
Direct Estimation of Differential Functional Graphical Models
We consider the problem of estimating the difference between two functio...
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Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes
The covariance structure of multivariate functional data can be highly c...
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Nonparametric and highdimensional functional graphical models
We consider the problem of constructing nonparametric undirected graphic...
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Graph Estimation From Multiattribute Data
Many real world network problems often concern multivariate nodal attrib...
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Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity
Functional brain networks are well described and estimated from data wit...
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RegionReferenced Spectral Power Dynamics of EEG Signals: A Hierarchical Modeling Approach
Functional brain imaging through electroencephalography (EEG) relies upo...
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AdaPtive Noisy Data Augmentation (PANDA) for Simultaneous Construction Multiple Graph Models
We extend the data augmentation technique (PANDA) by Li et al. (2018) fo...
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FuDGE: Functional Differential Graph Estimation with fully and discretely observed curves
We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as highdimensional random function vectors rather than multivariate scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time. In these problems, not only can the number of functions measured per sample be large, but each function is itself an infinite dimensional object, making estimation of model parameters challenging. In practice, curves are usually discretely observed, which makes graph structure recovery even more challenging. We formally characterize when two functional graphical models are comparable and propose a method that directly estimates the functional differential graph, which we term FuDGE. FuDGE avoids separate estimation of each graph, which allows for estimation in problems where individual graphs are dense, but their difference is sparse. We show that FuDGE consistently estimates the functional differential graph in a highdimensional setting for both discretely observed and fully observed function paths. We illustrate finite sample properties of our method through simulation studies. In order to demonstrate the benefits of our method, we propose Joint Functional Graphical Lasso as a competitor, which is a generalization of the Joint Graphical Lasso. Finally, we apply our method to EEG data to uncover differences in functional brain connectivity between alcoholics and control subjects.
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