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


Conference Paper


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.

Author(s): Zscheischler, J. and Janzing, D. and Zhang, K.
Pages: 839-847
Year: 2011
Month: July
Day: 0
Editors: Cozman, F.G. , A. Pfeffer
Publisher: AUAI Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011)
Event Place: Barcelona, Spain

Address: Corvallis, OR, USA
Digital: 0
ISBN: 978-0-9749039-7-2

Links: PDF


  title = {Testing whether linear equations are causal: A free probability theory approach},
  author = {Zscheischler, J. and Janzing, D. and Zhang, K.},
  pages = {839-847},
  editors = {Cozman, F.G. , A. Pfeffer},
  publisher = {AUAI Press},
  address = {Corvallis, OR, USA},
  month = jul,
  year = {2011},
  month_numeric = {7}