标题： 半监督学习中的最优精确恢复：谱方法与图卷积网络的研究 显示英文标题

标题： Optimal Exact Recovery in Semi-Supervised Learning: A Study of Spectral Methods and Graph Convolutional Networks

摘要： 我们深入研究了在Contextual Stochastic Block Model (CSBM)数据集上半监督节点分类的挑战。 在这里，来自两聚类Stochastic Block Model (SBM)的节点与特征向量耦合在一起，这些特征向量来源于一个高斯混合模型（GMM），该模型对应于它们各自的节点标签。 由于只能使用CSBM节点标签的一小部分用于训练，我们的主要目标是准确地对剩余的节点进行分类。 进入归纳学习领域，我们首次指出了CSBM中所有测试节点精确恢复的信息论阈值。 同时，我们设计了一种基于主成分分析（PCA）的最优谱估计器，该估计器结合了训练标签以及邻接矩阵和特征向量中的关键数据。 我们还评估了图岭回归和Graph Convolutional Networks (GCN)在这个合成数据集上的有效性。 我们的研究结果表明，当使用最优加权自循环时，图岭回归和GCN有能力以接近最优估计器的方式达到精确恢复的信息论阈值。 这突显了特征学习在增强GCN能力方面的潜在作用，特别是在半监督学习领域。 显示英文摘要

摘要： We delve into the challenge of semi-supervised node classification on the Contextual Stochastic Block Model (CSBM) dataset. Here, nodes from the two-cluster Stochastic Block Model (SBM) are coupled with feature vectors, which are derived from a Gaussian Mixture Model (GMM) that corresponds to their respective node labels. With only a subset of the CSBM node labels accessible for training, our primary objective becomes the accurate classification of the remaining nodes. Venturing into the transductive learning landscape, we, for the first time, pinpoint the information-theoretical threshold for the exact recovery of all test nodes in CSBM. Concurrently, we design an optimal spectral estimator inspired by Principal Component Analysis (PCA) with the training labels and essential data from both the adjacency matrix and feature vectors. We also evaluate the efficacy of graph ridge regression and Graph Convolutional Networks (GCN) on this synthetic dataset. Our findings underscore that graph ridge regression and GCN possess the ability to achieve the information threshold of exact recovery in a manner akin to the optimal estimator when using the optimal weighted self-loops. This highlights the potential role of feature learning in augmenting the proficiency of GCN, especially in the realm of semi-supervised learning.