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A characterization of Markov equivalence for directed cyclic graphs

Thomas Richardson
1997 International Journal of Approximate Reasoning  
Hence, the theorem can be easily adapted into a polynomial time algorithm for deciding the Markov equivalence of two directed cyclic graphs . © 1997 Elsevier Science Inc.  ...  In other words, when two directed cyclic graphs are Markov equivalent, the set of distributions that satisfy a natural extension of the global directed Markov condition (Lauritzen et al., 1990) is exactly  ...  directed Markov property for cyclic graphs (see also [9] ).  ... 
doi:10.1016/s0888-613x(97)00020-0 fatcat:gdvzgj3gbjacxj4gnqyh4vajzy

A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models [article]

Thomas S. Richardson
2013 arXiv   pre-print
Hence, the theorem can be easily adapted into a polynomial time algorithm for deciding the Markov equivalence of two directed cyclic graphs.  ...  In this paper I state a theorem that gives necessary and sufficient conditions for the Markov equivalence of two directed cyclic graphs, where each of the conditions can be checked in polynomial time.  ...  Meek for helpful conversations. Research for this paper was supported by ONR grant N00014-93-l-0568.  ... 
arXiv:1302.3600v1 fatcat:jhkg45gsofcgpi76qtpzxezwby

Directed Cyclic Graphical Representations of Feedback Models [article]

Peter L. Spirtes
2013 arXiv   pre-print
However, non-recursive structural equation models of the kinds used to model economic processes are naturally represented by directed cyclic graphs with independent errors, a characterization of conditional  ...  The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways.  ...  Acknowledgements Research for this paper was supported by the National Science Foundation through grant 9102169 and the Navy Personnel Research and Development Center and the Office of Naval Research through  ... 
arXiv:1302.4982v1 fatcat:lnrgb2mkz5aovlm5melqee4fga

A graphical characterization of the largest chain graphs

Martin Volf, Milan Studený
1999 International Journal of Approximate Reasoning  
The characterization is a basis for an algorithm constructing, for a given chain graph, the largest chain graph equivalent to it.  ...  The paper presents a graphical characterization of the largest chain graphs which serve as unique representatives of classes of Markov equivalent chain graphs.  ...  We give a simple direct graphical characterization of those chain graphs which are the largest chain graphs of (some) classes of Markov equivalent chain graphs.  ... 
doi:10.1016/s0888-613x(99)00003-1 fatcat:vcuctt3no5dibbqaluqy7enocm

Special issue on the 1996 uncertainty in AI (UAI'96) conference—preface

Piero P. Bonissone
1997 International Journal of Approximate Reasoning  
a more complete analysis of their results.  ...  Every year, the Uncertainty in Artificial Intelligence (UAI) Conference provides a highly selected forum in which the most important innovations in the field of reasoning with uncertain, imprecise, and  ...  The first paper, "A Characterization of Markov Equivalence for Directed Cyclic Graphs," by Richardson, proposes a set of necessary and sufficient conditions, verifiable in polynomial time, for deciding  ... 
doi:10.1016/s0888-613x(97)00022-4 fatcat:lq2iblwdsbdshcb3btkrsr7mau

Page 160 of Naval Research Logistics Vol. 4, Issue 2 [page]

1957 Naval Research Logistics  
The graph G(Rp) of a stochastic matrix P of order n is thus a finite directed graph in which the indexed points or vertices correspond to states and the edges correspond to one-step transitions between  ...  it is clear that a uniform convention for all maximal cyclic nets is convenient).  ... 

Page 5897 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
| Richardson, Thomas Stuart] (1-WA-S; Seattle, WA) A characterization of Markov equivalence for directed cyclic graphs.  ...  and sufficient conditions for two directed cyclic graphs to be Markov equivalent.  ... 

Page 7558 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
It is shown that the Markov properiy determined by a graph is equivalent to the existence of a Gibbs factorization of the density. {For the entire collection see MR 98e:00011.} Robert P.  ...  Recently, however, it has been shown that graphs containing directed cycles may be given a proper Markov interpretation. This paper generalizes the scope of graphical models.  ... 

