Collaborative Research: Covariate-Driven Approaches to Network Estimation

在这个研究项目中，PI将开发新的统计方法，从科学数据中估计网络。在统计网络推理中，网络中的每个节点对应一个变量，每条边代表一个依赖关系。该项目将解决具有挑战性的场景，其中一组外部协变量可能会影响网络内节点的值或连接的强度。PI将开发新的贝叶斯建模方法，用于学习有向和无向网络及其对协变量的依赖性，包括可以处理非正态分布数据的方法，并使用有效的计算算法实现所提出的方法。PI将开发的统计模型应用于高维数据，包括功能性脑成像和微生物组分析。这项工作意义重大，因为它将在贝叶斯建模和计算中开辟新天地。该项目的更广泛影响包括软件的公共共享，研究生的培训，以及将这些方法应用于真实世界的神经成像和微生物组数据。该项目将在图形模型和协变量效应的同时估计方面开辟新天地。PI将开发一个框架，根据时间序列数据的向量自回归模型推断有向图，并将开发一种新的配方，其中协变量可能会以非线性方式影响边缘的强度。该框架将允许确定关键协变量如何调节网络关系。PI还将开发贝叶斯方法，用于同时选择无向图中的协变量和边，重点关注非高斯数据的模型。他们将使用有效的变分推理方法来实现这些模型，从而实现对现实世界应用的可扩展性。该项目在贝叶斯建模方法和用于实现高效推理的计算方法方面实现了创新。该奖项反映了NSF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。

In this research project, the PIs will develop new statistical methods for estimating networks from scientific data. In statistical network inference, each node in the network corresponds to a variable, and each edge represents a dependence relation. The project will address challenging scenarios where a set of external covariates may influence either the values of the nodes within the network or the strength of the connections. The PIs will develop new Bayesian modeling approaches for learning both directed and undirected networks and their dependence on covariates, including methods that can handle data that are not normally distributed, and implement the proposed methods using efficient computational algorithms. The PIs will apply the developed statistical models to high-dimensional data, including functional brain imaging and microbiome profiling. This work is significant, as it will break new ground in Bayesian modeling and computation. The broader impacts of this project include the public sharing of software, training of graduate students, and the application of the methods to real-world neuroimaging and microbiome data.This project will break new ground in the simultaneous estimation of graphical models and covariate effects. The PIs will develop a framework to infer directed graphs based on vector autoregressive models for time series data and will develop a novel formulation where covariates may influence the strength of an edge in a non-linear fashion. This framework will allow the determination of how key covariates modulate network relations. The PIs will also develop Bayesian methods for the simultaneous selection of covariates and edges in an undirected graph, focusing on models for non-Gaussian data. They will implement these models using efficient Variational Inference approaches, enabling scalability to real-world applications. This project achieves innovation both in terms of the Bayesian modeling approaches and the computational methods employed to enable efficient inference.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.