Causal Discovery from Unseen Environments

Existing causal discovery methods for interventional data typically follow one of two paradigms: they either require explicit environment labels and known intervention targets, or, in the absence of such metadata, they rely on computationally intensive procedures such as first inferring intervention targets or employing complex models to account for the latent variables of environment labels. Surprisingly, we show that neither explicit environment labels nor auxiliary inference algorithms are strictly necessary: under certain conditions, the classical ICA-LiNGAM algorithm consistently recovers the causal graph from simply pooled interventional and observational data. We first demonstrate that in linear Gaussian structural equation models where interventions independently perturb the noise distributions across nodes, pooling produces exactly independent, non-Gaussian sources, the appropriate setting for Independent Component Analysis (ICA). Because the assumption of strictly independent interventions can be overly restrictive, we extend our analysis to the practical setting of single-node (atomic) interventions. While pooling atomic interventions induces the necessary non-Gaussianity, it also introduces source *dependence*, violating a core ICA assumption. However, theoretical analysis establishes that this dependence decays as $\mathcal{O}(1/n^2)$ with the number of variables $n$, whereas non-Gaussianity decays only as $\mathcal{O}(1/n)$. This yields a regime of mild misspecification at moderate $n$ where sources are near-independent yet sufficiently non-Gaussian for ICA to succeed. In synthetic experiments, where data is pooled across many different environments, our label-free approach matches or exceeds label-aware methods. On real-world data, our approach performs comparably to methods that explicitly require environment labels. Ultimately, our work challenges the assumed necessity of environment labels and complex inference mechanisms in interventional causal discovery and suggests a re-evaluation of the often-overlooked classical ICA-LiNGAM algorithm.