发表机构
The University of Melbourne（墨尔本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带边翻转噪声的符号图，提出谱方法进行节点标签恢复，并首次给出与图结构无关的理论保证，包括近似推断和角度偏差界，通过合成实验验证了理论。
AI 中文摘要
结构化预测是对多个标签的同时预测，广泛应用于自然语言处理和计算机视觉等各个领域。在本文中，我们研究带有边翻转噪声的符号图上的二值节点标签恢复问题，该模型由(Globerson等人，2015)引入，我们采用一种简单的谱方法，该方法从带噪声的符号邻接矩阵的主特征向量的符号中解码节点标签。我们为节点标签的近似推断开发了与图结构无关的理论保证，以及关于相对于真实节点标签的最大角度偏差的保证。通过利用矩阵集中理论和特征向量扰动分析的工具，我们推导出新的集中不等式，这些不等式明确量化了邻接矩阵的谱间隙、节点数量、度分布和噪声水平的影响。作为推论，我们将我们的通用结果与Cheeger常数联系起来，并为不同类别的图提供结果。我们进行了多次合成实验来验证我们的理论。据我们所知，我们是第一个为基于谱的方法提供理论保证的。作为我们分析的副产品，我们推导出可能具有独立意义并对其他机器学习问题有用的技术结果。
英文摘要
Structured prediction is the simultaneous prediction of multiple labels, and is widely used in various fields, such as natural language processing and computer vision. In this paper, we study binary node label recovery on signed graphs with edge-flip noise, a model introduced by (Globerson et al., 2015), via a simple spectral method that decodes node labels from the signs of the principal eigenvector of the noisy signed adjacency matrix. We develop graph structure-agnostic theoretical guarantees for approximate inference of node labels as well as guarantees for maximum angle deviation with respect to the ground truth node labels. By leveraging tools from matrix concentration theory and eigenvector perturbation analysis, we derive new concentration inequalities that explicitly quantify the effect of the spectral gap of the adjacency matrix, number of nodes, degree distribution, and noise level. As a corollary, we relate our general results to the Cheeger constant and provide results for different classes of graphs. We perform several synthetic experiments to validate our theory. To the best of our knowledge, we are the first to provide theoretical guarantees for the spectral-based approach. As a byproduct of our analysis, we derive technical results that might be of independent interest and useful for other machine learning problems.
