Related papers: Mixtures Closest to a Given Measure: A Semidefinit…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…
Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…
Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
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…
This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…