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稀疏正则化多边际最优传输与重心的中心极限定理及自助法AI 解读

Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimensionality, making regularization essential in many applications. While regularized optimal transport methods are widely used, approaches based on entropic…

高维依赖数据的中心极限定理AI 解读

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles, simple convex sets and sparsely convex sets. We investigate the quantitative effect of temporal dependence on the rates of convergence to a Gaussian random vector over three different dependency frameworks ($α$-mixing, $m$-dependent, and…