Boosting Causal Additive Models
Maximilian Kertel Nadja Klein
We present a boosting-based method to learn additive Structural Equation
Models (SEMs) from observational data, with a focus on the theoretical aspects
of determining the causal order among variables. We introduce a family of score
functions based on arbitrary regression techniques, for which we establish
necessary conditions to consistently favor the true causal ordering. Our
analysis reveals that boosting with early stopping meets these criteria and
thus offers a consistent score function for causal orderings. To address the
challenges posed by high-dimensional data sets, we adapt our approach through a
component-wise gradient descent in the space of additive SEMs. Our simulation
study underlines our theoretical results for lower dimensions and demonstrates
that our high-dimensional adaptation is competitive with state-of-the-art
methods. In addition, it exhibits robustness with respect to the choice of the
hyperparameters making the procedure easy to tune.