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Published June 2016 | Published
Book Section - Chapter Open

Stability of Causal Inference


We consider the sensitivity of causal identification to small perturbations in the input. A long line of work culminating in papers by Shpitser and Pearl (2006) and Huang and Valtorta (2008) led to a complete procedure for the causal identification problem. In our main result in this paper, we show that the identification function computed by these procedures is in some cases extremely unstable numerically. Specifically, the "condition number" of causal identification can be of the order of Ω(exp(n ^(0.49))) on an identifiable semiMarkovian model with n visible nodes. That is, in order to give an output accurate to d bits, the empirical probabilities of the observable events need to be obtained to accuracy d + Ω(n ^(0.49)) bits.

Additional Information

This research was supported by NSF grant CCF-1319745. We thank the reviewers for helpful comments.

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