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Keywords = MCMC-SAEM

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27 pages, 462 KiB  
Article
Stochastic Expectation Maximization Algorithm for Linear Mixed-Effects Model with Interactions in the Presence of Incomplete Data
by Alandra Zakkour, Cyril Perret and Yousri Slaoui
Entropy 2023, 25(3), 473; https://doi.org/10.3390/e25030473 - 8 Mar 2023
Cited by 3 | Viewed by 2781
Abstract
The purpose of this paper is to propose a new algorithm based on stochastic expectation maximization (SEM) to deal with the problem of unobserved values when multiple interactions in a linear mixed-effects model (LMEM) are present. We test the effectiveness of the proposed [...] Read more.
The purpose of this paper is to propose a new algorithm based on stochastic expectation maximization (SEM) to deal with the problem of unobserved values when multiple interactions in a linear mixed-effects model (LMEM) are present. We test the effectiveness of the proposed algorithm with the stochastic approximation expectation maximization (SAEM) and Monte Carlo Markov chain (MCMC) algorithms. This comparison is implemented to highlight the importance of including the maximum effects that can affect the model. The applications are made on both simulated psychological and real data. The findings demonstrate that our proposed SEM algorithm is highly preferable to the other competitor algorithms. Full article
(This article belongs to the Special Issue Monte Carlo Simulation in Statistical Physics)
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34 pages, 1413 KiB  
Article
Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold
by Clément Mantoux, Baptiste Couvy-Duchesne, Federica Cacciamani, Stéphane Epelbaum, Stanley Durrleman and Stéphanie Allassonnière
Entropy 2021, 23(4), 490; https://doi.org/10.3390/e23040490 - 20 Apr 2021
Cited by 4 | Viewed by 4036
Abstract
Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of [...] Read more.
Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom. Full article
(This article belongs to the Special Issue Approximate Bayesian Inference)
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