标题： 异质性调整及其在图模型推理中的应用 显示英文标题

标题： Heterogeneity Adjustment with Applications to Graphical Model Inference

摘要： 异质性是在分析来自多个来源的聚合数据集时的一种不需要的变化。尽管已经提出了不同的异质性调整方法，但没有系统性的理论可以证明这些方法的有效性。在这项工作中，我们提出了一种通用框架，称为ALPHA（Adaptive Low-rank Principal Heterogeneity Adjustment的缩写），用于从原始数据建模、估计和调整异质性。一旦异质性被调整，我们就可以通过从多个来源聚合同质残差来消除批次效应的偏差并增强推断能力。在假设潜在的异质性因素同时影响大量观察变量的一个普遍假设下，我们提供了严格的理论来证明所提出的框架。我们的框架还允许结合信息性协变量，并利用“维度的祝福”。作为一个通用框架的说明性应用，我们考虑了一个基于多个数据集进行图模型推理的高维精度矩阵估计问题。我们还通过对合成数据集和脑成像数据集进行彻底的数值研究，展示了所开发的理论和方法的有效性。 显示英文摘要

摘要： Heterogeneity is an unwanted variation when analyzing aggregated datasets from multiple sources. Though different methods have been proposed for heterogeneity adjustment, no systematic theory exists to justify these methods. In this work, we propose a generic framework named ALPHA (short for Adaptive Low-rank Principal Heterogeneity Adjustment) to model, estimate, and adjust heterogeneity from the original data. Once the heterogeneity is adjusted, we are able to remove the biases of batch effects and to enhance the inferential power by aggregating the homogeneous residuals from multiple sources. Under a pervasive assumption that the latent heterogeneity factors simultaneously affect a large fraction of observed variables, we provide a rigorous theory to justify the proposed framework. Our framework also allows the incorporation of informative covariates and appeals to the "Bless of Dimensionality". As an illustrative application of this generic framework, we consider a problem of estimating high-dimensional precision matrix for graphical model inference based on multiple datasets. We also provide thorough numerical studies on both synthetic datasets and a brain imaging dataset to demonstrate the efficacy of the developed theory and methods.