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）的概念已被证明对于实现公平、鲁棒且可泛化至现实世界的预测器至关重要。我们提出了图准则，该准则基于观测分布中的条件独立性，为预测器满足反事实不变性提供了充分条件。为了学习此类预测器，我们提出了一种与模型无关的框架，称为反事实不变预测（CIP），该框架建立在希尔伯特-施密特条件独立性准则（HSCIC）——一种基于核的条件依赖性度量——之上。我们的实验结果表明，CIP在多种模拟和真实世界数据集（包括标量和多变量设置）中强制实现反事实不变性方面具有显著效果。