Valid Inference after Causal Discovery

Causal discovery and causal estimation are fundamental tasks in causal reasoning and decision-making. Causal discovery aims to identify the underlying structure of the causal problem, often in the form of a graphical representation which makes explicit which variables causally influence which other variables, while causal estimation aims to quantify the magnitude of the effect of one variable on another. These two goals frequently go hand in hand: quantifying causal effects requires adjustments that rely on either assuming or discovering the underlying graphical structure. Methodologies for causal discovery and causal estimation have mostly been developed separately, and the statistical challenges that arise when solving these problems jointly have largely been overlooked. Indeed, a naive black-box combination of causal discovery algorithms and standard inference methods for causal effects suffers from "double dipping." That is, classical confidence intervals, such as those used for linear regression coefficients, need no longer cover the target estimand if the causal structure is not fixed a priori but is estimated on the same data used to compute the intervals.