CAM: Causal additive models, high-dimensional order search and penalized regression
This work addresses causal inference in high-dimensional settings, offering a more efficient approach for researchers in statistics and machine learning, though it appears incremental as it builds on existing methods like sparse regression.
The paper tackles the problem of estimating high-dimensional additive structural equation models by decoupling order search from edge selection, simplifying structure search and estimation. It establishes consistency for low- and high-dimensional scenarios and demonstrates accuracy on simulated and real data.
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structure search and estimation for an important class of causal models. We establish consistency of the (restricted) maximum likelihood estimator for low- and high-dimensional scenarios, and we also allow for misspecification of the error distribution. Furthermore, we develop an efficient computational algorithm which can deal with many variables, and the new method's accuracy and performance is illustrated on simulated and real data.