# Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression

arXiv: https://arxiv.org/abs/1511.08963 · HTML: https://mlsanity.com/paper/1511.08963/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2015.

## Built on by (most cited first, 12 of 12)

- [Sample, estimate, aggregate: A recipe for causal discovery foundation models](https://mlsanity.com/paper/2402.01929/) (2024)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families](https://mlsanity.com/paper/2110.04719/) (2021)
- [Multi-task Learning of Order-Consistent Causal Graphs](https://mlsanity.com/paper/2111.02545/) (2021)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Directed Acyclic Graph Structure Learning from Dynamic Graphs](https://mlsanity.com/paper/2211.17029/) (2022)
- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)
- [ExDAG: an MIQP Algorithm for Learning DAGs](https://mlsanity.com/paper/2406.15229/) (2024)
- [Consistent Bayesian causal discovery for structural equation models with equal error variances](https://mlsanity.com/paper/2509.15197/) (2025)
- [Distributionally Robust Skeleton Learning of Discrete Bayesian Networks](https://mlsanity.com/paper/2311.06117/) (2023)
- [Learning Temporal Causal Structure via Smooth Differentiable Optimization](https://mlsanity.com/paper/2606.03227/) (2026)

## Abstract (arXiv)

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 pgg 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.