2025/01/31 by Frederik Hytting Jørgensen, Jørgensen, Frederik Hytting, Luigi Gresele +3 · 3 citations
Arts and Humanities · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Philosophy and History of Science #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2501.19335
openalex publication_date 2025/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which interventions in the model. For example, to interpret an action as an intervention on a treatment variable, the action will presumably have to a) change the distribution of treatment in a way that corresponds to the intervention, and b) not change other aspects, such as how the outcome depends on the treatment; while the marginal distributions of some variables may change as an effect. We introduce a formal framework to make such requirements for different interpretations of actions as interventions precise. We prove that the seemingly natural interpretation of actions as interventions is circular: Under this interpretation, every causal Bayesian network that correctly models the observational distribution is trivially also interventionally valid, and no action yields empirical data that could possibly falsify such a model. We prove an impossibility result: No interpretation exists that is non-circular and simultaneously satisfies a set of natural desiderata. Instead, we examine non-circular interpretations that may violate some desiderata and show how this may in turn enable the falsification of causal models. By rigorously examining how a causal Bayesian network could be a 'causal' model of the world instead of merely a mathematical object, our formal framework contributes to the conceptual foundations of causal representation learning, causal discovery, and causal abstraction, while also highlighting some limitations of existing approaches.