Testing whether linear equations are causal: A free probability theory approach
arXiv:1202.3779
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.
References in corpus (13)
- Discussion of "Least angle regression" by Efron et al
- Rejoinder to "Least angle regression" by Efron et al
- Least Angle Regression
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Discussion of "Least angle regression" by Efron et al
- Inferring deterministic causal relations
- Gaussian Process Networks
- Telling cause from effect based on high-dimensional observations
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- Latent Instrumental Variables as Priors in Causal Inference based on Independence of Cause and Mechanism
- Detecting confounding in multivariate linear models via spectral analysis
- Independent mechanism analysis, a new concept?
- Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations