Nested Markov Properties for Acyclic Directed Mixed Graphs
By Thomas S. Richardson, James M. Robins, Ilya Shpitser. 2012
154 citations recorded by the source corpus.
Directed acyclic graph (DAG) models may be characterized in four different ways: via a factorization, the d-separation criterion, the moralization criterion, and the local Markov property. As pointed out by Robins [2, 1], Verma and Pearl [6], and Tian and Pearl [5], marginals of DAG models also imply equality constraints that are not conditional independences. The well-known 'Verma constraint' is an example. Constraints of this type were used for testing edges [3], and an efficient variable elimination scheme [4]. Using acyclic directed mixed graphs (ADMGs) we provide a graphical characterization of the constraints given in [5] via a nested Markov property that uses a 'fixing' transformation on graphs. We give four characterizations of our nested model that are analogous to those given for DAGs. We show that marginal distributions of DAG models obey this property.
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Jan Peters
- Bernhard Schölkopf
- Ilya Shpitser
- Thomas S. Richardson
- Stefan Bauer
- Judea Pearl
- Robin J. Evans
- Niklas Pfister
Citations in the corpus
- Causal Models for Dynamical Systems (2020, background): “…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 al., 2006], more work is needed in the case of dynamical systems.”
- Parameter and Structure Learning in Nested Markov Models (2012, methodology): “A recent paper [11] has given a nested factorization for mixed graph models which implies, along with the standard conditional independences in mixed graphs, post-truncation independences of the type shown in (1).”
- Constraint-based causal discovery from multiple interventions over overlapping variable sets (2014, methodology): “Based on this parametrization, score-based methods have also recently been explored Richardson et al. (2012); Shpitser et al. (2013), but are still limited to small sets of discrete variables.”