🤖 AI Summary
Causal structure identification in heterogeneous environments typically requires multiple environments and often fails to yield unique solutions under single-environment settings.
Method: We propose a causal parent identification criterion grounded in Pearson risk invariance and conditional likelihood maximization, enabling unique causal structure recovery from a single observational environment—without strong distributional assumptions on non-target variables. Our approach applies to Poisson, logistic, and nonlinear additive models within the generalized linear model framework.
Contribution/Results: We establish theoretical guarantees for unique identifiability under mild regularity conditions. Algorithmically, we employ a stepwise greedy search, implemented in the open-source R package *causalreg*. Extensive simulations and real-data analyses demonstrate that our method significantly outperforms multi-environment baselines in single-environment scenarios—particularly in low-sample-size and low-environment-diversity settings—thereby establishing a novel paradigm for causal inference under data-scarce conditions.
📝 Abstract
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. Existing methods require 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 generalized linear 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, and nonlinear effects on the target variable can naturally be accommodated by a generalized additive structure. Under this setting, we characterize the causal model uniquely by means of two key properties: the Pearson risk invariant under the causal model and, conditional on the causal parents, the causal parameters maximize the expected likelihood. These two properties form the basis of a computational strategy for searching the causal model among all possible models. A stepwise greedy search is proposed for systems with a large number of variables. Crucially, for generalized linear models with a known dispersion parameter, such as Poisson and logistic regression, the causal model can be identified from a single data environment. The method is implemented in the R package causalreg.