# High-Dimensional Poisson DAG Model Learning Using ℓ1-Regularized Regression

arXiv: https://arxiv.org/abs/1810.02501 · HTML: https://mlsanity.com/paper/1810.02501/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2018.

## Built on by (most cited first, 10 of 10)

- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing](https://mlsanity.com/paper/2301.12930/) (2023)
- [Markov Equivalence and Consistency in Differentiable Structure Learning](https://mlsanity.com/paper/2410.06163/) (2024)
- [Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers](https://mlsanity.com/paper/2111.01560/) (2021)
- [Graphical estimation of multivariate count time series](https://mlsanity.com/paper/2302.08801/) (2023)
- [A novel hybrid approach for positive-valued DAG learning](https://mlsanity.com/paper/2604.08935/) (2026)
- [Discrete Score Matching Enables Causal Discovery from Count Data](https://mlsanity.com/paper/2609.39326/) (2026)

## Abstract (arXiv)

In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our method is to decouple the ordering estimation or parent search where the problems can be efficiently addressed using ℓ1-regularized regression and the mean-variance relationship. We show that sample size n = Omega( d2 log9 p) is sufficient for our polynomial time Mean-variance Ratio Scoring (MRS) algorithm to recover the true directed graph, where p is the number of nodes and d is the maximum indegree. We verify through simulations that our algorithm is statistically consistent in the high-dimensional p>n setting, and performs well compared to state-of-the-art ODS, GES, and MMHC algorithms. We also demonstrate through multivariate real count data that our MRS algorithm is well-suited to estimating DAG models for multivariate count data in comparison to other methods used for discrete data.