DeepAI AI Chat
Log In Sign Up

Priors on exchangeable directed graphs

by   Diana Cai, et al.

Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraphons, we first show how to construct models for exchangeable directed graphs, including special cases such as tournaments, linear orderings, directed acyclic graphs, and partial orderings. We then show how to construct priors on digraphons via the infinite relational digraphon model (di-IRM), a new Bayesian nonparametric block model for exchangeable directed graphs, and demonstrate inference on synthetic data.


page 3

page 16

page 21


An Alternative Markov Property for Chain Graphs

Graphical Markov models use graphs, either undirected, directed, or mixe...

The Indian Chefs Process

This paper introduces the Indian Chefs Process (ICP), a Bayesian nonpara...

Bipartitioning of directed and mixed random graphs

We show that an intricate relation of cluster properties and optimal bip...

Learning Sparse Nonparametric DAGs

We develop a framework for learning sparse nonparametric directed acycli...

A Bayesian Nonparametric Stochastic Block Model for Directed Acyclic Graphs

Directed acyclic graphs (DAGs) are commonly used in statistics as models...

Exact Estimation of Multiple Directed Acyclic Graphs

This paper considers the problem of estimating the structure of multiple...

Individualized Inference in Bayesian Quantile Directed Acyclic Graphical Models

We propose an approach termed "qDAGx" for Bayesian covariate-dependent q...