Causal discovery from Bayesian symbolic regression

Causal discovery from observational data is central to scientific reasoning, yet established constraint-based and score-based methods often recover only a Markov equivalence class and provide no signal in bivariate or strongly autocorrelated regimes typical in some areas of science. Here, we recast causal discovery as a Bayesian symbolic regression problem. Given a set of candidate parents for each target variable, the Bayesian symbolic regression samples closed-form expressions from a posterior over symbolic models. The fraction of sampled expressions in which each candidate variable appears defines a posterior inclusion probability that we use as the causal score. This replaces pointwise model selection by an ensemble of plausible mechanisms. We evaluate the method on coupled nonlinear bivariate dynamics, on the CauseMe benchmark suite spanning linear, chaotic, nonlinear, higher-dimensional and high-noise settings, and on a four-variable biogeoscience structural causal model under Gaussian, heavy-tailed and mixed-noise regimes. Our approach is competitive with, and often outperforms, specialized causal discovery algorithms. Additionally, the method returns closed-form mechanisms leading to explicit causality and interpretability.