Measurement Error and Causal Discovery

Algorithms for causal discovery emerged in the early 1990s and have since proliferated [4, 10]. After directed acyclic graphical representations of causal structures (causal graphs) were connected to conditional independence relations (the Causal Markov Condition1 and dseparation2), graphical characterizations of Markov equivalence classes of causal graphs (patterns) soon followed, along with pointwise consistent algorithms to search for patterns. Researchers in Philosophy, Statistics, and Computer Science have produced constraint-based algorithms, score-based algorithms, information-theoretic algorithms, algorithms for linear models with non-Gaussian errors, algorithms for systems that involve causal feedback, algorithms for equivalence classes that contain unmeasured common causes, algorithms for time-series, algorithms for handling both experimental and non-experimental data, algorithms for dealing with datasets that overlap on a proper subset of their variables, and algorithms for discovering the measurement model structure for psychometric models involving dozens of “indicators”. In many cases we have proofs of the asymptotic reliability of these algorithms, and in almost all cases we have simulation studies that give us some sense of the finite-sample accuracy of these algorithms. The FGES algorithm (Fast Greedy Equivalence Search, [6]), which we feature here, is highly accurate in a wide variety of circumstances and is computationally tractable on a million variables for sparse graphs. Many algorithms have been applied to serious scientific problems like distinguishing between Autistic and neurotypical subjects from fMRI data [2], and interest in the field seems to be exploding.