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# A Note on Cyclic Graphs and Dynamical Feedback Systems

*Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics*, PMLR R1:421-428, 1997.

#### Abstract

Directed acyclic graphical (DAG) models were motivated in large part by the desire to have a general formalism to represent causal hypotheses and the restrictions on probability distributions they imply. DAG models exploited a fundamental kinship in a variety of statistical formalisms often treated as distinct "models": factor models, structural equation models, regression models, logistic regression models, survival models, etc. The fundamental connection is through either of two equivalent (for DAGs) properties, a "local" Markov condition, or the property of d-separation, sometimes called the "global" Markov condition. (Pearl 1988, Lauritzen et al. 1990). In much the same spirit, directed cyclic graphs (DCGs) have been introduced to represent the causal ·structure of feedback processes and the restrictions on probability distributions those structures imply. Developments in our understanding of DCGs have proceeded so rapidly that it is appropriate to consider the prospects and limitations of cyclic representations of feedback systems. (For an alternative approach to extending graphical models to the temporal domain see Aliferis and Cooper, 1996)