Counterfactual invariance has proven an essential property for predictors that are fair, robust, and generalizable in the real world. We propose a general definition of counterfactual invariance and provide simple graphical criteria that yield a sufficient condition for a predictor to be counterfactually invariant in terms of (conditional independence in) the observational distribution. Any predictor that satisfies our criterion is provably counterfactually invariant. In order to learn such predictors, we propose a model-agnostic framework, called Counterfactual Invariance Prediction (CIP), based on a kernel-based conditional dependence measure called Hilbert-Schmidt Conditional Independence Criterion (HSCIC). Our experimental results demonstrate the effectiveness of CIP in enforcing counterfactual invariance across various types of data including tabular, high-dimensional, and real-world dataset.

翻译：反事实不变性已被证明是预测器在现实世界中实现公平、鲁棒和泛化的重要属性。我们提出了反事实不变性的一般性定义，并给出了简单的图论准则，这些准则在观测分布中（基于条件独立性）为预测器满足反事实不变性提供了充分条件。任何符合我们准则的预测器均可证明具有反事实不变性。为学习此类预测器，我们提出了一种模型无关框架，称为反事实不变预测（CIP），该框架基于一种核条件依赖性度量——希尔伯特-施密特条件独立性准则（HSCIC）。我们的实验结果表明，CIP在表格数据、高维数据和真实世界数据集等多种数据类型上实施反事实不变性方面具有有效性。