English
Related papers

Related papers: Tractable Measure of Component Overlap for Gaussia…

200 papers

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well…

Methodology · Statistics 2016-06-23 Gertraud Malsiner-Walli , Sylvia Frühwirth-Schnatter , Bettina Grün

We present a new algorithm for clustering points in R^n. The key property of the algorithm is that it is affine-invariant, i.e., it produces the same partition for any affine transformation of the input. It has strong guarantees when the…

Machine Learning · Computer Science 2008-08-04 S. Charles Brubaker , Santosh S. Vempala

Gaussian mixture models are a popular tool for model-based clustering, and mixtures of factor analyzers are Gaussian mixture models having parsimonious factor covariance structure for mixture components. There are several recent extensions…

Methodology · Statistics 2023-06-29 Lucas Kock , Nadja Klein , David J. Nott

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…

Statistical Mechanics · Physics 2018-12-05 Joël Bun , Jean-Philippe Bouchaud , Marc Potters

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the…

Machine Learning · Statistics 2026-04-08 Huan Qing

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…

Machine Learning · Statistics 2021-11-30 Damek Davis , Mateo Díaz , Kaizheng Wang

Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…

Methodology · Statistics 2020-07-10 Deborah Kunkel , Mario Peruggia

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…

Methodology · Statistics 2016-08-08 L. A. García-Escudero , A. Gordaliza , F. Greselin , S. Ingrassia , A. Mayo-Iscar

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…

Machine Learning · Statistics 2025-04-03 Daniel Frisch , Uwe D. Hanebeck

Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation…

Machine Learning · Computer Science 2012-09-05 Qiaoliang Xiang , Qi Mao , Kian Ming Chai , Hai Leong Chieu , Ivor Tsang , Zhendong Zhao

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…

Robotics · Computer Science 2021-04-02 Tim Pfeifer , Sven Lange , Peter Protzel

We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances,…

Machine Learning · Statistics 2024-05-29 Khen Cohen , Noam Levi , Yaron Oz

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

Machine Learning · Computer Science 2015-03-11 Rong Ge , Qingqing Huang , Sham M. Kakade

Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with…

Methodology · Statistics 2015-10-01 Matthieu Marbac , Christophe Biernacki , Vincent Vandewalle

The class of index-mixed copulas is introduced and its properties are investigated. Index-mixed copulas are constructed from given base copulas and a random index vector, and show a rather remarkable degree of analytical tractability. The…

Methodology · Statistics 2023-08-10 Klaus Herrmann , Marius Hofert , Nahid Sadr

Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…

Machine Learning · Computer Science 2020-03-31 Yuanzhi Li , Yingyu Liang

Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability…

Machine Learning · Computer Science 2024-07-30 Ryosuke Motegi , Yoichi Seki

By a "covering" we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model. Between families of Gaussian mixture models,…

Computer Vision and Pattern Recognition · Computer Science 2011-01-11 Fionn Murtagh , Pedro Contreras , Jean-Luc Starck

In model-based clustering using finite mixture models, it is a significant challenge to determine the number of clusters (cluster size). It used to be equal to the number of mixture components (mixture size); however, this may not be valid…

Machine Learning · Computer Science 2020-07-16 Shunki Kyoya , Kenji Yamanishi

Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep…

Machine Learning · Computer Science 2024-08-13 Patrick Burauel , Frederick Eberhardt , Michel Besserve