Residual-Based Causal Discovery via Pretrained In-Context Quantile Regression

Residual-based causal discovery assumes that each variable is generated from its parents and an independent noise source. It estimates this noise and tests its independence from candidate causes. For identifiable functions such as additive-noise models (ANMs) and the broader class of location-scale noise models (LSNMs), this principle identifies the causal direction, as only the causal model admits this independence. Existing LSNM methods rely on parametric assumptions to obtain standardized residuals, risking model misspecification. In contrast, the RESIT-framework allows for nonparametric estimation of residuals to iteratively identify sink nodes, but was proposed for ANMs. To close this gap, we propose Loscar, an extension of RESIT to LSNMs that estimates the conditional mean and scale via quantile regression, enabling pretrained tabular foundation models as plug-in estimators. We compare it with a feasible generalized least squares (FGLS) variant, which is consistent given suitable basis functions. Across bivariate and multivariate causal-discovery benchmarks, in-context quantile regression substantially outperforms FGLS with flexible function classes, particularly for multivariate causes.