arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
By Somnath Chakraborty, Hariharan Narayanan
arXiv:2603.19657v2 Announce Type: replace-cross
Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
By Xinyu Liu, Hai Zhang
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
By Manuel Fernandez V, Yizhe Zhu
arXiv:2401. 10927v3 Announce Type: replace-cross Abstract: In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$.
By Shuheng Zhou
arXiv:2607. 01993v1 Announce Type: cross Abstract: The silhouette is one of the most widely used measures to assess the quality of a $k$-clustering of a dataset of $n$ elements.
By Ilie Sarpe, Federico Altieri, Andrea Pietracaprina, Geppino Pucci, Fabio Vandin
arXiv:2608.21466v1 Announce Type: new
Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...
By Michael C. H. Choi, Youjia Wang
arXiv:2608. 14215v1 Announce Type: new Abstract: Constrained optimization extends classical optimization by integrating side information, making it widely applicable across scientific and engineering domains.
By Johanna Hillebrand, Jan H\"ockendorff, J\"urgen Kusche, Kelin Luo, Heiko R\"oglin, Melanie Schmidt, Christian Sohler, Bernd Uebbing
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
By Sre\'cko {\DJ}ura\v{s}inovi\'c, Jean-Bernard Lasserre, Victor Magron
arXiv:2610. 01088v1 Announce Type: cross Abstract: The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions.
By Hansheng Jiang
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
By Yuga Iguchi, Paul Fearnhead
arXiv:2411. 01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al.
By Maximilian Fleissner, Maedeh Zarvandi, Debarghya Ghoshdastidar
arXiv:2609. 30477v1 Announce Type: cross Abstract: Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential.
By Yordan P. Raykov, Max A. Little