Inferring Structural Causal Models from Data with Grammatical Evolution

Causal models allow representing complex systems by going beyond statistical correlations and explicitly capturing cause–effect relationships among variables. Structural causal models (SCMs) offer a rigorous formalism to describe causal models, encoding, in the form of equations systems, both the causal graph that specifies directional dependencies among variables and the functional mechanisms governing these relationships. Among SCMs, additive noise models (ANMs) include exogenous stochasticity, hence capturing noisy data. In practice, the underlying causal structure is rarely known a priori and must be inferred from data. This is a challenging task, as it requires jointly identifying the causal graph and the associated structural equations. We propose an evolutionary approach for learning SCMs from data. We express ANMs as probabilistic programs and use grammatical evolution for synthesizing them. Our contribution comprises a dedicated grammar, formally yielding ANMs, and a fitness function that accounts for (a) statistical adequacy of the candidate ANM with respect to the observed data, quantified via the likelihood, and quality of the causal structure, assessed by computing likelihoods under the candidate ANM when interventions are applied. (b) We assess experimentally our approach on five problems and show that it infers effective and simple causal models from data.