向量的分布。对于模型的一个限制版本,MAP估计量被证明是渐近正态的。
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Asymptotic analysis of a matrix latent decomposition model
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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来源期刊
Esaim-Probability and Statistics
Esaim-Probability and Statistics STATISTICS & PROBABILITY-
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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