Counterfactual fairness requires that a person would have been classified in
the same way by an AI or other algorithmic system if they had a different
protected class, such as a different race or gender. This is an intuitive
standard, as reflected in the U.S. legal system, but its use is limited because
counterfactuals cannot be directly observed in real-world data. On the other
hand, group fairness metrics (e.g., demographic parity or equalized odds) are
less intuitive but more readily observed. In this paper, we use $\textit{causal
context}$ to bridge the gaps between counterfactual fairness, robust
prediction, and group fairness. First, we motivate counterfactual fairness by
showing that there is not necessarily a fundamental trade-off between fairness
and accuracy because, under plausible conditions, the counterfactually fair
predictor is in fact accuracy-optimal in an unbiased target distribution.
Second, we develop a correspondence between the causal graph of the
data-generating process and which, if any, group fairness metrics are
equivalent to counterfactual fairness. Third, we show that in three common
fairness contexts$\unicode{x2013}$measurement error, selection on label, and
selection on predictors$\unicode{x2013}$counterfactual fairness is equivalent
to demographic parity, equalized odds, and calibration, respectively.
Counterfactual fairness can sometimes be tested by measuring relatively simple
group fairness metrics.

我们利用因果上下文桥接了反事实公平、鲁棒预测和群体公平之间的差距，展示了它们之间的等价关系，并通过测量相对简单的群体公平指标来测试反事实公平。

因果背景连接反事实公平与稳健预测和群体公平

Causal Context Connects Counterfactual Fairness to Robust Prediction and  Group Fairness

We consider the problem of robustly predicting as well as the best linear
combination of $d$ given functions in least squares regression, and variants of
this problem including constraints on the parameters of the linear combination.
For the ridge estimator and the ordinary least squares estimator, and their
variants, we provide new risk bounds of order $d/n$ without logarithmic factor
unlike some standard results, where $n$ is the size of the training data. We
also provide a new estimator with better deviations in the presence of
heavy-tailed noise. It is based on truncating differences of losses in a
min--max framework and satisfies a $d/n$ risk bound both in expectation and in
deviations. The key common surprising factor of these results is the absence of
exponential moment condition on the output distribution while achieving
exponential deviations. All risk bounds are obtained through a PAC-Bayesian
analysis on truncated differences of losses. Experimental results strongly back
up our truncated min--max estimator.

针对在普通最小二乘法回归中预测的偏差问题，我们提出了一个更好的估算方法 —— 基于截断误差差值的极小 - 极大框架，其期望和差距都为 d/n。