标题： 因果正则化：样本内风险与样本外风险保证之间的权衡 显示英文标题

标题： Causal Regularization: On the trade-off between in-sample risk and out-of-sample risk guarantees

摘要： 近年来，引入了许多在实践中处理因果关系的方法，例如倾向得分匹配、PC算法和不变因果预测。 除了具有解释上的吸引力，因果模型提供了最佳的样本外预测保证。 在本文中，我们研究了从样本内数据中识别因果类似模型的问题，这些模型在从一组协变量预测目标变量时提供样本外风险保证。 与普通最小二乘法相比，普通最小二乘法在样本内风险上表现最佳但样本外保证有限，而因果模型则具有最佳的样本外保证，但在样本内风险上表现较差。 通过定义这些属性之间的权衡，我们引入了$\textit{causal regularization}$。 随着正则化的增加，它提供了在子样本中风险更稳定的估计量，但以增加整体样本内风险为代价。 增加的风险稳定性被证明可以带来样本外风险保证。 我们为所有模型提供了有限样本风险边界，并证明了交叉验证对于达到这些边界是充分的。 显示英文摘要

摘要： In recent decades, a number of ways of dealing with causality in practice, such as propensity score matching, the PC algorithm and invariant causal prediction, have been introduced. Besides its interpretational appeal, the causal model provides the best out-of-sample prediction guarantees. In this paper, we study the identification of causal-like models from in-sample data that provide out-of-sample risk guarantees when predicting a target variable from a set of covariates. Whereas ordinary least squares provides the best in-sample risk with limited out-of-sample guarantees, causal models have the best out-of-sample guarantees but achieve an inferior in-sample risk. By defining a trade-off of these properties, we introduce $\textit{causal regularization}$. As the regularization is increased, it provides estimators whose risk is more stable across sub-samples at the cost of increasing their overall in-sample risk. The increased risk stability is shown to lead to out-of-sample risk guarantees. We provide finite sample risk bounds for all models and prove the adequacy of cross-validation for attaining these bounds.