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利用局部球面高效逼近流形AI 解读

Abstract In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most of the literature relies on linear or locally linear approximations. In this article, we propose a simple and general alternative, which instead uses…

利用 Fisher–Gaussian 核估计具有非线性支撑的密度AI 解读

Summary Current tools for multivariate density estimation struggle when the density is concentrated near a non-linear subspace or manifold. Most approaches require the choice of a kernel, with the multivariate Gaussian kernel by far the most commonly used. Although heavy-tailed and skewed extensions have been proposed, such kernels cannot capture curvature in the support of the data. This leads to poor performance unless the sample size is very large relative to the…

面向高维特征预测的定向随机投影AI 解读

Minerva Mukhopadhyaya & David B. Dunsonb Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India Department of Statistical Science, Duke University, Durham, NC Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA. Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA. CONTACT Minerva Mukhopadhyay minervam@iitk.ac.in Department of…