# Structure Learning in Graphical Modeling

arXiv: https://arxiv.org/abs/1606.02359 · HTML: https://mlsanity.com/paper/1606.02359/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2016.

## Built on by (most cited first, 30 of 66)

- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
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- [textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery](https://mlsanity.com/paper/2306.10816/) (2023)
- [Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG](https://mlsanity.com/paper/2105.00488/) (2021)
- [Learning non-Gaussian graphical models via Hessian scores and triangular transport](https://mlsanity.com/paper/2101.03093/) (2021)
- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [The Future of Fundamental Science Led by Generative Closed-Loop Artificial Intelligence](https://mlsanity.com/paper/2307.07522/) (2023)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [Ensemble transport smoothing. Part II: Nonlinear updates](https://mlsanity.com/paper/2210.17435/) (2022)
- [Learning Linear Non-Gaussian Polytree Models](https://mlsanity.com/paper/2208.06701/) (2022)
- [Interpretable Machine Learning for Discovery: Statistical Challenges & Opportunities](https://mlsanity.com/paper/2308.01475/) (2023)
- [Estimating a Directed Tree for Extremes](https://mlsanity.com/paper/2102.06197/) (2021)
- [Batch Bayesian Optimization on Permutations using the Acquisition Weighted Kernel](https://mlsanity.com/paper/2102.13382/) (2021)
- [Learning Graph Structure from Convolutional Mixtures](https://mlsanity.com/paper/2205.09575/) (2022)
- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [Localized Diffusion Models](https://mlsanity.com/paper/2505.04417/) (2025)
- [Nonlinear Causal Discovery for Grouped Data](https://mlsanity.com/paper/2506.05120/) (2025)
- [Structure Learning with Adaptive Random Neighborhood Informed MCMC](https://mlsanity.com/paper/2311.00599/) (2023)
- [Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models](https://mlsanity.com/paper/2404.12592/) (2024)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)
- [Recursive Bayesian Networks: Generalising and Unifying Probabilistic Context-Free Grammars and Dynamic Bayesian Networks](https://mlsanity.com/paper/2111.01853/) (2021)
- [Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment Effect Estimation](https://mlsanity.com/paper/2307.04988/) (2023)
- [Multiview Graph Learning with Consensus Graph](https://mlsanity.com/paper/2401.13769/) (2024)
- [Prequential MDL for Causal Structure Learning with Neural Networks](https://mlsanity.com/paper/2107.05481/) (2021)
- [CKH: Causal Knowledge Hierarchy for Estimating Structural Causal Models from Data and Priors](https://mlsanity.com/paper/2204.13775/) (2022)
- [Scalable network reconstruction in subquadratic time](https://mlsanity.com/paper/2401.01404/) (2024)

## Abstract (arXiv)

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for tractable modeling of multivariate distributions. More recently, applications such as reconstructing gene regulatory networks from gene expression data have driven major advances in structure learning, that is, estimating the graph underlying a model. We review some of these advances and discuss methods such as the graphical lasso and neighborhood selection for undirected graphical models (or Markov random fields), and the PC algorithm and score-based search methods for directed graphical models (or Bayesian networks). We further review extensions that account for effects of latent variables and heterogeneous data sources.