Predicting properties of nodes in a graph is an important problem with applications in a variety of domains. Graph-based Semi Supervised Learning (SSL) methods aim to address this problem by labeling a small subset of the nodes as seeds, and then utilizing the graph structure to predict label scores for the rest of the nodes in the graph. Recently, Graph Convolutional Networks (GCNs) have achieved impressive performance on the graph-based SSL task. In addition to label scores, it is also desirable to have a confidence score associated with them. Unfortunately, confidence estimation in the context of GCN has not been previously explored. We fill this important gap in this paper and propose ConfGCN, which estimates labels scores along with their confidences jointly in GCN-based setting. ConfGCN uses these estimated confidences to determine the influence of one node on another during neighborhood aggregation, thereby acquiring anisotropic capabilities. Through extensive analysis and experiments on standard benchmarks, we find that ConfGCN is able to significantly outperform state-of-the-art baselines. We have made ConfGCN’s source code available to encourage reproducible research. Graphs are all around us, ranging from citation and social networks to knowledge graphs. Predicting properties of nodes in such graphs is often desirable. For example, given a citation network, we may want to predict the research area of an author. Making such predictions, especially in the semisupervised setting, has been the focus of graph-based semi-supervised learning (SSL) BID25 . In graph-based SSL, a small set of nodes are initially labeled. Starting with such supervision and while utilizing the rest of the graph structure, the initially unlabeled nodes are labeled. Conventionally, the graph structure has been incorporated as an explicit regularizer which enforces a smoothness constraint on the labels estimated on nodes BID36 BID2 BID31 . Recently proposed Graph Convolutional Networks (GCN) BID8 BID14 provide a framework to apply deep neural networks to graphstructured data. GCNs have been employed successfully for improving performance on tasks such as semantic role labeling , machine translation BID1 , relation extraction BID28 BID35 , event extraction BID20 , shape segmentation BID34 , and action recognition BID12 . GCN formulations for graph-based SSL have also attained state-of-the-art performance BID14 BID18 BID29 . In this paper, we also focus on the task of graphbased SSL using GCNs.GCN iteratively estimates embedding of nodes in the graph by aggregating embeddings of neighborhood nodes, while backpropagating errors from a target loss function. Finally, the learned node embeddings are used to estimate label scores on the nodes. In addition to the label scores, it is desirable to also have confidence estimates associated with them. Such confidence scores may be used to determine how much to trust the label scores estimated on a given node. While methods to estimate label score confidence in non-deep graph-based SSL has been previously proposed BID21 , confidence-based GCN is still unexplored. Figure 1: Label prediction on node a by Kipf-GCN and ConfGCN (this paper). L 0 is a's true label. Shade intensity of a node reflects the estimated score of label L 1 assigned to that node. Since Kipf-GCN is not capable of estimating influence of one node on another, it is misled by the dominant label L 1 in node a's neighborhood and thereby making the wrong assignment. ConfGCN, on the other hand, estimates confidences (shown by bars) over the label scores, and uses them to increase influence of nodes b and c to estimate the right label on a. Please see Section 1 for details. In this paper we present ConfGCN, a confidence based Graph Convolutional Network which estimates label scores along with their confidences jointly in GCN-based setting. In ConfGCN, the influence of one node on another during aggregation is determined using the estimated confidences and label scores, thus inducing anisotropic behavior to GCN. We demonstrate the effectiveness of ConfGCN against recent methods for semi-supervised node classification task and analyze its performance in different settings. We make ConfGCN's source code available.
We propose a confidence based Graph Convolutional Network for Semi-Supervised Learning.
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