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高维线性回归中的残差重要性加权迁移学习AI 解读

Transfer learning is an emerging paradigm for leveraging multiple sources to improve the statistical inference on a single target. In this paper, we propose a novel approach named residual importance weighted transfer learning (RIW-TL) for high-dimensional linear models built on penalized likelihood. Compared to existing methods such as Trans-Lasso that selects sources in an (approximately) all-in-or-all-out manner, RIW-TL includes samples via importance weighting and thus…

高斯图模型中的枢纽节点检测AI 解读

Graphical models are popular tools for exploring relationships among a set of variables. The Gaussian graphical model (GGM) is an important class of graphical models, where the conditional dependence among variables is represented by nodes and edges in a graph. In many real applications, we are interested in detecting hubs in graphical models, which refer to nodes with a significant higher degree of connectivity compared to non-hub nodes. A typical strategy for hub detection…

网络的分组稀疏 β 模型AI 解读

Sparsity, homogeneity, and heterogeneity are three important characteristics of many real-life networks. The recently proposed Sparse β-Model divides nodes into core ones and peripheral ones to accommodate sparsity, but the parameters of core nodes are assumed to be of similar magnitude, which may not be in line with applications. In this article, we propose the Group Sparse β-Model that splits the core nodes into groups and assumes different orders of magnitude of…

离散化的近似误差及其应用AI 解读

Converting a continuous variable into a discrete one is a commonly used technique for solving various problems in both statistics and machine learning. It is well known that discretizations result in biases. However, this issue has not been studied systematically. In this paper, a general framework is proposed to understand and compare the approximation errors of different slicing strategies. Poincaré-type inequalities are first established for univariate discretizations and…

高维线性模型中线性泛函的估计：从稀疏到非稀疏AI 解读

can be sparse or non-sparse and predictors can be strongly or weakly correlated. The proposed method is simple for implementation. Numerical and theoretical results demonstrate the competitive advantages of the proposed method for a wide range of problems.

网络数据中协变量的降维AI 解读

Summary A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach, called network-supervised dimension reduction, in which covariates are projected onto low-dimensional spaces to reveal the linkage pattern without assuming a model. We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer…

高维回归空间中的多重影响点检测AI 解读

Summary Influence diagnosis is an integrated component of data analysis but has been severely underinvestigated in a high dimensional regression setting. One of the key challenges, even in a fixed dimensional setting, is how to deal with multiple influential points that give rise to masking and swamping effects. The paper proposes a novel group deletion procedure referred to as multiple influential point detection by studying two extreme statistics based on a…

高维影响度量AI 解读

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the…