Geometric Deep Learning is an emerging paradigm to process graph-structured data with end-to-end trainable models, Graph Neural Networks (GNNs), with the ability to leverage prior knowledge about the data domain while offering large expressive power. Such attractive tradeoff has resulted in state-of-the-art performance over diverse domains, ranging from social networks, biology, knowledge bases, or finance. In this talk, I will present recent advances in our group covering both theory and applications. On the theory side, we quantify both the approximation power of GNN architectures and their stability to graph perturbations, resulting in a principled architecture design. We will illustrate these theoretical advances with applications in semi-supervised learning and forecasting in dynamic graphs modeling Social Network data, and discuss broader applications to recommender systems and fraud detection.
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