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Title: Partial separability and graphical models for multivariate functional data Authors:  Alexander Petersen - Brigham Young University (United States) [presenting]
Sang-Yun Oh - University of California Santa Barbara (United States)
Javier Zapata - University of California Santa Barbara (United States)
Abstract: Graphical models are a ubiquitous tool for identifying dependencies among components of high-dimensional multivariate data. Recently, these tools have been extended to estimate dependencies between components of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. A key difficulty compared to multivariate data is that the covariance operator is compact, and thus not invertible. We present two important developments in this area for multivariate Gaussian processes. The first is to identify sufficient conditions under which absence of an edge in the conditional independence graph can be shown to correspond with zeros in a suitable inverse covariance operator. We then propose a new notion of partial separability as a useful tool for simplifying estimation, and show that the estimators are robust to certain types of model misspecification. Finally, we will demonstrate the empirical findings of our method through simulation and analysis of functional brain connectivity during a motor task.