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Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
We consider a simulation optimization problem for a context-dependent decision-making. A Gaussian mixture model is proposed to capture the performance clustering phenomena of context-dependent designs. Under a Bayesian framework, we develop…
Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…
A major challenge in cluster analysis is that the number of data clusters is mostly unknown and it must be estimated prior to clustering the observed data. In real-world applications, the observed data is often subject to heavy tailed noise…
In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…
Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Mixture models are a natural choice in many applications, but it can be difficult to place an a priori upper bound on the number of components. To circumvent this, investigators are turning increasingly to Dirichlet process mixture models…
Highly size-asymmetrical fluid mixtures arise in a variety of physical contexts, notably in suspensions of colloidal particles to which much smaller particles have been added in the form of polymers or nanoparticles. Conventional schemes…
Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…
The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…
We show how observations of the evolution of the galaxy cluster number abundance can be used to constrain primordial non-Gaussianity in the universe. We carry out a maximum likelihood analysis incorporating a number of current datasets and…
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are…