Keywords: causal discovery, independent component analysis, lingam, Jacobian
TL;DR: The Jacobian of the inference function mapping from observables to independent variables can be used to extract the causal graph for general nonlinear functional relationships.
Abstract: Today's methods for uncovering the causal relationship(s) from observational data either constrain the function class (linearity/additive noise) or the data. We make assumptions on the data to develop a framework for Causal Discovery (CD) that works for general non-linear dependencies. Similar to previous work, we use nonlinear Independent Component Analysis (ICA) to infer the underlying sources from the observed variables. Instead of using conditional independence tests to determine the causal directions, we rely on the Jacobian of the inference function; thus, generalizing LiNGAM's approach to the nonlinear case. We show that causal models resolve the permutation indeterminacy of ICA and prove that under strong identifiability, the inference function's Jacobian captures the sparsity structure of the causal graph. We demonstrate that our method can infer the causal graph on multiple synthetic data sets.