Colloquium: "Statistical Tools for Inference on Samples of Networks with Applications to Neuroimaging"

Speaker: Daniel Kessler, University of Michigan-Ann Arbor

Abstract: Networks are an increasingly common data structure, and their growing popularity demands the development of new statistical methodology. In this talk I'll discuss several projects motivated by applications in human neuroimaging that develop statistical tools for analyzing a sample of networks and associated unit-level covariates. In this setting, a unit of observation is a person, unit-level covariates contain information such as demographics, diagnoses, etc., and a signed, weighted network represents functional connectivity. All networks are observed on a common node set, corresponding to one of the known brain atlases. Like many networks encountered in practice, brain connectivity networks exhibit marked community structure, and this can be exploited to improve interpretability when conducting modeling and inference.

I will first briefly discuss the challenge of characterizing the distribution of a network given a unit-level covariate as well as the converse problem of predicting a unit-level covariate given a network. The rest of the talk will focus on the setting with multiple unit-level covariates. In our motivating application, these are scores obtained from a battery of behavioral assessments. A useful tool in this setting is Canonical Correlation Analysis (CCA), a method for analyzing two sets of variables. CCA learns a sequence of linear transformations (canonical directions) to obtain new variables that are maximally correlated with one another. CCA has seen a resurgence of popularity with applications including brain imaging and genomics where the goal is often to identify relationships between high-dimensional data such as connectivity with more moderately sized phenotypic measurements. Inference in CCA applications is typically limited to testing whether the transformed variables are correlated, whereas inference for the canonical directions has received comparatively little attention. I will present several proposed approaches for conducting inference on canonical directions obtained by CCA and illustrate them on both synthetic data and data from the Adolescent Brain Cognitive Development (ABCD) study.

Host: Robert Lunde

Tea will be available at 3:30pm in room 200.