  We model time-varying network data as realizations from multivariate Gaussian
distributions with precision matrices that change over time. To facilitate
parameter estimation, we require not only that each precision matrix at any
given time point be sparse, but also that precision matrices at neighboring
time points be similar. We accomplish this with two different algorithms, by
generalizing the elastic net and the fused LASSO, respectively. Our main
focuses are efficient computational algorithms and convenient degree-of-freedom
formulae for choosing tuning parameters. We illustrate our methods with two
simulation studies. By applying them to an fMRI data set, we also detect some
interesting differences in brain connectivity between healthy individuals and
ADHD patients.
