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Error probabilities for inference of causal directions

Zhang, Jiji (2008) Error probabilities for inference of causal directions. Synthese, 163 (3). pp. 409-418. ISSN 0039-7857. doi:10.1007/s11229-007-9295-1.

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A main message from the causal modelling literature in the last several decades is that under some plausible assumptions, there can be statistically consistent procedures for inferring (features of) the causal structure of a set of random variables from observational data. But whether we can control the error probabilities with a finite sample size depends on the kind of consistency the procedures can achieve. It has been shown that in general, under the standard causal Markov and Faithfulness assumptions, the procedures can only be pointwise but not uniformly consistent without substantial background knowledge. This implies the impossibility of choosing a finite sample size to control the worst case error probabilities. In this paper, I consider the simpler task of inferring causal directions when the skeleton of the causal structure is known, and establish a similarly negative result concerning the possibility of controlling error probabilities. Although the result is negative in form, it has an interesting positive implication for causal discovery methods.

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Additional Information:© 2008 Springer Science+Business Media B.V. Received 9 November 2007. Accepted: 9 November 2007. Published online: 19 February 2008.
Subject Keywords:Bayesian network; Causal inference; Consistency; Error probability
Issue or Number:3
Record Number:CaltechAUTHORS:20100510-151847788
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Official Citation:Zhang, J. Synthese (2008) 163: 409.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18226
Deposited By: Ruth Sustaita
Deposited On:10 May 2010 22:50
Last Modified:08 Nov 2021 23:42

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