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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…

Methodology · Statistics 2024-06-04 Lorenzo Ghilotti , Mario Beraha , Alessandra Guglielmi

Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…

Machine Learning · Statistics 2020-10-23 Zhiyue Zhang , Kenneth Lange , Jason Xu

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…

Methodology · Statistics 2018-08-23 Sylvia Frühwirth-Schnatter , Gertraud Malsiner-Walli

We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…

Statistics Theory · Mathematics 2014-09-05 Emilie Devijver

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

Machine Learning · Statistics 2016-11-17 Mohammad Hossein Rohban , Prakash Ishwar , Birant Orten , William C. Karl , Venkatesh Saligrama

Suppose that we are given independent, identically distributed samples $x_l$ from a mixture $\mu$ of no more than $k$ of $d$-dimensional spherical gaussian distributions $\mu_i$ with variance $1$, such that the minimum $\ell_2$ distance…

Data Structures and Algorithms · Computer Science 2025-09-10 Somnath Chakraborty , Hariharan Narayanan

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…

Optimization and Control · Mathematics 2025-11-24 Shibshankar Dey , Sanjay Mehrotra , Anirudh Subramanyam

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

Statistics Theory · Mathematics 2023-02-20 Luca Pesce , Florent Krzakala , Bruno Loureiro , Ludovic Stephan

This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a…

Statistics Theory · Mathematics 2011-08-18 John T. Flam , Saikat Chatterjee , Kimmo Kansanen , Torbjorn Ekman

The clustering algorithms that view each object data as a single sample drawn from a certain distribution, Gaussian distribution, for example, has been a hot topic for decades. Many clustering algorithms: such as k-means and spectral…

Machine Learning · Computer Science 2019-10-25 Xiang Wang , Tie Liu

This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…

Data Structures and Algorithms · Computer Science 2021-07-27 Allen Liu , Ankur Moitra

Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…

Methodology · Statistics 2009-04-21 Heng Lian

This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a…

Statistics Theory · Mathematics 2015-06-04 Zongming Ma , Yihong Wu

Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…

Optimization and Control · Mathematics 2025-10-08 Anna Livia Croella , Veronica Piccialli , Antonio M. Sudoso

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…

Methodology · Statistics 2014-10-29 Ye Wang , Antonio Canale , David Dunson

We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $\mathbb{R}^d$. Specifically, we investigate the requisite minimal distance $\Delta$ between mean vectors to partially…

Statistics Theory · Mathematics 2026-02-27 Alexandra Carpentier , Nicolas Verzelen

We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…

Information Theory · Computer Science 2023-02-28 Marat V. Burnashev

Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…

Machine Learning · Statistics 2025-01-23 Takashi Furuya , Hiroyuki Kusumoto , Koichi Taniguchi , Naoya Kanno , Kazuma Suetake

Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity…

Machine Learning · Computer Science 2019-10-22 Shuai Yang , Wenqi Zhu , Yuesheng Zhu

Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…

Methodology · Statistics 2012-01-30 Alberto Cozzini , Ajay Jasra , Giovanni Montana