Direct Estimation of Differential Functional Graphical Models
This work addresses the challenge of high-dimensional functional data analysis for applications like neuroscience, but it is incremental as it builds on existing graphical model frameworks.
The paper tackles the problem of estimating differences between two functional undirected graphical models with shared structures, such as in EEG data, by developing a direct estimation method that avoids separate graph estimation and shows consistency in high-dimensional settings, with application to EEG data revealing differences in brain connectivity between alcoholics and controls.
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 high-dimensional 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. We develop a method that directly estimates the difference of graphs, avoiding separate estimation of each graph, and show it is consistent in certain high-dimensional settings. We illustrate finite sample properties of our method through simulation studies. Finally, we apply our method to EEG data to uncover differences in functional brain connectivity between alcoholics and control subjects.