Low-rank quantile surfaces improve detecting cause and effect
Causal Discovery via Transformed Low-Rank Quantile Surfaces
Artificial IntelligenceMachine Learning
Summary
Finding out if one thing causes another is often tricky when the relationship is complex or noisy. The authors propose a method called Low-Rank Quantile Surfaces (LRQS) that looks at how parts of the outcome distribution change and uses a special transformation to identify cause and effect. Their approach works better than previous ones when the data follows complicated patterns or distortions beyond simple shifts or scale changes. They tested LRQS on simulated and standard datasets and showed it reliably detects causal directions in such complex cases.
What this means in practice
- •For data analysts in finance: Identify causal links between financial indicators when their relationships involve complex distribution changes and nonlinear effects.
- •For healthcare data engineers: Improve detection of causal directions in patient data where measurement noise and condition effects vary nonlinearly across groups.
Authors
Ryo Kamimura, Thong Pham
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.