Abstract

Learning directionality between variables is crucial yet challenging, especially for mechanistic

relationships without a priori ordering assumptions. We propose a coefficient of asymmetry to quantify

directional asymmetry using Shannon’s entropy within a generative exposure mapping (GEM) framework. GEMs arise from experiments where a generative function g maps exposure X to outcome Y

through Y = g(X), extended to noise-perturbed GEMs as Y = g(X) + ϵ. Our approach considers a

rich class of generative functions while providing statistical inference for uncertainty quantification—a

gap in existing bivariate causal discovery techniques. We establish large-sample theoretical guarantees

through data-splitting and cross-fitting techniques, implementing fast Fourier transformation-based

density estimation to avoid parameter tuning. The methodology accommodates contamination in outcome measurements. Extensive simulations demonstrate superior performance compared to competing

causal discovery methods. Applied to epigenetic data examining DNA methylation and blood pressure

relationships, our method unveils novel pathways for cardiovascular disease genes FGF5 and HSD11B2.

This framework serves as a discovery tool for improving scientific research rigor, with GEM-induced

asymmetry representing a low-dimensional imprint of underlying causality.

Information

Preprint No.SS-2025-0236
Manuscript IDSS-2025-0236
Complete AuthorsSoumik Purkayastha, Peter Xuekun Song
Corresponding AuthorsSoumik Purkayastha
Emailssoumik@pitt.edu

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Acknowledgments

This work is supported by NSF DMS-2113564 and NIH R01ES033656 (for Song), and the

University of Michigan Rackham Predoctoral Fellowship (for Purkayastha). This research

was further supported in part by the University of Pittsburgh Center for Research Computing

and Data, RRID:SCR022735, through the resources provided. Specifically, this work used

the HTC cluster, which is supported by NIH award number S10OD028483.

Supplementary Materials

• Section I: Proofs.

• Section II: Behavior of ˆCX→Y in NPGEMs.

• Section III: Methylation Data Application.

• Section IV: Data-splitting and Cross-fitting.

• Section V: Resolving ambiguity in causal direction X →Y or Y →X when nature of

generative function is unknown.

• Section VI: Diagnostics.

Supplementary materials are available for download.