Tell cause from effect: models and evaluation

Causal relationships differ from statistical relationships, and distinguishing cause from effect is a fundamental scientific problem that has attracted the interest of many researchers. Among causal discovery problems, discovering bivariate causal relationships is a special case. Causal relationships between two variables (“X causes Y” or “Y causes X”) belong to the same Markov equivalence class, and the well-known independence tests and conditional independence tests cannot distinguish directed acyclic graphs in the same Markov equivalence class. We empirically evaluated the performance of three state-of-the-art models for causal discovery in the bivariate case using both simulation and real-world data: the additive-noise model (ANM), the post-nonlinear (PNL) model, and the information geometric causal inference (IGCI) model. The performance metrics were accuracy, area under the ROC curve, and time to make a decision. The IGCI model was the fastest in terms of algorithm efficiency even when the dataset was large, while the PNL model took the most time to make a decision. In terms of decision accuracy, the IGCI model was susceptible to noise and thus performed well only under low-noise conditions. The PNL model was the most robust to noise. Simulation experiments showed that the IGCI model was the most susceptible to “confounding,” while the ANM and PNL models were able to avoid the effects of confounding to some degree.