Causal Discovery via Transformed Low-Rank Quantile Surfaces

Abstract:We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface is low rank in the causal direction, whereas reverse representability under the corresponding constraints occurs only for exceptional, fine-tuned cause marginals. We provide a simple-yet-powerful causal score using a nonparametric fitting procedure that alternates between rank-constrained approximation of discretized quantile surfaces and isotonic estimation of the unknown monotone transformation. Experiments on synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, together with standard bivariate benchmarks, show that LRQS is especially effective when conditional distributional shape or observation distortion goes beyond existing location-scale assumptions.

Methodology (stat.ME); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2609.16931 [stat.ME]

(or arXiv:2609.16931v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2609.16931 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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