Notions of counterfactual invariance (CI) have proven essential for predictors that are fair, robust, and generalizable in the real world. We propose graphical criteria that yield a sufficient condition for a predictor to be counterfactually invariant in terms of a conditional independence in the observational distribution. In order to learn such predictors, we propose a model-agnostic framework, called Counterfactually Invariant Prediction (CIP), building on the Hilbert-Schmidt Conditional Independence Criterion (HSCIC), a kernel-based conditional dependence measure. Our experimental results demonstrate the effectiveness of CIP in enforcing counterfactual invariance across various simulated and real-world datasets including scalar and multi-variate settings.

翻译：反事实不变性（CI）概念已被证明对于在实际应用中实现公平、鲁棒且具有泛化能力的预测器至关重要。我们提出了基于图模型的判断准则，该准则通过观测分布中的条件独立性给出了预测器满足反事实不变性的充分条件。为学习此类预测器，我们提出了一个与模型无关的框架——反事实不变预测（CIP），该框架基于希尔伯特-施密特条件独立性准则（HSCIC）——一种基于核函数的条件依赖性度量方法。实验结果表明，CIP在标量和多变量设置下的多种模拟及真实数据集上，均能有效强制执行反事实不变性。