Causal Discovery via Transformed Low-Rank Quantile Surfaces
This research introduces a new method for causal discovery that is particularly effective for complex, non-linear data scenarios, which could be useful for researchers working on data analysis and machine learning.
A new bivariate causal model called Low-Rank Quantile Surfaces (LRQS) is proposed. It uses a low-rank functional decomposition for an unknown monotone transformation of the conditional quantile surface in the causal direction. LRQS is shown to be effective for synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, outperforming standard location-scale assumptions in such cases.
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.