A characterization of Markov equivalence classes for acyclic digraphs

By Steen A. Andersson, David Madigan, Michael D. Perlman. 1997

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Citations in the corpus

Causal inference by using invariant prediction: identification and confidence intervals (2015, background): “…in the context of unknown causal structure, is to characterise the Markov equivalence class of structures (or graphs) [Verma and Pearl, 1991, Andersson et al., 1997, Hauser and B¨uhlmann, 2012], estimate such a class based on observational or interventional data [Spirtes et al., 2000,…”
Identifiability of Gaussian structural equation models with equal error variances (2012, background): “But the Markov equivalence class may still be large [cf. Andersson et al., 1997] and the directed acyclic graph G0 is not identifiable.”
Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs (2011, methodology): “Thanks to this, the proofs of Andersson et al. (1997)”
Order-independent constraint-based causal structure learning (2012, background): “Markov equivalent DAGs have the same skeleton and the same v-structures, and a Markov equivalence class can be described uniquely by a completed partially directed acyclic graph (CPDAG) (Andersson et al., 1997; Chickering, 2002).”
Structural Intervention Distance (SID) for Evaluating Causal Graphs (2013, methodology): “We make use of the fact that the PDAG C represents a Markov equivalence class of DAGs only if each chain component is chordal (Andersson et al., 1997).”
Causal Structure Learning (2017, background): “For DAGs and DGs this again reduces to a directed path, and for CPDAGs it is path with edges (cid:98) (cid:98) and → .”
$\ell_0$-penalized maximum likelihood for sparse directed acyclic graphs (2012, background): “Assuming faith-fulness (see below), the set of all such other DAGs build the so-called Markov equivalence class E ( D 0 ) which can be characterized in terms of a chain graph with undirected and directed edges; cf. Andersson, Madigan and Perlman (1997).”
On Inclusion-Driven Learning of Bayesian Networks (2003, methodology): “The use of a score equivalent scoring metric imposes strong constraints on the prior distribution of both, the graphs and the parameters (Andersson et al., 1997a, Section 7.2).”
Causal Dantzig: Fast inference in linear structural equation models with hidden variables under additive interventions (2017, background): “…1989, Robins et al., 2000, Pearl, 2009], one possibility is to characterize the Markov equivalence class of graphs under the assumption of acyclicity and usually faithfulness [Verma and Pearl, 1991, Andersson et al., 1997, Tian and Pearl, 2001, Hauser and B¨uhlmann, 2012, Chickering, 2002].”
Active Learning of Causal Networks with Intervention Experiments and Optimal Designs (2008, methodology): “According to the above results, we first learn an essential graph from observational data, which is a chain graph (Andersson et al., 1997) and depicts a Markov equivalence class (Heckerman et al., 1995; Verma and Pearl, 1990; Castelo and Perlman, 2002).”
Permutation-based Causal Inference Algorithms with Interventions (2017, background): “The MEC of G is represented combinatorially by a partially directed graph Ĝ := ([p], D,E), called its CP-DAG or essential graph [1].”
Efficient Sampling and Structure Learning of Bayesian Networks (2018, background): “The equivalence class of DAGs can be represented as an essential graph (Andersson et al., 1997) or a completed partially directed acyclic graph (CPDAG) (Chickering, 2002b).”
Structure Learning in Graphical Modeling (2016, background): “Each Markov equivalence class can be represented by a completed partially directed acyclic graph (CPDAG) that may have directed and undirected edges (e.g., Andersson et al., 1997; Roverato, 2005).”
DiBS: Differentiable Bayesian Structure Learning (2021, background): “G p(G | D) · SHD(G,G∗) (18) where SHD(G,G∗) counts the edge changes that separate the essential graphs representing the MECs of G and G∗ [8, 55].”
Sparse graphical models for exploring gene expression data (2004, unknown): “Geiger and Heckerman [8] prove that, under priors for the regression parameters induced by the inverse Wishart prior on the covariance matrix S; any two DAGs in the same equivalence class [2] have the same marginal likelihood.”
High-dimensional consistency in score-based and hybrid structure learning (2015, background): “A Markov equivalence class of DAGs can be uniquely represented by a completed partially directed acyclic graph (CPDAG), which is a PDAG that satisfies the following: Xi → Xk in the CPDAG ifXi → Xk in every DAG in the Markov equivalence class, and Xi−Xk in the CPDAG if the Markov equivalence class co”
A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables (2007, methodology): “Characterizations of Markov equivalence classes of DAGs (with no latent variables) are available in the literature (Meek 1995, Chickering 1995, Andersson et al. 1997).”