TY - JOUR
T1 - Segregated graphs and marginals of chain graph models
AU - Shpitser, Ilya
N1 - Funding Information:
The author would like to thank Thomas Richardson for suggesting mixed graphs where - and edges do not meet as interesting objects to think about, and Elizabeth Ogburn and Eric Tchetgen Tchetgen for clarifying discussions of interference. This work was supported in part by an NIH grant R01 AI104459-01A1.
PY - 2015
Y1 - 2015
N2 - Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) generalizes both Bayesian networks and MRFs, and can represent asymmetric and symmetric relationships together. As in other graphical models, the set of marginals from distributions in a chain graph model induced by the presence of hidden variables forms a complex model. One recent approach to the study of marginal graphical models is to consider a well-behaved supermodel. Such a supermodel of marginals of Bayesian networks, defined only by conditional independences, and termed the ordinary Markov model, was studied at length in [6]. In this paper, we show that special mixed graphs which we call segregated graphs can be associated, via a Markov property, with supermodels of marginals of chain graphs defined only by conditional independences. Special features of segregated graphs imply the existence of a very natural factorization for these supermodels, and imply many existing results on the chain graph model, and the ordinary Markov model carry over. Our results suggest that segregated graphs define an analogue of the ordinary Markov model for marginals of chain graph models. We illustrate the utility of segregated graphs for analyzing outcome interference in causal inference via simulated datasets.
AB - Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) generalizes both Bayesian networks and MRFs, and can represent asymmetric and symmetric relationships together. As in other graphical models, the set of marginals from distributions in a chain graph model induced by the presence of hidden variables forms a complex model. One recent approach to the study of marginal graphical models is to consider a well-behaved supermodel. Such a supermodel of marginals of Bayesian networks, defined only by conditional independences, and termed the ordinary Markov model, was studied at length in [6]. In this paper, we show that special mixed graphs which we call segregated graphs can be associated, via a Markov property, with supermodels of marginals of chain graphs defined only by conditional independences. Special features of segregated graphs imply the existence of a very natural factorization for these supermodels, and imply many existing results on the chain graph model, and the ordinary Markov model carry over. Our results suggest that segregated graphs define an analogue of the ordinary Markov model for marginals of chain graph models. We illustrate the utility of segregated graphs for analyzing outcome interference in causal inference via simulated datasets.
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M3 - Conference article
AN - SCOPUS:84965127235
SN - 1049-5258
VL - 2015-January
SP - 1720
EP - 1728
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 29th Annual Conference on Neural Information Processing Systems, NIPS 2015
Y2 - 7 December 2015 through 12 December 2015
ER -