[2211.05690] Sturdy Mannequin Number of Gaussian Graphical Fashions

View a PDF of the paper titled Sturdy Mannequin Number of Gaussian Graphical Fashions, by Abrar Zahin and 4 different authors

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Summary:In Gaussian graphical mannequin choice, noise-corrupted samples current important challenges. It’s recognized that even minimal quantities of noise can obscure the underlying construction, resulting in basic identifiability points. A latest line of labor addressing this “strong mannequin choice” downside narrows its focus to tree-structured graphical fashions. Even inside this particular class of fashions, precise construction restoration is proven to be unimaginable. Nevertheless, a number of algorithms have been developed which might be recognized to provably get well the underlying tree-structure as much as an (unavoidable) equivalence class.

On this paper, we lengthen these outcomes past tree-structured graphs. We first characterize the equivalence class as much as which common graphs will be recovered within the presence of noise. Regardless of the inherent ambiguity (which we show is unavoidable), the construction that may be recovered reveals native clustering info and international connectivity patterns within the underlying mannequin. Such info is helpful in a variety of real-world issues, together with energy grids, social networks, protein-protein interactions, and neural buildings. We then suggest an algorithm which provably recovers the underlying graph as much as the recognized ambiguity. We additional present finite pattern ensures within the high-dimensional regime for our algorithm and validate our outcomes by way of numerical simulations.