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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 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.
