Abstract
An abundance of neural network models and algorithms for diverse tasks on graphs have been developed in the past five years. However, very few provable guarantees have been available for the performance of graph neural network models. In this paper we present the first provable guarantees for one of the best-studied families of graph neural network models, Graph Convolutional Networks (GCNs), for semi-supervised community detection tasks. We show that with high probability over the initialization and training data, a GCN will efficiently learn to detect communities on graphs drawn from a stochastic block model.The thesis starts with general introduction to machine learning and machine learning on graphs, in particular graph neural network models. Then we introduce PAC learning framework, which is a mathematical framework to analyze the performance of a machine learning model. Afterwards, we present a detailed description of stochastic block model and Graph Convolutional Networks, then the main results on learning guarantee. We demonstrate the idea of our proof before giving the detailed proofs. Our proof relies on a fine-grained analysis of the training dynamics in order to overcome the complexity of a non-convex optimization landscape with many poorly-performing local minima. We also show some experimental results and visualization to verify our results.