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Discovering underlying structures of causal relations from observationalstudies poses a great challenge in scientific research where randomized trialsor intervention-based studies are infeasible. This challenge pertains to thelack of knowledge on pre-specified roles of cause and effect in observationsstudies. Leveraging Shannon's seminal work on information theory, we propose anew conceptual framework of asymmetry where any causal link between putativecause and effect is captured by unequal information flows from one variable toanother. We present an entropy-based asymmetry coefficient that not onlyenables us to assess for whether one variable is a stronger predictor of theother, but also detects an imprint of the underlying causal relation inobservational studies. Our causal discovery analytics can accommodatelow-dimensional confounders naturally. The proposed methodology relies onscalable non-parametric density estimation using fast Fourier transformation,making the resulting estimation method manyfold faster than the classicalbandwidth-based density estimation while maintaining comparable mean integratedsquared error rates. We investigate key asymptotic properties of ourmethodology and utilize a data-splitting and cross-fitting technique tofacilitate inference for the direction of causal relations. We illustrate theperformance of our methodology through simulation studies and real dataexamples.

Generative causality: using Shannon's information theory to infer underlying asymmetry in causal relations