Robust Model Selection of Gaussian Graphical Models
Abstract: In Gaussian graphical model selection, noise-corrupted samples present significant challenges.
It is known that even minimal amounts of noise can obscure the underlying structure,
leading to fundamental identifiability issues. A recent line of work addressing this “robust
model selection” problem narrows its focus to tree-structured graphical models. Even within
this specific class of models, exact structure recovery is shown to be impossible. However,
several algorithms have been developed that are known to provably recover the underlying
tree-structure up to an (unavoidable) equivalence class.
In this paper, we extend these results beyond tree-structured graphs. We first characterize
the equivalence class up to which general graphs can be recovered in the presence of noise.
Despite the inherent ambiguity (which we prove is unavoidable), the structure that can
be recovered reveals local clustering information and global connectivity patterns in the
underlying model. Such information is useful in a range of real-world problems, including
power grids, social networks, protein-protein interactions, and neural structures. We then
propose an algorithm which provably recovers the underlying graph up to the identified
ambiguity. We further provide finite sample guarantees in the high-dimensional regime for
our algorithm and validate our results through numerical simulations.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Bryon_Aragam1
Submission Number: 3506
Loading