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We systematically study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model within the framework of decentralized federated learning. Our theoretical investigation reveals that directly extending the…
The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…
This paper introduces a Bayesian image segmentation algorithm based on finite mixtures. An EM algorithm is developed to estimate parameters of the Gaussian mixtures. The finite mixture is a flexible and powerful probabilistic modeling tool.…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful…
We consider the problem of inferring an unknown number of clusters in replicated multinomial data. Under a model based clustering point of view, this task can be treated by estimating finite mixtures of multinomial distributions with or…
Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among…
Variational autoencoder (VAE) and generative adversarial networks (GAN) have found widespread applications in clustering and have achieved significant success. However, the potential of these approaches may be limited due to VAE's mediocre…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM),…
This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when…
Finite mixture model is an important branch of clustering methods and can be applied on data sets with mixed types of variables. However, challenges exist in its applications. First, it typically relies on the EM algorithm which could be…
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…
Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…