标题： 网络关联数据上异质图模型的非参数学习 显示英文标题

标题： Nonparametric learning of heterogeneous graphical model on network-linked data

摘要： 图模型已被广泛用于捕捉多变量数据中的条件独立结构，这些模型通常基于独立同分布的观测数据，这限制了它们在复杂数据集（如网络链接数据）中的适用性。 本文提出了一种非参数图模型，通过适应异构图结构而不施加任何特定分布假设来解决这些限制。 所提出的估计方法有效地将网络嵌入与非参数图模型估计相结合。 它进一步利用向量值再生核希尔伯特空间的性质，将图学习任务转化为求解有限维线性方程组。 此外，从估计一致性和异构图结构的精确恢复方面建立了所提方法的理论保证。 其有效性还通过各种模拟示例和对统计学家合著数据集的真实应用得到了证明。 显示英文摘要

摘要： Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex datasets such as network-linked data. This paper proposes a nonparametric graphical model that addresses these limitations by accommodating heterogeneous graph structures without imposing any specific distributional assumptions. The proposed estimation method effectively integrates network embedding with nonparametric graphical model estimation. It further transforms the graph learning task into solving a finite-dimensional linear equation system by leveraging the properties of vector-valued reproducing kernel Hilbert space. Moreover, theoretical guarantees are established for the proposed method in terms of the estimation consistency and exact recovery of the heterogeneous graph structures. Its effectiveness is also demonstrated through a variety of simulated examples and a real application to the statistician coauthorship dataset.