Graph attention networks (GATs) are widely used and often appear robust to noise in node covariates and edges, yet rigorous statistical guarantees demonstrating a provable advantage of GATs over non-attention graph neural networks~(GNNs) are scarce. We partially address this gap for node regression with graph-based errors-in-variables models under simultaneous covariate and edge corruption: responses are generated from latent node-level covariates, but only noise-perturbed versions of the latent covariates are observed; and the sample graph is a random geometric graph created from the node covariates but contaminated by independent Erdős--Rényi edges. We propose and analyze a carefully designed, task-specific GAT that constructs denoised proxy features for regression. We prove that regressing the response variables on the proxies achieves lower error asymptotically in (a) estimating the regression coefficient compared to the ordinary least squares (OLS) estimator on the noisy node covariates, and (b) predicting the response for an unlabelled node compared to a vanilla graph convolutional network~(GCN) -- under mild growth conditions. Our analysis leverages high-dimensional geometric tail bounds and concentration for neighbourhood counts and sample covariances. We verify our theoretical findings through experiments on synthetically generated data. We also perform experiments on real-world graphs and demonstrate the effectiveness of the attention mechanism in several node regression tasks.

翻译：图注意力网络（GATs）被广泛使用，且通常对节点协变量和边中的噪声表现出鲁棒性，但能够证明GAT相对于非注意力图神经网络（GNNs）具有可证优势的严格统计保证仍然稀缺。本文针对基于图的变量误差模型在协变量与边同时污染下的节点回归问题，部分填补了这一空白：响应变量由潜在的节点级协变量生成，但观测到的仅是潜在协变量的噪声扰动版本；样本图是由节点协变量生成的随机几何图，但受到独立Erdős--Rényi边的污染。我们提出并分析了一个精心设计的、任务特定的GAT，该网络为回归构建去噪代理特征。我们证明，在温和的增长条件下，基于代理特征对响应变量进行回归，在以下方面渐近地实现了更低误差：（a）与基于噪声节点协变量的普通最小二乘（OLS）估计量相比，在回归系数估计上；（b）与普通图卷积网络（GCN）相比，在未标记节点的响应预测上。我们的分析利用了邻域计数和样本协方差的高维几何尾界和集中性。我们通过在合成生成数据上的实验验证了理论发现。我们还在真实世界图上进行了实验，并在多个节点回归任务中证明了注意力机制的有效性。