Inferring deterministic causal relations
This addresses the challenge of determining causal direction in deterministic systems, which is incremental as it extends prior work on noisy cases to noise-free settings.
The paper tackles the problem of causal inference in deterministic (noise-free) scenarios by exploiting asymmetries between variables related by an invertible function, showing that the distribution of the effect depends on the function when the cause's density is chosen independently, and reports strong empirical results on real-world datasets.
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.