# Structure Learning with Adaptive Random Neighborhood Informed MCMC

arXiv: https://arxiv.org/abs/2311.00599 · HTML: https://mlsanity.com/paper/2311.00599/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Efficient Sampling and Structure Learning of Bayesian Networks](https://mlsanity.com/paper/1803.07859/) (2018)
- [Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget](https://mlsanity.com/paper/1304.5299/) (2013)
- [Firefly Monte Carlo: Exact MCMC with Subsets of Data](https://mlsanity.com/paper/1403.5693/) (2014)
- [On the Computational Complexity of High-Dimensional Bayesian Variable Selection](https://mlsanity.com/paper/1505.07925/) (2015)
- [Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG](https://mlsanity.com/paper/2105.00488/) (2021)
- [Dimension-free Mixing for High-dimensional Bayesian Variable Selection](https://mlsanity.com/paper/2105.05719/) (2021)
- [Adaptive MCMC for Bayesian variable selection in generalised linear models and survival models](https://mlsanity.com/paper/2308.00869/) (2023)

## Built on by (most cited first, 4 of 4)

- [BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo](https://mlsanity.com/paper/2408.08062/) (2024)
- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)
- [Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage](https://mlsanity.com/paper/2509.13267/) (2025)
- [Interpretable Causal Discovery via Causal-Effect Constraints](https://mlsanity.com/paper/2608.12640/) (2026)

## Abstract (arXiv)

In this paper, we introduce a novel MCMC sampler, PARNI-DAG, for a fully-Bayesian approach to the problem of structure learning under observational data. Under the assumption of causal sufficiency, the algorithm allows for approximate sampling directly from the posterior distribution on Directed Acyclic Graphs (DAGs). PARNI-DAG performs efficient sampling of DAGs via locally informed, adaptive random neighborhood proposal that results in better mixing properties. In addition, to ensure better scalability with the number of nodes, we couple PARNI-DAG with a pre-tuning procedure of the sampler's parameters that exploits a skeleton graph derived through some constraint-based or scoring-based algorithms. Thanks to these novel features, PARNI-DAG quickly converges to high-probability regions and is less likely to get stuck in local modes in the presence of high correlation between nodes in high-dimensional settings. After introducing the technical novelties in PARNI-DAG, we empirically demonstrate its mixing efficiency and accuracy in learning DAG structures on a variety of experiments.