As a technology ML is oblivious to societal good or bad, and thus, the field of fair machine learning has stepped up to propose multiple mathematical definitions, algorithms, and systems to ensure different notions of fairness in ML applications. Given the multitude of propositions, it has become imperative to formally verify the fairness metrics satisfied by different algorithms on different datasets. In this paper, we propose a \textit{stochastic satisfiability} (SSAT) framework, Justicia, that formally verifies different fairness measures of supervised learning algorithms with respect to the underlying data distribution. We instantiate Justicia on multiple classification and bias mitigation algorithms, and datasets to verify different fairness metrics, such as disparate impact, statistical parity, and equalized odds. Justicia is scalable, accurate, and operates on non-Boolean and compound sensitive attributes unlike existing distribution-based verifiers, such as FairSquare and VeriFair. Being distribution-based by design, Justicia is more robust than the verifiers, such as AIF360, that operate on specific test samples. We also theoretically bound the finite-sample error of the verified fairness measure.

中文翻译：

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Justicia：一种正式验证公平性的随机 SAT 方法

作为一项技术，ML 无视社会好坏，因此，公平机器学习领域已加紧提出多种数学定义、算法和系统，以确保 ML 应用程序中的不同公平概念。鉴于存在众多命题，正式验证不同算法在不同数据集上满足的公平性指标已变得势在必行。在本文中，我们提出了一个 \textit{随机可满足性}（SSAT）框架 Justicia，它正式验证了监督学习算法相对于基础数据分布的不同公平性措施。我们在多种分类和偏见缓解算法以及数据集上实例化 Justicia，以验证不同的公平性指标，例如不同的影响、统计平价和均衡赔率。Justicia 是可扩展的，与现有的基于分布的验证器（如 FairSquare 和 VeriFair）不同，它对非布尔和复合敏感属性进行操作。由于设计基于分布，Justicia 比在特定测试样本上运行的验证器（例如 AIF360）更强大。我们还在理论上限制了经过验证的公平性度量的有限样本误差。