The Statistics Seminar Speaker for December 4, 2014, will be Xi (Rossi) Luo of Brown University.
Title: Covariance Estimation Methods for Understanding Brain Networks
Abstract: The brain can be conceptualized as a dynamic network of many nodes. Neuroimaging techniques, such as MRI, make it possible to measure the activities of hundreds of thousands of brain nodes. This talk focuses on two statistical problems in understanding brain networks from fMRI: inferring brain connectivity via sparse inverse covariance estimation and quantifying information flow via structural equation models. Covariance estimation plays important but different roles in solving these two problems. We study the first problem under the high dimensional (“large p, small n”) setting. We will first review several existing methods, and their limitations for inferring brain networks. We will then introduce an optimization method to embed a lower dimensional sparse graphical model for big data with millions of variables. This approach enjoys the advantages in interpretation and computation. In the fMRI application for example, it enables simultaneous brain region extraction and network estimation. For the second problem, we will consider a generalized mediation model with correlated errors under the “small p, large n” setting. We first propose a constrained optimization approach for this model, and interestingly we show that the parameters are not identifiable when the error covariance matrix is unknown, even if the sample size is infinitely large. To address this issue, we will extend our model to a multi-level setting, motivated by multi-subject and multi-session fMRI experiments. We will employ optimization methods to identify and estimate the multi-level parameters and the covariance matrix jointly. For both problems, the numerical merits are illustrated using simulated and real fMRI datasets.
Refreshments will be served after the seminar in 1181 Comstock Hall.