Related papers: Minimax Theory for High-dimensional Gaussian Mixtu…
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…
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…
Sparse feature selection is necessary when we fit statistical models, we have access to a large group of features, don't know which are relevant, but assume that most are not. Alternatively, when the number of features is larger than the…
The semantic segmentation task aims at dense classification at the pixel-wise level. Deep models exhibited progress in tackling this task. However, one remaining problem with these approaches is the loss of spatial precision, often produced…
We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent…
We consider clustering based on significance tests for Gaussian Mixture Models (GMMs). Our starting point is the SigClust method developed by Liu et al. (2008), which introduces a test based on the k-means objective (with k = 2) to decide…
In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a classification problem, this transformation induces complete separation among the associated Gaussian…
This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
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…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…
We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of…
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
We investigate the existence of a fundamental computation-information gap for the problem of clustering a mixture of isotropic Gaussian in the high-dimensional regime, where the ambient dimension $p$ is larger than the number $n$ of points.…
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…
Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…