Boosting Causal Additive Models
This work addresses the challenge of causal inference in high-dimensional data for researchers in statistics and machine learning, representing an incremental improvement with theoretical backing.
The authors tackled the problem of learning additive Structural Equation Models (SEMs) from observational data by developing a boosting-based method that establishes theoretical conditions for consistent causal ordering and adapts it for high-dimensional settings. Their simulation results showed competitive performance with state-of-the-art methods and robustness in hyperparameter tuning.
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.