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用于线性与非线性充分降维的带瓶颈层集成神经网络AI 解读

We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the targets of estimation. This unified framework is achieved by a specially structured neural network—the Belted and Ensembled Neural Network (BENN)—that consists of a narrow latent layer, which we call the belt, and a family of transformations…

基于概率核嵌入的椭圆分布非参数检验AI 解读

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data dependence structure. Before applying such methods, we need to decide whether the data are elliptically distributed. Currently existing tests either focus exclusively on spherical distributions, or rely on bootstrap to determine the null…