  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.

Machine Learning;Machine Learning;Methodology