Identifying Causal Direction via Variational Bayesian Compression

Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic Markov condition, which postulates that the joint distribution, when factorized according to the causal direction, yields a more succinct codelength compared to the anti-causal direction. Previous approaches approximate these codelengths by relying on simple functions or Gaussian processes (GPs) with easily evaluable complexity, compromising between model fitness and computational complexity. To overcome these limitations, we propose leveraging the variational Bayesian learning of neural networks as an interpretation of the codelengths. Consequently, we can enhance the model fitness while promoting the succinctness of the codelengths, while avoiding the significant computational complexity of the GP-based approaches. Extensive experiments on both synthetic and real-world benchmarks in cause-effect identification demonstrate the effectiveness of our proposed method, surpassing the overall performance of related complexity-based and structural causal model regression-based approaches.