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高维数据整合中的最优网络引导协变量选择AI 解读

Modern data often arise with multiple modalities. For example, covariates and a network are observed on the same subjects, and both contain useful information. Effectively integrating these modalities is important and challenging, especially when the response is unavailable. We study the fundamental covariate selection problem for high-dimensional data by leveraging network information.We propose the Network-Guided Covariate Selection (NGCS) algorithm. NGCS exploits the…

高维线性模型中遗传关联性的最优估计AI 解读

Estimating the genetic relatedness between two traits based on the genome-wide association data is an important problem in genetics research. In the framework of high-dimensional linear models, we introduce two measures of genetic relatedness and develop optimal estimators for them. One is genetic covariance, which is defined to be the inner product of the two regression vectors, and another is genetic correlation, which is a normalized inner product by their lengths. We…

高维聚类及相关问题的相变AI 解读

Consider a two-class clustering problem where we observe $X_{i}=\ell_{i}\mu+Z_{i}$, $Z_{i}\stackrel{\mathit{i.i.d.}}{\sim}N(0,I_{p})$, $1\leq i\leq n$. The feature vector $\mu\in R^{p}$ is unknown but is presumably sparse. The class labels $\ell_{i}\in\{-1,1\}$ are also unknown and the main interest is to estimate them. We are interested in the statistical limits. In the two-dimensional phase space calibrating the rarity and strengths of useful features, we find the precise…

高维聚类中的重要特征主成分分析AI 解读

We consider a clustering problem where we observe feature vectors $X_{i}\in R^{p}$, $i=1,2,\ldots,n$, from $K$ possible classes. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the modern regime of $p\gg n$, where classical clustering methods face challenges. We propose Influential Features PCA (IF-PCA) as a new clustering procedure. In IF-PCA, we select a small fraction of features with the largest Kolmogorov–Smirnov…