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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

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  • ReceivedMay 30, 2019
  • AcceptedDec 5, 2019
  • PublishedAug 5, 2020

Abstract

Fairness learning is one of research hotspots in machine learning. The purpose of preventing discrimination is to eliminate the impact of unfair training sets on classifiers before performing prediction tasks. To ensure the fairness and accuracy of classification, this paper presents a method for generating fair data sets by identifying and eliminating discriminatory samples in original data sets. This is a margin-based weighted method for dealing with discrimination in binary classification tasks and obtaining the demographic parity and equalized odds. To improve the classification accuracy, the target set is selected after projecting based on the margin principle. For each sample in the target set, a weighted distance measurement method is used to identify the discriminatory sample and then correct it. The experimental results on three real data sets demonstrate that the proposed method can obtain better classification fairness and accuracy than existing methods; the conclusion is not limited to specific fairness criteria or classifiers.


Funded by

国家自然科学基金(61603197,61772284,61876091,61802205)


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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