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Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables [article]

Ayesha R. Ali, Thomas S. Richardson, Peter L. Spirtes, Jiji Zhang
2012 arXiv   pre-print
In this paper we present a set of orientation rules that construct the Markov equivalence class representative for ancestral graphs, given a member of the equivalence class.  ...  Ancestral graphs provide a class of graphs that can encode conditional independence relations that arise in DAG models with latent and selection variables.  ...  Acknowledgments The authors are thankful to Michael Perlman, for posing the question of whether the essential graph for DAG D is equal to sup[G] if D ∈ [G], and to the William and Flora Hewlett Foundation  ... 
arXiv:1207.1365v1 fatcat:svmvlc67ovfojg77vcnzu5pbx4

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

Thomas S. Richardson
2013 arXiv   pre-print
When exactly the same set of d-separation relations hold in two directed graphs, no matter whether respectively cyclic or acyclic, we say that they are Markov equivalent.  ...  Although the concept of d-separation was originally defined for directed acyclic graphs (see Pearl 1988), there is a natural extension of he concept to directed cyclic graphs.  ...  Meek for helpful conversations. Research for this paper was supported by ONR grant N00014-93-l-0568.  ... 
arXiv:1302.3600v1 fatcat:jhkg45gsofcgpi76qtpzxezwby

A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables [article]

Jiji Zhang, Peter L. Spirtes
2012 arXiv   pre-print
Chickering (1995) provided a transformational characterization of Markov equivalence for DAGs (with no latent variables), which is useful in deriving properties shared by Markov equivalent DAGs, and, with  ...  Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables.  ...  Acknowledgement We thank Thomas Richardson and Clark Glymour for reading an earlier draft of the paper, and anonymous referees for valuable comments.  ... 
arXiv:1207.1419v1 fatcat:bgu7mlxewjb2pfsna4doctqhr4

A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables [article]

Jiji Zhang
2012 arXiv   pre-print
Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly identify all arrow orientations shared by all DAGs in  ...  Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables.  ...  Acknowledgement I thank Peter Spirtes and Thomas Richardson for checking the proofs in Zhang (2006) .  ... 
arXiv:1206.5282v1 fatcat:abwtqieirvby5onel5w2wtspee

A review of Gaussian Markov models for conditional independence [article]

Irene Córdoba, Concha Bielza, Pedro Larrañaga
2019 arXiv   pre-print
We review model selection and estimation in directed and undirected Markov models with Gaussian parametrization, emphasizing the main similarities and differences.  ...  These two model classes are similar but not equivalent, although they share a common intersection.  ...  It has been recently shown that a Gaussian MVR chain graph is Markov equivalent to an acyclic directed Gaussian Markov model with latent variables when its bidirected part is chordal (Fox et al., 2015  ... 
arXiv:1606.07282v4 fatcat:ra7sd6j4lrgjnd3famsh4klpne

Graphs for Margins of Bayesian Networks

Robin J. Evans
2015 Scandinavian Journal of Statistics  
Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning  ...  We introduce a new class of hyper-graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG.  ...  Latent projection leads to an acyclic directed mixed graph (ADMG) (equivalent to summary graph without undirected edges). Can read off independences with d/m-separation.  ... 
doi:10.1111/sjos.12194 fatcat:nfraq6hqwjexhe5ysrzvpcm6me

PAG2ADMG: An Algorithm for the Complete Causal Enumeration of a Markov Equivalence Class [article]

Nishant Subramani
2018 arXiv   pre-print
Causal graphs, such as directed acyclic graphs (DAGs) and partial ancestral graphs (PAGs), represent causal relationships among variables in a model.  ...  However, these methods are significantly limited in that they only output a single causal graph consistent with the independencies and dependencies (the Markov equivalence class M) estimated from the data  ...  M-separation relationships help define a Markov equivalence class, but many different characterizations of Markov Equivalence exist [1] [15] [18] [19] .  ... 
arXiv:1612.00099v3 fatcat:mbrnv42x4je4bmgsx5g7ynshly

Causal Discovery from Soft Interventions with Unknown Targets: Characterization and Learning

