Abstract
AbstractAn intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can represent both interference and non-interference relationships for Gaussian distributions. Specifically, we define the new class of models, introduce global and local and pairwise Markov properties for them, and prove their equivalence. We also propose an algorithm for maximum likelihood parameter estimation for the new models, and report experimental results. Finally, we show how to compute the effects of interventions in the new models.
Highlights
We propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can represent both interference and non-interference relationships for Gaussian distributions
LWF chain graph (CG) have been extended into segregated graphs, which have been shown to be suitable for representing causal models with interference [21]
We have shown how to combine LWF and AMP CGs to represent causal models of domains with both interference and non-interference relationships
Summary
Graphical models are among the most studied and used formalisms for causal inference. G., a virus) remains unaltered and, so does the risk of infecting the other This model is not correct: In reality, the mother’s healthy carrier gene protects her but has no protective effect on the child, and vice versa This non-interference relation is not represented by the model. It is possible to describe how UCGs exactly model interference in the Gaussian case Works such as Ogburn et al [12], Shpitser [21], Shpitser et al [22], and Tchetgen et al [27] use LWF CGs to model interference and compute some causal effect of interest. The formal proofs of all the results are contained in Appendix A
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