Imputing Sparse and Noisy Labels for GNNs

This paper studies how to impute labels in training data of GNNs for node classification. We introduce Label Boosting Rules (LBRs), which extend graded bisimilarity and embed ML labeling models as predicates. With LBRs, we show how to (a) assign labels to unlabeled nodes via graded bisimilarity, which is at least as expressive as node-classification GNNs; (b) correct the labels of mislabeled nodes by both logic reasoning and ML prediction; (c) improve the accuracy of ML label cleaning with logic conditions; and (d) leverage the interaction of (a) and (b) to improve the overall labeling quality. We develop an algorithm to recursively rectify noisy labels and enhance sparse labels in a unified process; we show that the algorithm is Church-Rosser, tractable and parallelly scalable. We empirically verify that the method improves the accuracy of GNNs by 14.4% on average, up to 18.2%, and it scales with large graphs.