lmps13.doc - Variable Definition and Causal Inference Peter Spirtes Carnegie-Mellon University Abstract In the last several decades a confluence of work

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Variable Definition and Causal Inference Peter Spirtes Carnegie-Mellon University Abstract In the last several decades, a confluence of work in the social sciences, philosophy, statistics, and computer science has developed a theory of causal inference using directed graphs. This theory typically rests either explicitly or implicitly on two major assumptions: Causal Markov Assumption: For a set of variables in which there are no hidden common causes, variables are independent of their non-effects conditional on their immediate causes. Causal Faithfulness Assumption: There are no independencies other than those entailed by the Causal Markov Assumption. A number of algorithms have been introduced into the literature that are asymptotically correct given these assumptions, together with various assumptions about how the data has been gathered. These algorithms do not generally address the problem of variables selection however. For example, are commonly used psychological traits such as extraversion, agreeableness, conscientiousness, etc. actually mixtures of different personality traits? In fMRI research, there are typically measurements of thousands of different tiny regions of the brain, which are then clustered into larger regions, and the causal relations among the larger regions are explored. Have the smaller regions been clustered into larger regions in the “right” way, or have functionally different regions of the brain been mixed together? In this paper I will consider the reasonableness of the basic assumptions, and in what ways causal inferences becomes more difficult when the set of random variables used to describe a given causal system is replaced by a different, but equivalent, set of random variables that serves as a redescription of the same causal system.
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Variable Definition and Causal Inference Peter Spirtes 1 Professor, Department of Philosophy Carnegie-Mellon University 1 Introduction In the last several decades, a confluence of work in the social sciences, philosophy, statistics, and computer science has developed a theory of causal inference using directed graphs. This theory typically rests either explicitly or implicitly on two major assumptions: Causal Markov Assumption: For a set of variables in which there are no hidden common causes, variables are independent of their non-effects conditional on their immediate causes. Causal Faithfulness Assumption: There are no independencies other than those entailed by the Causal Markov Assumption. A number of algorithms have been introduced into the literature that are asymptotically correct given these assumptions, together with various assumptions about how the data has been gathered. These algorithms do not generally address the problem of variables selection however. For example, are commonly used psychological traits such as extraversion, agreeableness, conscientiousness, etc. actually mixtures of different personality traits? In fMRI research, there are typically measurements of thousands of
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  • Spring '16
  • Aryca Arizaga Marron

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