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  Testing whether linear equations are causal: A free probability theory approach

Zscheischler, J., Janzing, D., & Zhang, K. (2011). Testing whether linear equations are causal: A free probability theory approach. In 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011) (pp. 839-847). Corvallis, OR, USA: AUAI Press.

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 Creators:
Zscheischler, J1, Author           
Janzing, D2, Author           
Zhang, K1, Author           
Cozman A. Pfeffer, F.G., Editor
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 Abstract: We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where the dimension of the observed variables exceeds the sample size. Based on previous work, we postulate conditions that characterize a causal relation between X and Y . Moreover, we describe a statistical test and argue that both causal directions are typically rejected if there is a common cause. A full theoretical analysis is presented for the deterministic case but our approach seems to be valid for the noisy case, too, for which we additionally present an approach based on a sparsity constraint. The discussed method yields promising results for both simulated and real world data.

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 Dates: 2011-07
 Publication Status: Issued
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 Rev. Type: -
 Identifiers: ISBN: 978-0-9749039-7-2
URI: http://www.auai.org/uai2011/
BibTex Citekey: ZscheischlerJZ2011
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Title: 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011)
Place of Event: Barcelona, Spain
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Title: 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011)
Source Genre: Proceedings
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Publ. Info: Corvallis, OR, USA : AUAI Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 839 - 847 Identifier: -