  In neuroscience, researchers seek to uncover the connectivity of neurons from
large-scale neural recordings or imaging; often people employ graphical model
selection and estimation techniques for this purpose. But, existing
technologies can only record from a small subset of neurons leading to a
challenging problem of graph selection in the presence of extensive latent
variables. Chandrasekaran et al. (2012) proposed a convex program to address
this problem that poses challenges from both a computational and statistical
perspective. To solve this problem, we propose an incredibly simple solution:
apply a hard thresholding operator to existing graph selection methods.
Conceptually simple and computationally attractive, we demonstrate that
thresholding the graphical Lasso, neighborhood selection, or CLIME estimators
have superior theoretical properties in terms of graph selection consistency as
well as stronger empirical results than existing approaches for the latent
variable graphical model problem. We also demonstrate the applicability of our
approach through a neuroscience case study on calcium-imaging data to estimate
functional neural connections.
