Graph convolutional networks (GCNs) are powerful deep neural networks for graph-structured data. However, GCN computes the representation of a node recursively from its neighbors, making the receptive field size grow exponentially with the number of layers. Previous attempts on reducing the receptive field size by subsampling neighbors do not have convergence guarantee, and their receptive field size per node is still in the order of hundreds. In this paper, we develop control variate based algorithms with new theoretical guarantee to converge to a local optimum of GCN regardless of the neighbor sampling size.Empirical results show that our algorithms enjoy similar convergence rate and model quality with the exact algorithm using only two neighbors per node. The running time of our algorithms on a large Reddit dataset is only one seventh of previous neighbor sampling algorithms.

Recent deep learning approaches for representation learning on graphs follow a neighborhood aggregation procedure. We analyze some important properties of these models, and propose a strategy to overcome those. In particular, the range of "neighboring" nodes that a node's representation draws from strongly depends on the graph structure, analogous to the spread of a random walk. To adapt to local neighborhood properties and tasks, we explore an architecture -- jumping knowledge (JK) networks -- that flexibly leverages, for each node, different neighborhood ranges to enable better structure-aware representation. In a number of experiments on social, bioinformatics and citation networks, we demonstrate that our model achieves state-of-the-art performance. Furthermore, combining the JK framework with models like Graph Convolutional Networks, GraphSAGE and Graph Attention Networks consistently improves those models' performance.

In this paper we advocate for a hyperparametric approach to learn diffusion in the independent cascade (IC) model. The sample complexity of this model is a function of the number of edges in the network and consequently learning becomes infeasible when the network is large. We study a natural restriction of the hypothesis class using additional information available in order to dramatically reduce the sample complexity of the learning process. In particular we assume that diffusion probabilities can be described as a function of a global hyperparameter and features of the individuals in the network. One of the main challenges with this approach is that training a model reduces to optimizing a non-convex objective. Despite this obstacle, we can shrink the best-known sample complexity bound for learning IC by a factor of |E|/d where |E| is the number of edges in the graph and d is the dimension of the hyperparameter. We show that under mild assumptions about the distribution generating the samples one can provably train a model with low generalization error. Finally, we use large-scale diffusion data from Facebook to show that a hyperparametric model using approximately 20 features per node achieves remarkably high accuracy.

The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) seems like a natural solution; however, current implementations of CP on standard Knowledge Base Completion benchmarks are lagging behind their competitors. In this work, we attempt to understand the limits of CP for knowledge base completion. First, we motivate and test a novel regularizer, based on tensor nuclear p-norms. Then, we present a reformulation of the problem that makes it invariant to arbitrary choices in the inclusion of predicates or their reciprocals in the dataset. These two methods combined allow us to beat the current state of the art on several datasets with a CP decomposition, and obtain even better results using the more advanced ComplEx model.