A note on the correctness of the causal ordering algorithm

  • Authors:
  • Denver Dash;Marek J. Druzdzel

  • Affiliations:
  • Intel Research Pittsburgh, 4720 Forbes Avenue, Pittsburgh, PA 15213, USA and Department of Biomedical Informatics, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15260, USA;Decision Systems Laboratory, School of Information Sciences and Intelligent Systems Program, University of Pittsburgh, Pittsburgh, PA 15260, USA and Faculty of Computer Science, Białystok Tec ...

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2008

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Abstract

In this paper we examine in detail the algorithm of Simon [H.A. Simon, Causal ordering and identifiability, in: W.C. Hood, T.C. Koopmans (Eds.), Studies in Econometric Method. Cowles Commission for Research in Economics, Monograph No. 14, John Wiley & Sons, Inc., New York, 1953, pp. 49-74, Chapter III], called the causal ordering algorithm (COA), used for constructing the ''causal ordering'' of a system given a complete specification of the system in terms of a set of ''structural'' equations that govern the variables in the system. This algorithm constructs a graphical characterization of the model in a form that we call a partial causal graph. Simon argued in [H.A. Simon, Causal ordering and identifiability, in: W.C. Hood, T.C. Koopmans (Eds.), Studies in Econometric Method. Cowles Commission for Research in Economics, Monograph No. 14, John Wiley & Sons, Inc., New York, 1953, pp. 49-74, Chapter III] and subsequent papers that a graph so generated explicates causal structure among variables in the model. We formalize this claim further by proving that any causal model based on a one-to-one correspondence between equations and variables must be consistent with the COA.