基于邻域选择的矩阵型数据图估计
Graph Estimation Based on Neighborhood Selection for Matrix-variate Data
AI总结：
针对矩阵型数据，提出基于回归和邻域选择的图估计方法，利用偏相关与回归系数关系及原始-对偶见证技术，实现高概率精确恢复边集，并在模拟和EEG数据上验证。
摘要：
无向图模型是揭示高维变量间复杂关系的强大工具。本文旨在当数据自然呈现矩阵形式（如时间多变量数据）时，完全恢复无向图模型的结构。由于传统的向量型分析在处理此类矩阵结构数据时存在明显局限性，已有多种方法被提出，大多依赖于具有可分离协方差结构的高斯分布似然。尽管其中一些方法提供了针对假阳性包含（即所有识别出的边均存在于真实图中）的理论保证，但它们可能面临关键限制：（1）无法检测重要的真实边，或（2）依赖于尚未验证的估计量条件。我们提出了一种基于回归的新型矩阵图模型估计方法，该方法基于偏相关系数与回归系数之间的关系。采用回归框架中的原始-对偶见证技术，我们推导出边集精确恢复的非渐近不等式。在适当的正则条件下，我们的方法能够以高概率一致地识别真实边集。通过模拟研究，我们将所提方法的支持恢复性能与现有替代方法进行比较。我们还将该方法应用于脑电图（EEG）数据集，以估计64个电极之间的空间脑网络以及256个时间点之间的时间网络。
英文摘要：
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form, such as temporal multivariate data. As conventional vector-variate analyses have clear limitations in handling such matrix-structured data, several approaches have been proposed, mostly relying on the likelihood of the Gaussian distribution with a separable covariance structure. Although some of these methods provide theoretical guarantees against false inclusions (i.e. all identified edges exist in the true graph), they may suffer from crucial limitations: (1) failure to detect important true edges, or (2) dependency on conditions for the estimators that have not been verified. We propose a novel regression-based method for estimating matrix graphical models, based on the relationship between partial correlations and regression coefficients. Adopting the primal-dual witness technique from the regression framework, we derive a non-asymptotic inequality for exact recovery of an edge set. Under suitable regularity conditions, our method consistently identifies the true edge set with high probability. Through simulation studies, we compare the support recovery performance of the proposed method against existing alternatives. We also apply our method to an electroencephalography (EEG) dataset to estimate both the spatial brain network among 64 electrodes and the temporal network across 256 time points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
