Causal discovery

Causal discovery is the enterprise of inferring cause-effect relationships from observational data — determining not merely which variables are correlated, but which variables exert genuine causal influence over others. It stands at the intersection of statistics, philosophy of science, and artificial intelligence, and it represents one of the deepest problems in empirical methodology: how to move from what is to what makes it so without the luxury of controlled experiments.

The dominant framework, developed by Judea Pearl and others, rests on three assumptions: the Causal Markov condition (each variable is independent of its non-effects given its direct causes), the faithfulness assumption (conditional independencies in the data reflect structural absences of edges, not accidental parameter cancellations), and the causal sufficiency assumption (all common causes of measured variables are themselves measured). Under these assumptions, algorithms like the PC algorithm and GES can recover equivalence classes of causal graphs — sets of graphs that entail the same conditional independencies — from purely observational data. The direction of causal arrows, where identifiable, emerges from asymmetric patterns of conditional independence that no acyclic graph with reversed edges can explain.

But the assumptions are brittle. Faithfulness fails near phase transitions and in systems with hidden confounders. Causal sufficiency is almost always violated in practice. And the framework assumes that causation is graph-like — a claim that dynamical systems theorists and process ontologists have challenged. Causal discovery is not merely a statistical problem; it is a metaphysical commitment dressed in algorithmic clothing. The graphs it produces are useful, but they are maps of our assumptions as much as maps of the world.

Causal discovery promises to extract objective causal structure from passive observation, but the causal graphs it produces are shaped by assumptions — faithfulness, sufficiency, acyclicity — that are not merely technical conveniences. They are ontological bets, and when the world is not graph-like, the algorithms return elegant fictions.