Ancestral graph Markov models

By Thomas S. Richardson, Peter Spirtes. 2002

708 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Signal Processing

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Citations in the corpus

Causal Models for Dynamical Systems (2020, background): “…on observed distributions, on the identiﬁcation of causal eﬀects and on causal discovery [e.g. Spirtes et al., 2000, Pearl, 2009, Shpitser, 2018, Richardson and Spirtes, 2002, Hern´an and Robins, 2006, Evans, 2015, Richardson et al., 2017, Hyttinen et al., 2012, Verma and Pearl, 1991, Silva et…”
Causal inference by using invariant prediction: identification and confidence intervals (2015, background): “…we primarily consider the situation with no hidden (confounder) variables: a rigorous treatment with hidden variables would be more involved [see Richardson and Spirtes, 2002, for graphical language] but we provide an example with instrumental variables in Section 5 to illustrate that the…”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “ called \faithfulness", conditional independences between subsets of observed variables allow one to draw partial conclusions regarding their causal relationships (Spirtes et al.,2000;Pearl,2000;Richardson and Spirtes, 2002). In this article, we focus on the bivariate case, assuming that only t”
Order-independent constraint-based causal structure learning (2012, background): “04 l l l l l l l l l l l l l l l l (b) Estimation performance of RFCI(-stable), CRFCI(-stable), and MRFCI(-stable) for the PAGs in terms of SHD edge marks.”
Structural Intervention Distance (SID) for Evaluating Causal Graphs (2013, background): “Alternatively, we can regard a maximal ancestral graph (MAG) (Richardson and Spirtes, 2002) as the ground truth, for which the characterization becomes more difficult.”
Causal Structure Learning (2017, background): “A MAG encodes conditional independencies via m-separation ( ?”
Bayesian reasoning and machine learning (2012, neutral): “Consider the distribution defined on variables t1, t2, y1, y2[232]: p(t1, t2, y1, y2) = p(t1)p(t2) ∑”
Joint response graphs and separation induced by triangular systems (2004, methodology): “The approach and formulation that are adopted here are different from other generalizations of directed acyclic graphs analysed by Koster (2002), by Richardson and Spirtes (2002) or by Cox and Wermuth (1996), chapter 8.”
Markov equivalence of marginalized local independence graphs (2018, methodology): “Starting from a DAG, one can ﬁnd graphs (e.g., maximal ancestral graphs or acyclic directed mixed graphs) that encode marginal independence models [8, 18, 19, 25, 33, 34, 36, 39].”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, neutral): “Richardson and Spirtes (2002) introduce a representation of graphs (so-called Maximal Ancestral Graphs, or MAGs) with hidden variables that is closed under marginalization and conditioning.”
A Complete Generalized Adjustment Criterion (2015, background): “Such MAGs form a Markov equivalence class which can be described uniquely by apartial ancestral graph (PAG) (Richardson and Spirtes, 2002; Ali et al., 2009).”
Explainable and Interpretable Models in Computer Vision and Machine Learning (2017, neutral): “This edge can model i) a direct causal relationship ( X → Y or Y → X ) ; ii) a causal relationship in either direction ( X − Y ); iii) a non-causal association ( X ↔ Y ) due to external common causes (Richardson and Spirtes, 2002).”
Global identifiability of linear structural equation models (2010, background): “Following [12], we call an acyclic mixed graph with this property ancestral.”
A survey of Bayesian Network structure learning (2021, background): “Ancestral graphs have three types of edge (Zhang, 2008b): • directed, e.g. 𝐴 ⟶ 𝐵: The mapping between edge types in the ancestral graph and relationships in the underlying DAG is given in Richardson and Spirtes (2002) but is somewhat complicated.”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “For example, in that case, and under a genericity condition called “faithfulness”, conditional independences between subsets of observed variables allow one to draw partial conclusions regarding their causal relationships (Spirtes et al., 2000; Pearl, 2000; Richardson and Spirtes, 2002; Zhang, 2008)”
Constraint-based causal discovery from multiple interventions over overlapping variable sets (2014, methodology): “Definition 2 (Maximal Ancestral Graph, MAG)(Richardson and Spirtes, 2002) A mixed graph is called ancestral if it contains no directed and almost directed cycles.”
A new criterion for confounder selection (2011, background): “Further discussion of the causal interpretation of directed acyclic graphs can be found elsewhere (Spirtes, Glymour, and Scheines, 1993; Pearl, 1995, 2009; Dawid, 2002; Richardson and Spirtes, 2002; Robins, 2003; Shpitser and Pearl, 2008).”