Paper Info
Title
Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs
Abstract
Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible irreducible Markov chains on the space of Markov equivalent classes by proposing a perfect set of operators that determine the transitions of the Markov chain. The stationary distribution of a proposed Markov chain has a closed form and can be computed easily. Specifically, we construct a concrete perfect set of operators on sparse Markov equivalence classes by introducing appropriate conditions on each possible operator. Algorithms and their accelerated versions are provided to efficiently generate Markov chains and to explore properties of Markov equivalence classes of sparse directed acyclic graphs (DAGs) with thousands of vertices. We find experimentally that in most Markov equivalence classes of sparse DAGs, (1) most edges are directed, (2) most undirected subgraphs are small and (3) the number of these undirected subgraphs grows approximately linearly with the number of vertices.
Year
DOI
Venue
2012
10.1214/13-AOS1125
ANNALS OF STATISTICS
Keywords
Field
DocType
Sparse graphical model,reversible Markov chain,Markov equivalence class,Causal inference
Discrete mathematics,Markov chain mixing time,Combinatorics,Markov process,Markov property,Markov model,Markov chain,Variable-order Markov model,Markov kernel,Statistics,Mathematics,Examples of Markov chains
Journal
Volume
Issue
ISSN
41
4
0090-5364
Citations 
PageRank 
References 
4
0.45
9
Authors
3
Name
Order
Citations
PageRank
Yangbo He163.88
Jinzhu Jia2665.47
Bin Yu31984241.03