Generalised Causal Dantzig

Prediction invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery, typically focussing on recovering the causal parents of a target variable of interest. When instrumental variables are not available, the causal Dantzig estimator exploits invariance under the more restrictive case of shift interventions. However, also in this case, one requires observational data from a number of sufficiently different environments, which is rarely available. In this paper, we consider a structural equation model where the target variable is described by a generalised additive model conditional on its parents. Besides having finite moments, no modelling assumptions are made on the conditional distributions of the other variables in the system. Under this setting, we characterise the causal model uniquely by means of two key properties: the Pearson residuals are invariant under the causal model and conditional on the causal parents the causal parameters maximise the population likelihood. These two properties form the basis of a computational strategy for searching the causal model among all possible models. Crucially, for generalised linear models with a known dispersion parameter, such as Poisson and logistic regression, the causal model can be identified from a single data environment.