FRG: Collaborative Research: Flexible Network Inference

Scientists have been studying many natural systems by viewing them as networks, a term used to describe collections of entities and their interactions. Networks are ubiquitous in many fields, including epidemiology, economics, sociology, genomics and ecology, to name a few. A number of statistical models have emerged over the last two decades to describe network data.

One common type of model is the latent space model, where each entity’s behavior is governed by its position in some unobserved (latent) space, and if we knew these positions, we could fully describe the statistical behavior of the network. While these models have been useful in many problems, real systems tend to be more complicated. The goal of this project is to fill this gap between models and reality by developing network analysis methods that still perform well even when the model does not fully match the data.

The specific aims of this project are to improve our understanding of existing network analysis methods under model misspecification, heterogeneous noise, and incomplete or missing data, and to develop novel network methods that are robust to these sources of error. We consider both these problems under one unified framework that represents the adjacency matrix of a network as its expectation plus entry-wise noise, which encompasses most popular network models.

Within this framework, the project will examine the effects of model misspecification on downstream inference, both for global inference tasks (e.g., network-level summary statistics) and local inference (e.g., node-level statistics). One core goal of the project is developing bootstrap and resampling algorithms for networks, two extremely useful tools in classical statistics that do not yet have full network analogues.

Another core goal is developing more general notions of community membership and node similarity, allowing the extension of robust algorithms to a broader collection of network models. Finally, the methods developed will be extended to the analysis of multiple networks. Taken together, these tools will substantially expand the toolbox of network techniques, while accounting for the realities of noisy and incomplete network data and imperfect network models.

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.