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基于 Hellinger 积分的降维方法AI 解读

Sufficient dimension reduction is a useful tool for studying the dependence between a response and a multi-dimensional predictor. In this article, a new formulation is proposed that is based on the Hellinger integral of order two, introduced as a natural measure of the regression information contained in the predictor subspace. The response may be either continuous or discrete. We establish links between local and global central subspaces, and propose an efficient local…

以最小调整实现向量正交化AI 解读

Two transformations are proposed that give orthogonal components with a one-to-one correspondence between the original vectors and the components. The aim is that each component should be close to the vector with which it is paired, orthogonality imposing a constraint. The transformations lead to a variety of new statistical methods, including a unified approach to the identification and diagnosis of collinearities, a method of setting prior weights for Bayesian model…