Robust Offline Active Learning on Graphs

We consider the problem of active learning on graphs, which has crucial applications in many real-world networks where labeling node responses is expensive. In this paper, we propose an offline active learning method that selects nodes to query by explicitly incorporating information from both the network structure and node covariates. Building on graph signal recovery theories and the random spectral sparsification technique, the proposed method adopts a two-stage biased sampling strategy that takes both informativeness and representativeness into consideration for node querying. Informativeness refers to the complexity of graph signals that are learnable from the responses of queried nodes, while representativeness refers to the capacity of queried nodes to control generalization errors given noisy node-level information. We establish a theoretical relationship between generalization error and the number of nodes selected by the proposed method. Our theoretical results demonstrate the trade-off between informativeness and representativeness in active learning. Extensive numerical experiments show that the proposed method is competitive with existing graph-based active learning methods, especially when node covariates and responses contain noises. Additionally, the proposed method is applicable to both regression and classification tasks on graphs.