RCDi: Robust Causal Direction Inference Using INUS-Inspired Asymmetry with the Solomonoff Prior

Investigating causal interactions between entities is a crucial task across various scientific domains. The traditional causal discovery methods often assume a predetermined causal direction, which is problematic when prior knowledge is insufficient. Identifying causal directions from observational data remains a key challenge. Causal discovery typically relies on two priors: the uniform prior and the Solomonoff prior. The Solomonoff prior theoretically outperforms the uniform prior in determining causal directions in bivariate scenarios by using the causal independence mechanism assumption. However, this approach has two main issues: it assumes that no unobserved variables affect the outcome, leading to method failure if violated, and it relies on the uncomputable Kolmogorov complexity (KC). In addition, we employ Kolmogorov’s structure function to analyze the use of the minimum description length (MDL) as an approximation for KC, which shows that the function class used for computing the MDL introduces prior biases, increasing the risk of misclassification. Inspired by the insufficient but necessary part of an unnecessary but sufficient condition (INUS condition), we propose an asymmetry where the expected complexity change in the cause, due to changes in the effect, is greater than the reverse. This criterion supplements the causal independence mechanism when its restrictive conditions are not met under the Solomonoff prior. To mitigate prior bias and reduce misclassification risk, we introduce a multilayer perceptron based on the universal approximation theorem as the backbone network, enhancing method stability. Our approach demonstrates a competitive performance against the SOTA methods on the TCEP real dataset. Additionally, the results on synthetic datasets show that our method maintains stability across various data generation mechanisms and noise distributions. This work advances causal direction determination research by addressing the limitations of the existing methods and offering a more robust and stable approach.