Journal Article

CAM: CAUSAL ADDITIVE MODELS, HIGH-DIMENSIONAL ORDER SEARCH AND PENALIZED REGRESSION

Bühlmann, Peter, Peters, Jonas, Ernest, Jan

2014

Overview

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.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 62G99 / 62H99 / 68T99 / Additivity / Causality / Consistent estimators / Decision making models / Directed acyclic graphs / Error rates / Estimating techniques / Estimation methods / Graphical modeling / Identifiability / intervention calculus / Machine learning / Maximum likelihood estimation / Maximum likelihood estimators / Maximum likelihood method / nonparametric regression / Probability distribution / Regression analysis / regularized estimation / sparsity / structural equation model / Structural equation models / Studies