Identifying sufficient statistics in information networks

Huaiyu Dai, Husheng Li
2008 2008 42nd Annual Conference on Information Sciences and Systems  
We give a simple information theoretic characterization for this problem, which naturally leads to a graph theoretic identifying procedure.  ...  Given a network targeting information transmission, this paper considers the problem of identifying a set of edges or nodes whose transmission is sufficient to determine information flow at some other  ...  This type of graph is a generalization of the reciprocal graph [14] , which strictly includes directed cyclic graph (DCG) and chain graph [12] .  ... 
doi:10.1109/ciss.2008.4558668 dblp:conf/ciss/DaiL08a fatcat:v4tlsdi4pncwtney7fbl2zibdu

Graphical modeling of stochastic processes driven by correlated errors [article]

Søren Wengel Mogensen, Niels Richard Hansen
2020 arXiv   pre-print
Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs.  ...  We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes.  ...  In this section, we formulate sufficient conditions for a cDG to be Markov equivalent with a permutation graph. Definition 33 (Cyclic set).  ... 
arXiv:2005.07568v2 fatcat:ocqubedr4fei3a2dlywox3gixq

Identifiability Assumptions and Algorithm for Directed Graphical Models with Feedback [article]

Gunwoong Park, Garvesh Raskutti
2016 arXiv   pre-print
In this paper we address the issue of identifiability for general directed cyclic graphical (DCG) models satisfying the Markov assumption.  ...  Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data.  ...  Acknowledgement GP and GR were both supported by NSF DMS-1407028 over the duration of this project.  ... 
arXiv:1602.04418v2 fatcat:hqu63rcozffdjlbonryaffmyhi

Distributional Invariances and Interventional Markov Equivalence for Mixed Graph Models [article]

Liam Solus
2020 arXiv   pre-print
For ancestral graphs, we prove the resulting interventional MECs admit a graphical characterization generalizing that of DAGs.  ...  We then define interventional distributions for acyclic directed mixed graph models, and prove that this generalization aligns with the graphical generalization of interventional Markov equivalence given  ...  graphical characterizations of I-Markov equivalence for the AGs G and H.  ... 
arXiv:1911.10114v2 fatcat:3uirbn7o75ds3dgdxhnsvforqy

Causal Structure Learning: a Combinatorial Perspective [article]

Chandler Squires, Caroline Uhler
2022 arXiv   pre-print
Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can  ...  In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data.  ...  Center at the Broad Institute, and a Simons Investigator Award.  ... 
arXiv:2206.01152v1 fatcat:k7bha6htu5cwlmhh2haquuja7m

Characterizing Distribution Equivalence and Structure Learning for Cyclic and Acyclic Directed Graphs [article]

AmirEmad Ghassami, Alan Yang, Negar Kiyavash, Kun Zhang
2020 arXiv   pre-print
In this paper, we present a general, unified notion of equivalence for linear Gaussian causal directed graphical models, whether they are cyclic or acyclic.  ...  in terms of the Markov equivalence.  ...  KZ would like to acknowledge the support by National Institutes of Health under Contract No.  ... 
arXiv:1910.12993v3 fatcat:vu2z7fp6x5e5vklrncbxtjkqhm

On meta-analyses of imaging data and the mixture of records

J.D. Ramsey, P. Spirtes, C. Glymour
2011 NeuroImage  
We provide sufficient conditions and necessary conditions for the merger of two or more probability distributions, each characterized by the Markov equivalence class of a directed acyclic graph, to be  ...  describable by a Markov equivalence class whose edges are a union of those for the individual distributions.  ...  Acknowledgment We thank Jane Neumann for very helpful comments on a draft of this note.  ... 
doi:10.1016/j.neuroimage.2010.07.065 pmid:20709178 fatcat:3c253nrkrndpzi4t46qlcex32i
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