Neural Net Learning for Graph Data

Graph structures are special data types that arise naturally in sociology, economics, public health, computer science, neuroscience, among other areas. In this project, we develop an innovative graph neural network architecture that is theoretically sound, computationally efficient, numerically superior, and versatile for a variety of graph structures.

The development will incorporate many recent advances in graph embedding, dependence testing, and convolutional neural network. This project will significantly advance the theoretical foundation of graph neural networks, enable scalable and better graph learning for data scientists, and is uniquely poised to accelerate discoveries in a many graph-based applications. The project also provides research training opportunities for graduate students.

In the project, the PIs will start with graph adjacency, and investigate the difference among spectral embedding, standard neural network, and a novel graph convolutional neural network. Then the PIs plan to prove that under certain graph models, the graph convolutional layer can be asymptotically Bayes optimal in supervised learning. When the graph data is further coupled with node attributes, the PIs develop an attributed neural network architecture via a distance correlation screening layer.

The project aims to prove its asymptotic optimality in the presence of node attributes, investigate the relationship between graph adjacency and node attributes to enable better machine learning, and demonstrate its superior performance against existing state-of-the-art methods in simulations and real data. Moreover, the project designs the algorithm in linear-time computation complexity, making it efficient and scalable to big data and sparse graphs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.