A Critical View of the Structural Causal Model
This work addresses causal inference for researchers, offering a novel perspective that challenges traditional structural causal models, though it appears incremental in building on complexity-based approaches.
The paper tackles causal direction identification by proposing that cause-effect decisions may rely on variable complexity rather than causality, showing that comparing autoencoder reconstruction errors performs well on benchmarks. In multivariate cases, their adversarial training method fits data only in the causal direction and outperforms existing methods on synthetic and real datasets.
In the univariate case, we show that by comparing the individual complexities of univariate cause and effect, one can identify the cause and the effect, without considering their interaction at all. In our framework, complexities are captured by the reconstruction error of an autoencoder that operates on the quantiles of the distribution. Comparing the reconstruction errors of the two autoencoders, one for each variable, is shown to perform surprisingly well on the accepted causality directionality benchmarks. Hence, the decision as to which of the two is the cause and which is the effect may not be based on causality but on complexity. In the multivariate case, where one can ensure that the complexities of the cause and effect are balanced, we propose a new adversarial training method that mimics the disentangled structure of the causal model. We prove that in the multidimensional case, such modeling is likely to fit the data only in the direction of causality. Furthermore, a uniqueness result shows that the learned model is able to identify the underlying causal and residual (noise) components. Our multidimensional method outperforms the literature methods on both synthetic and real world datasets.