Speaker: Bryon Aragam
Abstract: I will discuss the problem of estimating structural equation models from high-dimensional Gaussian data with p ≫ n. The main difficulty in establishing statistical guarantees in this setting arises from the nonidentifiability, nonsmoothness, and nonconvexity of the underlying M-estimator (aka score-based estimator). I will discuss how to establish nonasymptotic deviation bounds on the estimation error, sparsity bounds, and model selection consistency for a penalized least squares estimator. The proofs rely on interpreting the graphical model as a recursive linear structural equation model, which reduces the estimation problem to a series of tractable neighbourhood regressions, allowing us to avoid making any assumptions regarding identifiability, irrepresentability, or faithfulness. The techniques employed here provide insight into and can be used more broadly for general nonidentifiable and nonconvex problems. Reference: Mostly based on this preprint.