Related papers: Minimum Message Length Clustering Using Gibbs Samp…

Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Minimum message length is a general Bayesian principle for model selection and parameter estimation that is based on information theory. This paper applies the minimum message length principle to a small-sample model selection problem…

Gibbs sampling is one of the most popular Markov chain Monte Carlo algorithms because of its simplicity, scalability, and wide applicability within many fields of statistics, science, and engineering. In the labeled random finite sets…

The MC$^3$ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each…

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…

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…

Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization…

Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…

Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…

The classical mixture of Gaussians model is related to K-means via small-variance asymptotics: as the covariances of the Gaussians tend to zero, the negative log-likelihood of the mixture of Gaussians model approaches the K-means objective,…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates $C$ includes cluster-level partially observed…

We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization…