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二阶稀疏充分降维及其在二次判别分析中的应用AI 解读

Motivated by exploratory data analysis, sufficient dimension reduction (SDR) methods, especially inverse regression methods such as sliced inverse regression (SIR) and sliced averaged variance estimation (SAVE), have been central to multivariate analysis for more than three decades. Despite their popularity, the extension of these methods to high-dimensional settings remains challenging. This paper addresses the computational and theoretical limitations of the less explored…

通过广义 Dantzig 选择器构建可解释的标量对图像线性回归AI 解读

The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness constraints to control the bias-variance trade-off, and thus prevent overfitting. However, such assumptions can hinder interpretability, especially when only certain regions of an image influence changes in the response. In such a scenario,…

通过正则化进行高维二次回归模型选择AI 解读

Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects and interaction effects. Existing regularization methods generally achieve this goal by solving complex optimization problems, which usually demands high computational cost and hence are not feasible for high-dimensional data. This article…

通过旋转使 Fisher 线性判别稀疏化AI 解读

Summary Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis. To use them efficiently, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications, and rotations of data are required to create the sparsity needed. We propose a family of rotations to create the sparsity required. The basic idea is to use the principal components of the sample…

超高维数据的交互项筛选AI 解读

In ultrahigh-dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice is computational feasibility. For a dataset with n observations and p predictors, the augmented design matrix including all linear and order-2 terms is of size n × (p2 + 3p)/2. When p is large, say more than tens of hundreds, the number of interactions is enormous and beyond the capacity of standard machines and software tools for…

超高维回归中基于重拟合交叉验证的方差估计AI 解读

Summary Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality is much larger than the sample size, traditional variance estimation techniques are not applicable. Recent advances in variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved…