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.

我们提出了一种基于提升的方法来从观察数据中学习加法结构方程模型(SEMs)，重点研究确定变量之间因果顺序的理论方面。我们引入了一族基于任意回归技术的得分函数，并建立了一些必要条件，以一致地优选真实的因果顺序。我们的分析揭示了提前停止的提升在满足这些条件的同时，提供了一个一致的因果顺序得分函数。为了解决高维数据集带来的挑战，我们通过分量梯度下降在加法SEMs空间进行了适应。我们的模拟研究验证了我们在低维度下的理论结果，并证明我们的高维适应与最先进的方法相竞争。此外，它对超参数的选择表现出鲁棒性，使得该方法易于调整。

提升因果增加模型