Statistical Analysis of Network Data Objects, with Applications in Functional Neuroimaging

• Activity Number: 289
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Eric Kolaczyk* and Cedric Ginestet and Steve Rosenberg and Lizhen Lin
• Companies: Boston University and Boston University and Boston University and The University of Texas at Austin
• Keywords: Networks ; Shape analysis ; Geometry ; Neuroscience ; Asymptotics

Abstract

In the context of big data, a new paradigm is emerging, in which it will be critical to be able to analyze large collections of (sub)networks, i.e., datasets of network objects. Networks, however, are not Euclidean objects, and hence classical methods do not directly apply. We address this challenge by developing a framework for asymptotic inference with network data objects, drawing on concepts and techniques from geometry, shape analysis, and high-dimensional statistical inference. Our work relies on a precise geometric characterization of the space of graph Laplacian matrices and a nonparametric notion of averaging due to Frechet. We motivate and illustrate our resulting methodologies through the problem of hypothesis testing in the context of networks derived from functional neuroimaging, using data on human subjects from the 1000 Functional Connectomes Project. We show that the global test emerging from our work is more statistically powerful than a mass-univariate approach.