Neural Net Learning for Graph Data

图结构是社会学、经济学、公共卫生、计算机科学、神经科学等领域中自然产生的特殊数据类型。在这个项目中，我们开发了一种创新的图神经网络体系结构，该体系结构在理论上是合理的，计算效率高，数值上优越，并且对各种图结构具有通用性。这一发展将包括在图形嵌入、相关性测试和卷积神经网络方面的许多最新进展。该项目将极大地推进图形神经网络的理论基础，使数据科学家能够更好地进行可伸缩的图形学习，并有望加速许多基于图形的应用程序的发现。该项目还为研究生提供了研究培训机会。在这个项目中，PI将从图的邻接关系入手，研究谱嵌入、标准神经网络和一种新型的图卷积神经网络之间的差异。然后，PI计划证明在某些图模型下，在监督学习中，图卷积层可以是渐近贝叶斯最优的。当图形数据进一步与节点属性耦合时，PI通过距离相关筛选层来开发属性神经网络结构。该项目的目的是在存在节点属性的情况下证明其渐近最优性，研究图邻接和节点属性之间的关系以实现更好的机器学习，并在模拟和真实数据中展示其相对于现有最先进方法的优越性能。此外，该项目以线性时间计算复杂性设计了该算法，使其高效且可扩展到大数据和稀疏图形。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.