网络关联数据上异质图模型的非参数学习
Nonparametric learning of heterogeneous graphical model on network-linked data
AI总结：
本文针对网络关联数据提出一种无需分布假设的非参数异质图模型，结合网络嵌入与再生核希尔伯特空间方法将图学习转化为线性方程组求解，并给出理论保证与实验验证。
摘要：
图模型已被广泛用于刻画多元数据中的条件独立结构，但这类模型通常建立在独立同分布观测之上，限制了其对网络关联数据等复杂数据集的适用性。本文提出一种非参数图模型，通过容纳异质图结构且不施加任何特定分布假设来克服上述局限。所提估计方法有效结合了网络嵌入与非参数图模型估计，并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，本文从估计一致性和异质图结构的精确恢复两方面为所提方法建立了理论保证。通过多种模拟示例以及对统计学家合著者数据集的真实应用，也验证了该方法的有效性。
英文摘要：
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.
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。
