A Robust Method to Discover Causal or Anticausal Relation

Understanding whether the data generative process follows causal or anticausal relations is important for many applications. Existing causal discovery methods struggle with high-dimensional perceptual data such as images. Moreover, they require well-labeled data, which may not be feasible due to measurement error. In this paper, we propose a robust method to detect whether the data generative process is causal or anticausal. To determine the causal or anticausal relation, we identify an asymmetric property: under the causal relation, the instance distribution does not contain information about the noisy class-posterior distribution. We also propose a practical method to verify this via a noise injection approach. Our method is robust to label errors and is designed to handle both large-scale and high-dimensional datasets effectively. Both theoretical analyses and empirical results on a variety of datasets demonstrate the effectiveness of our proposed method in determining the causal or anticausal direction of the data generative process.