Neural Net Learning for Graph Data

图结构是在社会学、经济学、公共卫生、计算机科学、神经科学等领域中自然出现的特殊数据类型。在这个项目中，我们开发了一种创新的图神经网络架构，它在理论上是合理的，计算效率高，数字上优越，并且适用于各种图结构。该开发将结合图嵌入，依赖性测试和卷积神经网络的许多最新进展。该项目将显著推进图神经网络的理论基础，为数据科学家提供可扩展和更好的图学习，并在许多基于图的应用中加速发现。该项目还为研究生提供研究培训机会。在该项目中，pi将从图邻接开始，并研究频谱嵌入，标准神经网络和新型图卷积神经网络之间的区别。然后，pi计划证明在某些图模型下，图卷积层在监督学习中可以是渐近贝叶斯最优的。当图数据与节点属性进一步耦合时，pi通过距离相关筛选层开发出属性神经网络架构。该项目旨在证明其在节点属性存在下的渐近最优性，研究图邻接性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与现有最先进方法的优越性能。此外，该项目对算法进行了线性时间计算复杂度的设计，使其在大数据和稀疏图上具有高效和可扩展性。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.