Jacobian-Based Causal Discovery with Nonlinear ICA

Abstract

Today's methods for uncovering causal relationships from observational data either constrain functional assignments (linearity/additive noise assumptions) or the data generating process (e.g., non-i.i.d. assumptions). Unlike previous works, which use conditional independence tests, we rely on the inference function's Jacobian to determine nonlinear cause-effect relationships. We prove that, under strong identifiability, the inference function's Jacobian captures the sparsity structure of the causal graph; thus, generalizing the classic LiNGAM method to the nonlinear case. We use nonlinear Independent Component Analysis (ICA) to infer the underlying sources from the observed variables and show how nonlinear ICA is compatible with causal discovery via non-i.i.d data. Our approach avoids the cost of exponentially many independence tests and makes our method end-to-end differentiable. We demonstrate that the proposed method can infer the causal graph on multiple synthetic data sets, and in most scenarios outperforms previous work.