We propose a post-processing algorithm for fair classification that mitigates
model bias under a unified family of group fairness criteria covering
statistical parity, equal opportunity, and equalized odds, applicable to
multi-class problems and both attribute-aware and attribute-blind settings. It
achieves fairness by re-calibrating the output score of the given base model
with a "fairness cost" -- a linear combination of the (predicted) group
memberships. Our algorithm is based on a representation result showing that the
optimal fair classifier can be expressed as a linear post-processing of the
loss function and the group predictor, derived via using these as sufficient
statistics to reformulate the fair classification problem as a linear program.
The parameters of the post-processor are estimated by solving the empirical LP.
Experiments on benchmark datasets show the efficiency and effectiveness of our
algorithm at reducing disparity compared to existing algorithms, including
in-processing, especially on larger problems.

我们提出了一个后处理算法来进行公平分类，通过统一的族群公平度量准则，包括统计平衡、平等机会和平衡赔率，来减轻模型偏差，适用于多类问题和具有属性感知和属性盲的设置。通过使用 “公平代价” 来重新校准给定基准模型的输出分数，它通过线性组合（预测的）群体成员身份来实现公平性。我们的算法是基于一种表达结果的表示方法，该结果表明最优公平分类器可以通过线性后处理损失函数和群体预测器来表示，这是通过将它们用作足够统计量，将公平分类问题重新形式化为线性规划问题来推导出来的。通过解决经验线性规划来估计后处理器的参数。对基准数据集上的实验证明了我们的算法与现有算法相比在减小差异方面的效率和有效性，特别是在更大的问题上。

线性后处理的最佳组公平分类器

Optimal Group Fair Classifiers from Linear Post-Processing

Most work in algorithmic fairness to date has focused on discrete outcomes,
such as deciding whether to grant someone a loan or not. In these
classification settings, group fairness criteria such as independence,
separation and sufficiency can be measured directly by comparing rates of
outcomes between subpopulations. Many important problems however require the
prediction of a real-valued outcome, such as a risk score or insurance premium.
In such regression settings, measuring group fairness criteria is
computationally challenging, as it requires estimating information-theoretic
divergences between conditional probability density functions. This paper
introduces fast approximations of the independence, separation and sufficiency
group fairness criteria for regression models from their (conditional) mutual
information definitions, and uses such approximations as regularisers to
enforce fairness within a regularised risk minimisation framework. Experiments
in real-world datasets indicate that in spite of its superior computational
efficiency our algorithm still displays state-of-the-art accuracy/fairness
tradeoffs.

本文针对算法公平性和回归模型中的组公平标准，提出了快速近似的独立性、分离性和充分性，用于执行正则化风险最小化，从而实现公平性和准确性的折衷。