Causal inference

Causal inference is the project of drawing conclusions about cause and effect from data. It is not merely the study of correlation, association, or prediction. It is the attempt to answer what would happen if — the counterfactual question that underlies every intervention, every policy, every treatment, and every engineered system. The field has been transformed by two complementary but fundamentally different frameworks: the structural causal model tradition of Judea Pearl, which treats causality as a property of graphs and equations, and the potential outcomes tradition of Donald Rubin, which treats causality as a missing-data problem in which each unit has multiple potential outcomes, only one of which is observed.

The tension between these frameworks is not merely technical. It is ontological. Pearl's framework asks: what is the causal structure of the world? Rubin's framework asks: what is the causal effect of this treatment? The first is a question about the architecture of systems. The second is a question about the consequences of actions. They are related, but they are not the same question — and the methods that answer one do not necessarily answer the other.

The Graphical Approach: Structure as Causality

In Pearl's framework, causal inference begins with a directed acyclic graph (DAG) that encodes the investigator's assumptions about which variables influence which others. The DAG is not derived from data; it is supplied by the investigator, justified by background knowledge, and used to constrain what can be learned from data. The power of the framework lies in the do-calculus — a set of rules for determining when and how the causal effect of an intervention can be identified from observational data alone.

The do-calculus answers a precise question: given a causal graph and a joint probability distribution, can we compute P(Y | do(X)) — the probability of Y if we were to intervene on X — from P(Y | X) and the structure of the graph? The answer depends on whether the back-door paths between X and Y are blocked by conditioning on observed variables, whether front-door paths exist, and whether the graph structure admits an identification strategy at all. The Markov blanket of a variable in a Bayesian network is the set of variables that renders it independent of all others — a local separation that has global consequences for what can and cannot be inferred.

The graphical approach is powerful but brittle. It assumes that the causal graph is approximately correct, that the relevant variables have been measured, and that the system is acyclic — or that cycles can be handled by time-slicing. When these assumptions fail, the do-calculus produces nonsense with high confidence. The framework is a tool for systems that have been partially understood, not for systems that are genuinely mysterious.

The Dynamical Approach: Trajectories as Causality

An alternative to the graphical approach treats causality as a property of dynamical trajectories rather than static structure. Convergent Cross Mapping (CCM), developed by George Sugihara and colleagues, detects causality by asking whether the historical record of one variable contains enough information to reconstruct the state of another. If X causes Y, then the attractor of Y's reconstructed state space encodes information about X. If X does not cause Y, no such reconstruction is possible.

This approach does not require a DAG, an intervention, or even the ability to define variables independently. It is designed for systems where feedback loops dominate, where variables are tightly coupled, and where the notion of holding