Simultaneous Estimation of Connectivity and Dimensionality in Samples of Networks
提出一种方法，从多个网络样本中同时估计潜在连接概率矩阵及其嵌入维度，适用于有块模型结构的网络，并在脑网络数据中验证了实用性。
An overarching objective in contemporary statistical network analysis is extracting salient information from datasets consisting of multiple networks. To date, considerable attention has been devoted to node and network clustering, while comparatively less attention has been devoted to downstream connectivity estimation and parsimonious embedding dimension selection. Given a sample of potentially heterogeneous networks, this paper proposes a method to simultaneously estimate a latent matrix of connectivity probabilities and its embedding dimensionality or rank after first pre-estimating the number of communities and the node community memberships. The method is formulated as a convex optimization problem and solved using an alternating direction method of multipliers algorithm. We establish estimation error bounds under the Frobenius norm and nuclear norm for settings in which observable networks have blockmodel structure, even when node memberships are imperfectly recovered. When perfect membership recovery is possible and dimensionality is much smaller than the number of communities, the proposed method outperforms conventional averaging-based methods for estimating connectivity and dimensionality. Numerical studies empirically demonstrate the accuracy of our method across various scenarios. Additionally, analysis of a primate brain dataset demonstrates that posited connectivity is not necessarily full rank in practice, illustrating the need for flexible methodology.