Graphical methods for inequality constraints in marginalized DAGs
By Robin J. Evans. 2012
44 citations recorded by the source corpus.
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted if any two observed variables are neither adjacent in the graph, nor share a latent parent; this generalizes the well known instrumental inequality. The method also provides inequalities on interventional distributions, which can be used to bound causal effects. All these constraints are characterized in terms of a new graphical separation criterion, providing an easy and intuitive method for their derivation.
How researchers see this paper
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- Ilya Shpitser
- Ricardo M. A. Silva
- Thomas S. Richardson
- Robin J. Evans
- Judea Pearl
- James M. Robins
- Jan Peters
- A. P. Dawid
Citations in the corpus
- Causal Inference through a Witness Protection Program (2014, methodology): “R code for all methods is available at http://www.homepages.ucl.ac.uk/∼ucgtrbd/wpp. and complement other methods to find subsets of useful constraints such as the graphical approach of Evans (2012).”
- Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, background): “The best known of these are the instrumental inequalities of Pearl (1995), which were generalized by Bonet (2001), Evans (2012) and Kédagni and Mourifie (2020).”
- Margins of discrete Bayesian networks (2015, background): “mplicated (Drton, 2009b). 34 Inequality constraints are generally much more complicated than equality constraints, and efforts to characterize them fully have been limited by computational challenges. Evans (2012), generalizing a result first given by Pearl (1995), provides a graphical criterion for o”