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

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Zscheischler,  Jakob
IMPRS International Max Planck Research School for Global Biogeochemical Cycles, Max Planck Institute for Biogeochemistry, Max Planck Society;

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Citation

Zscheischler, J., Janzing, D., & Zhang, K. (2011). Testing whether linear equations are causal: A free probability theory approach. In Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI). AUAI Press.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0018-1819-B
Abstract
We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal in- uence 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.