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We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM's adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE)…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
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…
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 number density of galaxy clusters across mass and redshift has been established as a powerful cosmological probe. Cosmological analyses with galaxy clusters traditionally employ scaling relations. However, many challenges arise from…
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),…
Improved EM strategies, based on the idea of efficient data augmentation (Meng and van Dyk 1997, 1998), are presented for ML estimation of mixture proportions. The resulting algorithms inherit the simplicity, ease of implementation, and…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
We propose a new fast algorithm optimized for full-wave electromagnetic (EM) scattering analysis of a large-scale cloud of chaffs with arbitrary orientation, spatial distribution, and length. By leveraging the unique EM scattering…
Clusters of galaxies are the most massive objects in the Universe and mapping their location is an important astronomical problem. This paper describes an algorithm (based on statistical signal processing methods), a software architecture…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that…
This paper describes an algorithm for fitting finite mixtures of unrestricted Multivariate Skew t (FM-uMST) distributions. The package EMMIX-uskew implements a closed-form expectation-maximization (EM) algorithm for computing the maximum…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
Modern scientific studies often collect data sets in the forms of tensors, which call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
This paper deals with the problem of clustering data returned by a radar sensor network that monitors a region where multiple moving targets are present. The network is formed by nodes with limited functionalities that transmit the…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…