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超高维数据的无模型特征筛选AI 解读

With the recent explosion of scientific data of unprecedented size and complexity, feature ranking and screening are playing an increasingly important role in many scientific studies. In this article, we propose a novel feature screening procedure under a unified model framework, which covers a wide variety of commonly used parametric and semiparametric models. The new method does not require imposing a specific model structure on regression functions, and thus is…

通过累积切片估计实现回归充分降维AI 解读

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p=O(n1 / 2 / log n) and the asymptotic normality for p=o(n1 / 2) are established, where p is the dimension of the predictors and n…

预测变量数量增长且高度相关时的分布加权偏最小二乘AI 解读

Summary Because highly correlated data arise from many scientific fields, we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. For this, we first develop a distribution-weighted least squares estimator that can recover directions in the central subspace, then use the distribution-weighted least squares estimator as a seed vector and project it onto a Krylov space by partial least squares to…