Dissecting Causal Mechanism Shifts via FANS: Function And Noise Separation

Identifying the drivers of causal mechanism shifts, distinguishing functional changes from noise alterations, termed dissection, is a critical yet under-explored problem in data science (e.g., biomedical science and manufacturing). This paper introduces a more general and unified framework, the function and noise separation (FANS) framework, that detects and dissects shifts in non-additive, non-linear Structural Causal Models (SCMs) beyond existing additive noise models. Our approach is grounded in a theoretical independence criterion, where function shifts induce a statistical dependence between a node's parents and residual noise. Building on this foundation, we develop a practical two-stage algorithm to efficiently detect and dissect these shifts without retraining. Furthermore, we address the complex challenge of simultaneous function and noise shifts, introducing a formal assumption to resolve their inherent non-identifiability. Our results are corroborated by simulations. Our code is available at https://github.com/MLAI-Yonsei/FANS/.

When data collected in two different settings shows a changed relationship between variables, the harder question is why it changed: either the underlying rule linking the variables changed, or the distribution of the noise, the random part not explained by that rule, changed. Telling these apart matters, since confusing one for the other can lead to misleading conclusions in fields such as biomedicine and manufacturing. We developed a method, called FANS, that separates these two causes for complex, nonlinear relationships that earlier approaches could not handle. We train a flexible model once on data from one setting, apply it to the new setting, and examine what is left unexplained; a simple statistical test on this leftover noise reveals which type of change occurred, with no retraining needed. We also study the harder case where the rule and the noise change at the same time, and establish when the two can still be told apart.