Collaborative Research: Covariate-Driven Approaches to Network Estimation

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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.