Markov Properties for Acyclic Directed Mixed Graphs

By Thomas S. Richardson. 2003

287 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Statistical and Nonlinear Physics

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Citations in the corpus

Foundations of structural causal models with cycles and latent variables (2016, methodology): “Equivalently, an SCM M is acyclic if G ( M ) is an acyclic directed mixed graph (ADMG) [54].”
Causal Transfer Learning (2017, background): “The (causal) Markov assumption holds [Richardson, 2003], i.e., any d-separation )] in the marginal distribution P ( V ) induced by the SCM M .”
Minimal sufficient causation and directed acyclic graphs (2009, background): “Another direction of further research might involve the incorporation of the AND and OR nodes that arise from sufficient causation structures into other graphical models such as summary graphs [4], MC-graphs [12], chain graph models [2, 6, 14, 15, 16, 23, 34, 42] and ancestral graph models [24].”
Markov properties for mixed graphs (2011, background): “Other subclasses of LMGs that usem-separation and have been discussed in the literature are summary graphs [29], ancestral graphs [25], acyclic directed mixed graphs [27; 23], undirected or concentration graphs [6; 19], bidirected or covariance graphs [5; 15; 30; 9], and the class of directed acycli”
PROBABILITY DISTRIBUTIONS WITH SUMMARY GRAPH STRUCTURE (2010, methodology): “These two important properties are shared by two other types of graph, the MC-graphs of Koster (2002) and the ancestral graphs of Richardson and Spirtes (2002). In fact, the independence structures captured by an MC-graph, a summary graph and a maximal ancestral graph coincide whenever the same sets”
Discrete chain graph models (2009, background): “Four classes of Markov properties for chain graphs have been discussed in the literature, and we classify them as: Type I: the LWF or block concentration Markov property [12, 22]; Type II: the AMP or concentration regression Markov property [1]; Type III: a Markov property that is dual to the type I”
Mixed Cumulative Distribution Networks (2010, background): “[21, 19] show that DAGs ar e not closed under marginalization, but ADMGs are.”
Binary models for marginal independence (2007, methodology): “Maximum likelihood (ML) estimation and likelihood ratio tests in these Gaussian models can be carried out by using the iterative conditional fitting (ICF) algorithm (Drton and Richardson, 2003; Chaudhuri et al., 2007), which is implemented in the ‘ggm’ package in R (Marchetti, 2006).”
Constraint-based causal discovery from multiple interventions over overlapping variable sets (2014, methodology): “18 in Richardson and Spirtes (2002).”
Joint Causal Inference from Multiple Contexts (2016, background): “Global Markov Property holds for any solution (X;E) of Mwith respect to the functional graph G(M): A d ? G(M) BjC =)X A ?? P M(X) X BjX C 8A;B;CI: The acyclic case is well-known and was rst shown by Richardson (2003). The solvability conditions in the discrete and linear cases above are implied by s”
The Sensitivity of Counterfactual Fairness to Unmeasured Confounding (2019, methodology): “6= k: Cis the set of correlations that should be non-zero. A quick aside: the setting where there are zero correlations can be captured using the standard acyclic directed mixed graph notation (ADMG, Richardson, 2003). Speciﬁcally, this can be represented by ADMGs by removing bidirected edges betwee”
Learning Causal Structure from Undersampled Time Series (2013, background): “1 2 3 4 (c ) G 1 for (1a) 1 2 3 4 (d ) G 2 for (1b) Figure 1: Undersampling example Unrolling-and-marginalizing a DBN ADMG can be quite computationally complex and unilluminating, so we instead use compressed graphs, which encode temporal information in the edges, rather than the variables.”
Chain graph models of multivariate regression type for categorical data (2009, background): “The edges are undirected within the chain components, drawn as dashed lines [6] or as bi-directed arrows [21], and directed between components, all pointing in the same direction, that is, with no chance of semi-directed cycles.”
Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, methodology): “Richardson (2018). Acyclic linear SEMs obey the nested Markov property.”