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This research introduces novel statistical methods, Anticipated Asymmetric Geometries and Monotonicity Index, to determine causal directionality in bivariate data without relying on pre-existing domain knowledge. By evaluating various distance metrics and optimizing hyperparameters through a Design of Experiment, the study demonstrates that its proposed approach outperforms existing benchmarks like GRCI and CAREFL-H on real-world datasets. The findings offer a deterministic framework for inferring causation, which is essential for building more robust causal inference models in machine learning systems.
Identification of Bivariate Causal Directionality Based on Anticipated Asymmetric Geometries
arXiv:2603.26024v2 Announce Type: replace Abstract: Identification of causal directionality in bivariate numerical data is a fundamental research problem with important practical implications. This paper presents two alternative methods to identify direction of causation by considering conditional distributions: (1) Anticipated Asymmetric Geometries (AAG) and (2) Monotonicity Index (MI). The AAG method compares the actual conditional distributions to anticipated ones along two variables. Different comparison metrics, such as Pearson correlation, cosine distance, Jaccard index, K-L divergence, K-S distance, MAE, MSE, and mutual information have been evaluated. Anticipated distributions have been projected as normal based on dual response statistics: mean and standard deviation. The MI method compares the calculated monotonicity indexes of the gradients of conditional distributions along two axes and exhibits counts of gradient sign changes. Both methods assume stochastic properties of the bivariate data and exploit anticipated unimodality of conditional distributions of the effect. The proposed methods are straightforward and include only a limited number of hyperparameters that affect the accuracy of the identification. For a given set of hyperparameters, both the AAG and MI methods provide a unique, deterministic solution. To address sensitivity to hyperparameters, tuning has been done by utilizing a full factorial Design of Experiment. It turns out that the AAG method outperforms MI, achieving top weighted accuracies of 81.4% with simple tuning and 84.3% with size-adaptive tuning, compared with 81.6% for GRCI or 82.0% for CAREFL-H on the 99 pairs of the Tubingen real-world cause-effect examples. A decision tree has been fitted to distinguish misclassified cases using the input data's symmetrical bivariate statistics to address the question of: How decisive is the identification method of causal directionality?
arXiv:2603.26024 (cs)
Abstract:Identification of causal directionality in bivariate numerical data is a fundamental research problem with important practical implications. This paper presents two alternative methods to identify direction of causation by considering conditional distributions: (1) Anticipated Asymmetric Geometries (AAG) and (2) Monotonicity Index (MI). The AAG method compares the actual conditional distributions to anticipated ones along two variables. Different comparison metrics, such as Pearson correlation, cosine distance, Jaccard index, K-L divergence, K-S distance, MAE, MSE, and mutual information have been evaluated. Anticipated distributions have been projected as normal based on dual response statistics: mean and standard deviation. The MI method compares the calculated monotonicity indexes of the gradients of conditional distributions along two axes and exhibits counts of gradient sign changes. Both methods assume stochastic properties of the bivariate data and exploit anticipated unimodality of conditional distributions of the effect. The proposed methods are straightforward and include only a limited number of hyperparameters that affect the accuracy of the identification. For a given set of hyperparameters, both the AAG and MI methods provide a unique, deterministic solution. To address sensitivity to hyperparameters, tuning has been done by utilizing a full factorial Design of Experiment. It turns out that the AAG method outperforms MI, achieving top weighted accuracies of 81.4% with simple tuning and 84.3% with size-adaptive tuning, compared with 81.6% for GRCI or 82.0% for CAREFL-H on the 99 pairs of the Tubingen real-world cause-effect examples. A decision tree has been fitted to distinguish misclassified cases using the input data's symmetrical bivariate statistics to address the question of: How decisive is the identification method of causal directionality?
Machine Learning (cs.LG); Logic in Computer Science (cs.LO)
arXiv:2603.26024 [cs.LG]
(or arXiv:2603.26024v2 [cs.LG] for this version)
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