# Uniform random generation of large acyclic digraphs

@article{Kuipers2015UniformRG, title={Uniform random generation of large acyclic digraphs}, author={Jack Kuipers and Giusi Moffa}, journal={Statistics and Computing}, year={2015}, volume={25}, pages={227-242} }

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of…

## 19 Citations

Partition MCMC for Inference on Acyclic Digraphs

- Computer Science, Mathematics
- 2015

A novel algorithm is proposed, which employs the underlying combinatorial structure of DAGs to define a new grouping, and convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample.

Counting and Sampling Directed Acyclic Graphs for Learning Bayesian Networks

- Computer Science
- 2019

This thesis gives the first exact algorithm with a time complexity bound exponential in the number of nodes, and thus polynomial in the size of the input, which consists of all the possible per-node weights.

Efficient Structure Learning and Sampling of Bayesian Networks

- Computer ScienceArXiv
- 2018

This work synthesises constraint based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint based method.

Exact Sampling of Directed Acyclic Graphs from Modular Distributions

- Mathematics, Computer ScienceUAI
- 2019

This work gives an exact sampler that outperforms the previous best bound even for the uniform distribution, and considers the symmetric special case where the factors only depend on the size of the parent set—this covers uniform sampling under indegree constraints.

A Prior Distribution over Directed Acyclic Graphs for Sparse Bayesian Networks

- Mathematics, Computer Science
- 2015

A new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs and Monte Carlo schemes for finding the optimal aposteriori structure given a data matrix are described.

Unlabelled ordered DAGs and labelled DAGs: constructive enumeration and uniform random sampling

- Computer Science, MathematicsLAGOS
- 2021

Counting directed acyclic and elementary digraphs

- MathematicsArXiv
- 2020

The probability that a random digraph is elementary as a function of $\mu$ is expressed using techniques from analytic combinatorics, developed in particular to study random graphs.

Using node ordering to improve Structure MCMC for Bayesian Model Averaging

- Computer Science
- 2016

The contribution of this thesis includes a Markov Chain Monte Carlo simulation approach to sample network structures from a posterior and then using Bayesian model averaging approach to estimate the posterior of various features.

Structure Learning with Bow-free Acyclic Path Diagrams

- Computer Science
- 2015

A first method for structure learning for bow-free acyclic path diagrams using a greedy score-based search algorithm is presented, revealing that BAP models can represent the data much better than DAG models in these cases.

Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams

- Computer Science
- 2015

Some necessary and some sufficient conditions for distributional equivalence of BAPs are proved which are used in an algorithmic approach to compute (nearly) equivalent model structures, which allows us to infer lower bounds of causal effects.

## References

SHOWING 1-10 OF 44 REFERENCES

The size distribution for Markov equivalence classes of acyclic digraph models

- MathematicsArtif. Intell.
- 2002

A characterization of Markov equivalence classes for acyclic digraphs

- Mathematics
- 1997

Undirected graphs and acyclic digraphs (ADGs), as well as their mutual extension to chain graphs, are widely used to describe dependencies among variables in multivariate distributions. In…

Random Generation of Bayesian Networks

- Computer ScienceSBIA
- 2002

New methods for generation of random Bayesian networks using tools from the theory of Markov chains and methods for the uniform generation of multi-connected and singly-connected networks for a given number of nodes are presented.

Bayesian model averaging and model selection for markov equivalence classes of acyclic digraphs

- Mathematics
- 1996

Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive…

Learning high-dimensional directed acyclic graphs with latent and selection variables

- Computer Science
- 2012

This work proposes the new RFCI algorithm, which is much faster than FCI, and proves consistency of FCI and RFCI in sparse high-dimensional settings, and demonstrates in simulations that the estimation performances of the algorithms are very similar.

Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm

- Computer ScienceJ. Mach. Learn. Res.
- 2007

This work proves uniform consistency of the PC-algorithm for very high-dimensional, sparse DAGs where the number of nodes is allowed to quickly grow with sample size n, as fast as O(na) for any 0 < a < ∞.

Random generation of dags for graph drawing

- Computer Science, Mathematics
- 2000

This work proposes a simple algorithm for generating acyclic digraphs with a given number of vertices uniformly at random, and describes the overall shape and average edge density of an acy Cleric digraph.

Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

- Computer ScienceMachine Learning
- 2004

This paper shows how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables, and uses this result as the basis for an algorithm that approximates the Bayesian posterior of a feature.

Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move

- Computer ScienceMachine Learning
- 2008

A new and more extensive edge reversal move is proposed in the original structure space, and it is shown that this significantly improves the convergence of the classical structure MCMC scheme.