SCIENTIA SINICA Informationis, Volume 50 , Issue 8 : 1255-1266(2020) https://doi.org/10.1360/SSI-2019-0112

## Discriminatory sample identifying and removing algorithms based on margin in fairness machine learning

• AcceptedDec 5, 2019
• PublishedAug 5, 2020
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### References

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• Figure 1

Framework diagram of discriminatory sample identifying and removing algorithm

• Figure 2

(Color online) An illustrative example of the change of distribution characteristics of samples after attribute projection. Each data point in the original feature space (a) is decomposed along each dimension and projected to the margin vector feature space (b)

• Figure 3

Discrimination discovery on (a) German Credit, (b) Adult Income and (c) Dutch Census

• Figure 4

(Color online)Accuracy and fairness on three classifiers after modifying datasets. (a)$\sim$(c), (d)$\sim$(f), (g)$\sim$(i) show the experimental results of using three classifiers (log.reg., AdaBoost and SVM) on German credit, Adult income and Dutch census datasets, respectively

•

Algorithm 1 歧视性样本发现算法

Require:样本${\{x_i,y_i\}}$,参数$t$.

输出: 样本${\{x_i,y_i\}}$是否为歧视样本.

if $y_i=y^-$ and ${\rm~diff}(x_i,k)~\leq~-t$ then

return True;

else if$y_i=y^+$ and ${\rm~diff}(x_i,k)~\geq~t$

return True;

else

return False.

end if

• Table 1   Baseline, Luong et al., Zhang et al. and our method of discriminating defense results on the Dutch Census
 Classifier Baseline Luong et al. Accuarcy Fairness-DP Fairness-EO Accuarcy Fairness-DP Fairness-EO log.reg. 0.8436 0.8897 0.8601 0.7893 0.9252 0.9108 AdaBoost 0.8562 0.9085 0.9004 0.8089 0.9271 0.9342 SVM 0.8487 0.8998 0.8680 0.8024 0.9233 0.9472 Classifier Zhang et al. Our method Accuarcy Fairness-DP Fairness-EO Accuarcy Fairness-DP Fairness-EO log.reg. 0.7948 0.9730 0.9744 0.8388 0.9795 0.9894 AdaBoost 0.8378 0.9645 0.9624 0.8478 0.9806 0.9847 SVM 0.8096 0.9836 0.9731 0.8395 0.9851 0.9703
•

Algorithm 2 歧视性样本消除算法

Require:训练集$S=\{x_i,a_i,y_i\}_{i=1}^{n}$,参数$t,k,z$, 修改标签的数量$M$.

输出: 公平的分类模型$h$.

初始化$R^{+}=R^{-}=\emptyset$, $j=0$.

基于3.1小节所介绍的方法从训练集中筛选出目标集$D$.

将目标集$D$通过敏感属性$A$的值划分为保护集$D^+$和非保护集$D^-$.

for $i=1,2,\ldots$,$z$

$R^{+}=R^{+}~\cup\left\{{\rm~d~i~f~f}\left(x_{i},~k\right)>t,~y_{i}=y^{+},~x_{i}~\in~D^{+}\right\}$;

$R^{-}=R^{-}~\cup\left\{{\rm~d~i~f~f}\left(x_{i},~k\right)<-t,~y_{i}=y^{-},~x_{i}~\in~D^{-}\right\}$;

end for

while $j~\leq~M$ do

从$R^+$中随机挑选一个样本$x$,将标签从$y^+$修改为$y^-$;

从$R^-$中随机挑选一个样本$x$,将标签从$y^-$修改为$y^+$;

$j$+;

end while

用$R^{+}$, $R^{-}$中修改标签的样本替换训练集$S$中的对应样本,并用修正后的训练集训练分类模型$h$.

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