Counterfactual frameworks have grown popular in explainable and fair machine learning, as they offer a natural notion of causation. However, state-of-the-art models to compute counterfactuals are either unrealistic or unfeasible. In particular, while Pearl's causal inference provides appealing rules to calculate counterfactuals, it relies on a model that is unknown and hard to discover in practice. We address the problem of designing realistic and feasible counterfactuals in the absence of a causal model. We define transport-based counterfactual models as collections of joint probability distributions between observable distributions, and show their connection to causal counterfactuals. More specifically, we argue that optimal transport theory defines relevant transport-based counterfactual models, as they are numerically feasible, statistically-faithful, and can even coincide with causal counterfactual models. We illustrate the practicality of these models by defining sharper fairness criteria than typical group fairness conditions.
翻译:反事实框架在可解释和公正的机器学习中越来越受欢迎,因为它们提供了因果关系的自然概念。然而,计算反事实的最先进的模型要么不现实,要么不可行。 特别是,尽管珍珠的因果关系推论提供了计算反事实的具有吸引力的规则,但它依赖于一个未知和在实践中难以发现的模型。我们处理在没有因果关系模型的情况下设计现实和可行的反事实的问题。我们把基于运输的反事实模型定义为可观测分布之间联合概率分布的集合,并表明其与因果关系反事实的联系。更具体地说,我们认为,最佳运输理论定义了基于运输的反事实模型,因为它们在数字上是可行的,统计上是忠于实际的,甚至可以与因果关系反事实模型相吻合。我们通过界定比典型群体公平条件更精确的公平标准来说明这些模型的实际可行性。