Learning to quantify graph nodes

Network Quantification is the problem of estimating the class proportions in unlabeled subsets of graph nodes. When prior probability shift is at play, this task cannot be effectively addressed by first classifying the nodes and then counting the class predictions. In addition, unlike non-relational quantification on i.i.d. datapoints, Network Quantification demands enhanced flexibility to capture a broad range of connectivity patterns, resilience to the challenge of heterophily, and efficiency to scale to larger networks. To meet these stringent requirements we introduce XNQ, a novel method that synergizes the flexibility and efficiency of the unsupervised node embeddings computed by randomized recursive Graph Neural Networks, with an Expectation-Maximization algorithm that provides a robust quantification-aware adjustment to the output probabilities of a calibrated node classifier. We validate the design choices underpinning our method through comprehensive ablation experiments. In an extensive evaluation, we find that our approach consistently and significantly improves on the best Network Quantification methods to date, thereby setting the new state of the art for this challenging task. Simultaneously, it provides a training speed-up of up to 10x-100x over other graph learning based methods.