Amin Jaber, Murat Kocaoglu, Karthikeyan Shanmugam, Elias Bareinboim
2020 Neural Information Processing Systems  
targets belong to the same -Markov equivalence class.  ...  ., it discovers as many tails and arrowheads as can be oriented within a -Markov equivalence class.  ...  A prominent approach for causal discovery models the underlying system as a causal graph represented by a directed acyclic graph (DAG), where nodes denote random variables (measured or latent) and directed  ... 
dblp:conf/nips/JaberKSB20 fatcat:voiryydxinbebmhpgofuexcpea

Causal Structure Learning: a Combinatorial Perspective [article]

Chandler Squires, Caroline Uhler
2022 arXiv   pre-print
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.  ...  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  ...  Caroline Uhler was partially supported by NSF (DMS-1651995), ONR (N00014-17-1-2147 and N00014-22-1-2116), the MIT-IBM Watson AI Lab, MIT J-Clinic for Machine Learning and Health, the Eric and Wendy Schmidt  ... 
arXiv:2206.01152v1 fatcat:k7bha6htu5cwlmhh2haquuja7m

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

Liam Solus
2020 arXiv   pre-print
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  ...  latent cofounders and selection variables.  ...  The LMG G is called a directed acyclic graph (DAG) if it has only directed edges and no directed cycles.  ... 
arXiv:1911.10114v2 fatcat:3uirbn7o75ds3dgdxhnsvforqy

Foundations of Structural Causal Models with Cycles and Latent Variables [article]

Stephan Bongers, Patrick Forré, Jonas Peters, Joris M. Mooij
2021 arXiv   pre-print
; and their graphs are not always consistent with their causal semantics.  ...  We introduce the class of simple SCMs that extends the class of acyclic SCMs to the cyclic setting, while preserving many of the convenient properties of acyclic SCMs.  ...  The authors are grateful to Bernhard Schölkopf and Robin Evans for stimulating discussions, and to Noud de Kroon, Tineke Blom and Alexander Ly for providing helpful comments on earlier drafts.  ... 
arXiv:1611.06221v5 fatcat:ww4gea63kbbhdlubtcalfknzvi

Markov Equivalence Classes for Maximal Ancestral Graphs [article]

Ayesha R. Ali, Thomas S. Richardson
2012 arXiv   pre-print
associate a unique graph with a Markov equivalence class.  ...  Ancestral graphs are a class of graphs that encode conditional independence relations arising in DAG models with latent and selection variables, corresponding to marginalization and conditioning.  ...  Acknowledgments We would like to acknowledge Michael Perlman and the reviewers for their valuable comments on previ ous drafts of this paper. This research was supported by the U.S.  ... 
arXiv:1301.0550v1 fatcat:zd75p26cq5bhlmab2ismvek2f4

Generating Markov Equivalent Maximal Ancestral Graphs by Single Edge Replacement [article]

Jin Tian
2012 arXiv   pre-print
Maximal ancestral graphs (MAGs) are used to encode conditional independence relations in DAG models with hidden variables.  ...  This paper considers MAGs without undirected edges and shows conditions under which an arrow in a MAG can be reversed or interchanged with a bi-directed edge so as to yield a Markov equivalent MAG.  ...  Acknowledgements The author thanks the anonymous reviewers for helpful comments. This research was partly supported by NSF grant IIS-0347846.  ... 
arXiv:1207.1428v1 fatcat:dpybamytnjha5d55cighd4qxdq

On the Properties of MVR Chain Graphs [article]

Mohammad Ali Javidian, Marco Valtorta
2019 arXiv   pre-print
Except for pairwise Markov properties, we show that for MVR chain graphs all Markov properties in the literature are equivalent for semi-graphoids.  ...  We review Markov properties for MVR chain graphs and propose an alternative global and local Markov property for them.  ...  Definition 13 (Chain graph Markov property of type IV (Drton, 2009) ) Let G be a chain graph with chain components (T |T ∈ T ) and directed acyclic graph D of components.  ... 
arXiv:1803.04262v7 fatcat:yygfiwyb65fnxnkqch23szf5oy

Ordering-Based Causal Structure Learning in the Presence of Latent Variables [article]

Daniel Irving Bernstein, Basil Saeed, Chandler Squires, Caroline Uhler
2020 arXiv   pre-print
We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model.  ...  We consider the task of learning a causal graph in the presence of latent confounders given i.i.d. samples from the model.  ...  Basil Saeed was partially supported by the Abdul Latif Jameel Clinic for Machine Learning in Health at MIT.  ... 
arXiv:1910.09014v2 fatcat:mbphnu7nl5am5fgrkum2juspjm
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