CAM: Causal additive models, high-dimensional order search and penalized regression

About

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.

Peter Bühlmann, Jonas Peters, Jan Ernest · 2013

Related benchmarks

Task	Dataset	Result
Causal Discovery	Synthetic Data	Runtime270.2	57
Causal Discovery	Sachs real-world data protein signaling network	SHD12	41
Causal Structure Learning	Sachs	SHD14	38
Causal Discovery	Tübingen	AUROC46.6	37
Bivariate Causal Discovery	AN	Accuracy100	33
Bivariate Causal Discovery	LS	Accuracy100	33
Bivariate Causal Discovery	Net	Accuracy78	33
Bivariate Causal Discovery	SIM	Accuracy59	33
Bivariate Causal Discovery	SIM-c	Accuracy59	33
Bivariate Causal Discovery	D4 s1	Accuracy42	33