Papers › Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression
Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression
Bryon Aragam, Arash A. Amini, Qing Zhou
We study a family of regularized score-based estimators for learning the structure of a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with p≫n. Our main results establish support recovery guarantees and deviation bounds for a family of penalized least-squares estimators under concave regularization without assuming prior knowledge of a variable ordering. These results apply to a variety of practical situations that allow for arbitrary nondegenerate covariance structures as well as many popular regularizers including the MCP, SCAD, ℓ₀ and ℓ₁. The proof relies on interpreting a DAG as a recursive linear structural equation model, which reduces the estimation problem to a series of neighbourhood regressions. We provide a novel statistical analysis of these neighbourhood problems, establishing uniform control over the superexponential family of neighbourhoods associated with a Gaussian distribution. We then apply these results to study the statistical properties of score-based DAG estimators, learning causal DAGs, and inferring conditional independence relations via graphical models. Our results yield---for the first time---finite-sample guarantees for structure learning of Gaussian DAGs in high-dimensions via score-based estimation.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections