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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>mendations for Bias Mitigation Methods: Applicability and Legality</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Madeleine Waller</string-name>
          <email>madeleine.waller@kcl.ac.uk</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Odinaldo Rodrigues</string-name>
          <email>odinaldo.rodrigues@kcl.ac.uk</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oana Cocarascu</string-name>
          <email>oana.cocarascu@kcl.ac.uk</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>King's College London</string-name>
        </contrib>
      </contrib-group>
      <abstract>
        <p>With AI-based decision-making systems increasingly being deployed in various sectors, research on fairness in AI has become even more important. In this position paper, we highlight a number of significant practical applicability limitations and regulatory compliance issues associated with existing bias mitigation methods. These limitations indicate a pressing need for a change in the approach to their development. In order to address them, we provide a list of recommendations for new bias mitigation methods that are not only efective, but can also be applied in real-world scenarios and comply with legal requirements.</p>
      </abstract>
      <kwd-group>
        <kwd>fairness</kwd>
        <kwd>bias mitigation</kwd>
        <kwd>machine learning</kwd>
        <kwd>regulation</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Artificial Intelligence (AI) is increasingly being used in decision-making systems, in both the
public sector (e.g. social services [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] to predict a child’s risk of neglect or abuse [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]) and the
private sector (e.g. to reduce workload and free up resources in organisations [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ]).
AIbased decision-making systems typically rely on machine learning (ML) techniques which use
historical data for training to make a classification or prediction about an individual. However,
the data may contain biases against groups or individuals with certain characteristics, which
can lead to unfair decisions and discrimination. Thus, the potential harmful impact of these
systems is immense.
      </p>
      <p>
        There have been several examples of unfair decisions made by AI-based decision-making
systems in various domains, e.g. criminal justice, where COMPAS [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] incorrectly identified black
defendants as re-ofending at a higher rate than white defendants [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], and recruitment, where
Amazon’s recruitment tool was shown to be biased against women [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. In fact, individuals may
not even be aware they are impacted [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], making it dificult for users and developers to fully
comprehend and account for the scope and potential efects of these systems [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
      <p>
        As AI-based decision-making systems become more prevalent, the field of fairness in AI
has seen an influx of literature in recent years (see [
        <xref ref-type="bibr" rid="ref10 ref11 ref12 ref13">10, 11, 12, 13</xref>
        ] for surveys). Most works
tend to focus on fairness measures and metrics, overlooking the systemic social and legal
perspectives on fairness and bias. Ensuring AI systems are fair to individuals and communities
nEvelop-O
is an important cross-disciplinary issue which must consider the context and the application of
the systems deployed [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
      <p>
        In this paper, we describe a number of key hurdles that existing bias mitigation methods for
decision-making systems have, due to both their practical applicability in real-world contexts
and their misalignment with law and regulations. We suggest a list of recommendations to help
guide the future of fairness in AI research, resulting from our analysis on the limitations of the
most prominent bias mitigation methods [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. We hope that this paper will advance discussion
towards the design of bias mitigation methods that take into consideration the applicability in
diferent use cases as well as the social and legal perspectives on fairness and bias.
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Background</title>
      <p>
        A system is said to be fair if it does not discriminate based on protected personal characteristics,
also known as sensitive attributes. These features are outlined in law [
        <xref ref-type="bibr" rid="ref14 ref15">14, 15</xref>
        ] and include
characteristics such as race, sex and religion [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. Sensitive attributes also include proxies
for protected characteristics, i.e. non-protected characteristics that correspond to protected
characteristics [
        <xref ref-type="bibr" rid="ref17 ref18">17, 18</xref>
        ]. An individual is said to be in the unprivileged group if the value of their
sensitive attribute defines them in the historically disadvantaged group.
      </p>
      <p>
        Fairness is measured by defining metrics with respect to personal characteristics. Individual
fairness seeks to guarantee that individuals with similar attributes receive the same output [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ]
and group fairness aims to ensure that comparable outcomes are provided across all values of
a personal characteristic for diferent groups [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]. For binary classification, common group
fairness metrics include: disparate impact (i.e. the diference in positive outcomes between the
privileged and unprivileged groups; it is not concerned with the true label of the individual)
and equalised odds (i.e. the diference in the true positive and false positive rates between the
privileged and unprivileged groups).
      </p>
      <p>
        Bias mitigation methods are split into: pre-processing methods (e.g. [
        <xref ref-type="bibr" rid="ref21 ref22">21, 22</xref>
        ]) which mitigate
bias in the training data, in-processing methods (e.g. [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ]) which mitigate bias during model
training, and post-processing methods (e.g. [
        <xref ref-type="bibr" rid="ref24 ref25">24, 25</xref>
        ]) which mitigate bias in the model’s output.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Applicability and Legal Limitations</title>
      <p>In this section, we discuss the limitations of bias mitigation methods that are hurdles to their
practical applicability in real-world scenarios (i.e. lack of generalisability, non-robust
evaluations). We also consider the laws and regulations (i.e. data protection, positive discrimination,
right to an explanation) that may limit the usefulness of these methods in real life.</p>
      <sec id="sec-3-1">
        <title>3.1. Applicability Limitations</title>
        <sec id="sec-3-1-1">
          <title>Generalisability</title>
          <p>
            Bias mitigation methods have been proposed for a variety of problems: regression [
            <xref ref-type="bibr" rid="ref26 ref27 ref28">26, 27, 28</xref>
            ],
multi-class classification [
            <xref ref-type="bibr" rid="ref29 ref30">29, 30</xref>
            ], clustering [
            <xref ref-type="bibr" rid="ref31 ref32 ref33 ref34 ref35 ref36">31, 32, 33, 34, 35, 36</xref>
            ], online data streams [
            <xref ref-type="bibr" rid="ref23 ref37">23, 37</xref>
            ],
etc. Still, the majority of works focus on binary classification [
            <xref ref-type="bibr" rid="ref10">10</xref>
            ] and make assumptions about
the specific scenarios in which the proposed method can be applied, then design and evaluate
it. There is a generalisability issue as existing methods can only be applied in the context of
specific dataset characteristics, models, and metrics.
          </p>
          <p>Sensitive attributes The datasets used in bias mitigation methods may include one or
multiple sensitive attributes, that can be of diferent types, e.g. binary, multi-valued or numerical.</p>
          <p>
            Common group metrics (see Section 2) can be used with a single binary sensitive attribute,
meaning the bias mitigation methods that aim to improve fairness with respect to these metrics
can be applied to datasets that have only one sensitive attribute. In real-world scenarios, this
may not be the case [
            <xref ref-type="bibr" rid="ref38">38</xref>
            ]. Some works tackle this issue and allow multiple sensitive attributes.
For example, [
            <xref ref-type="bibr" rid="ref39">39</xref>
            ] optimises for fairness under constraints that represent fairness metrics with
respect to each sensitive attribute, while [
            <xref ref-type="bibr" rid="ref40">40</xref>
            ] creates its own fairness metric. However the use
of custom metrics may present its own issues (see discussion on metrics below).
          </p>
          <p>
            The type of sensitive attribute considered by bias mitigation methods may also restrict their
applicability. Here again, common group metrics can be applied to datasets that contain a
sensitive attribute which is binary. Therefore, we cannot account for multi-valued or numerical
sensitive attributes such as race or age. Some methods [
            <xref ref-type="bibr" rid="ref39 ref41">39, 41</xref>
            ] tackle this by allowing for
multi-valued and numerical sensitive attributes in their optimisation constraints, while [
            <xref ref-type="bibr" rid="ref42">42</xref>
            ]
allows for multi-valued sensitive attributes as long as they have a natural ordering.
Models In-processing methods designed for a specific model (e.g. for Naïve Bayes models [
            <xref ref-type="bibr" rid="ref40 ref43">40,
43</xref>
            ], logistic regression [44, 45], decision trees [46], neural networks [47]) can be more efective
than more general methods [48]. However, this greatly limits their applicability in real-world
scenarios. Furthermore, it may not be realistic to assume that there is access to the model in
order to apply an in-processing method [49].
          </p>
          <p>
            Pre-processing and most post-processing methods1 are model-agnostic and thus can be
applied in a wider range of scenarios, albeit having their own disadvantages. Pre-processing
methods are considered intrusive as they change the dataset [51], while post-processing methods
can be easily manipulated to ensure some existing fairness metric is satisfied, e.g. by simply
swapping the classifications of individuals in the unprivileged group to positive to have an equal
number of positive and negative classifications for the privileged and unprivileged groups [ 52].
Metrics The notion of fairness that should be satisfied by a system depends on the intended
use case, hence the metric deployed with a bias mitigation method must be representative of the
scenario in which it is applied. For example, a developer may choose to optimise for equalised
odds in a system that predicts who will pay back a loan, a suitable metric here as it is important
to ensure equal proportions of individuals who are correctly and incorrectly predicted to pay
back a loan across the unprivileged and privileged groups. This requires choosing a method
that optimises for equalised odds (e.g. [47, 53, 54]) over ones that do not (e.g. [
            <xref ref-type="bibr" rid="ref40">40, 55</xref>
            ]). Thus, the
metric the bias mitigation method aims to improve limits the applications in which it can be
used. Some bias mitigation methods allow the user to choose the fairness metric to optimise
for [
            <xref ref-type="bibr" rid="ref41">41, 45</xref>
            ]. This is useful as it allows the method to be applied in diferent scenarios.
          </p>
          <p>
            Many methods create new fairness metrics that are not widely used [
            <xref ref-type="bibr" rid="ref24 ref40">24, 40, 56, 57, 58</xref>
            ]. Often
their relationships with real-life notions of fairness are not explored thus it is dificult to know
in what scenarios they might be applied as well as their relationship with existing metrics.
          </p>
          <p>
            1A sub-category of post-processing methods, intra-processing methods, require some knowledge of the model
used (e.g. decision tree nodes [46], posterior probabilities [
            <xref ref-type="bibr" rid="ref43">43</xref>
            ]), to mitigate the bias in the output [50].
          </p>
        </sec>
        <sec id="sec-3-1-2">
          <title>Evaluation</title>
          <p>
            Whilst the works proposing bias mitigation methods provide results to evaluate their
efectiveness, these results are not robust as they are vulnerable to changes in the experimental setup.
Given a scenario, a bias mitigation method is chosen based on the characteristics of the dataset,
model used, and the notion of fairness targeted. However, one question arises: how can we
ensure that the method will indeed improve fairness? Each method includes experiments using
a chosen model trained on publicly available datasets, with results reported using diferent
metrics. However, the results are not easily comparable across methods due to the multitude of
these choices. Other factors also impact the values of computed fairness metrics, e.g. diferent
distributions of positive and negative labels across the (un)privileged groups in the training
data [54] or diferent proportions of training/testing data [
            <xref ref-type="bibr" rid="ref13">13</xref>
            ].
          </p>
          <p>
            Non-robust evaluations may be used as a justification for the use of a bias mitigation method,
allowing potentially discriminatory systems to be deployed. Bias might be mitigated for one
system but not for another [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ].
          </p>
          <p>
            Trade-ofs There is typically a trade-of between fairness and performance. For example, [ 59]
trained models on biased datasets to show that existing methods optimising for the disparate
impact metric [
            <xref ref-type="bibr" rid="ref42">42, 51</xref>
            ] improve fairness but decrease the model’s performance. Other methods
also showed a decrease in performance [60, 61], while [45] included a parameter to control the
fairness-performance trade-of. However, there is usually no discussion as to whether a decrease
in performance is acceptable to improve fairness. Further, from a regulatory perspective such
as the proposed EU AI Act [62], it is crucial to maximise the accuracy of a system used in
high-impact scenarios, thus it may be dificult to decide whether to prioritise performance or
fairness.
          </p>
          <p>
            Improving fairness with respect to one metric may be at a detriment to another [
            <xref ref-type="bibr" rid="ref41">41</xref>
            ]. The
notions of group and individual fairness are conflicting, thus targeting only one notion does not
fully capture fairness. For example, targeting only individual fairness [63] ensures that similar
individuals are treated the same. However, if the similar individuals are all female and their
classifications are negative, then group fairness with respect to gender would not be satisfied.
          </p>
          <p>
            These trade-ofs need to be considered when applying a bias mitigation method. The
variability in results using diferent datasets, models, and metrics, also impacts these trade-ofs, making
it dificult to ever be certain on a method’s applicability and efectiveness. However several
frameworks have been developed (e.g. [
            <xref ref-type="bibr" rid="ref16 ref21">16, 21, 59, 64</xref>
            ]) to explore these diferences.
          </p>
        </sec>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Legal Limitations</title>
        <sec id="sec-3-2-1">
          <title>Fairness Definitions</title>
          <p>
            As previously discussed, the notion of fairness should be chosen depending on the context of the
decision-making system. This context should also include the laws that apply to the application
of system [52]. Each regulatory body has its own definition of fairness to which decision-makers
must adhere. In the U.S. non-discrimination law,2 a system is defined as unfair if the disparate
impact of a system (see Section 2) is less than 80%. This definition has been widely adopted
throughout the algorithmic fairness literature [
            <xref ref-type="bibr" rid="ref39 ref42 ref43">39, 42, 43, 65</xref>
            ]. There are also considerations
2https://www.justice.gov/crt/fcs/T6Manual7
around disparate treatment which involves assessing the intent of the decision-maker, which
does not translate directly to algorithmic decision-makers [66]. Discrimination in EU law is
highly context dependent and cannot be easily reduced to metrics [
            <xref ref-type="bibr" rid="ref8">8, 67</xref>
            ]. The conditional
demographic disparity3 metric [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ] was created to represent the EU’s definition of fairness which,
combined with contextual information, enables the evaluation of a system’s fairness.
          </p>
        </sec>
        <sec id="sec-3-2-2">
          <title>Data Protection</title>
          <p>The majority of bias mitigation methods require the identification of the sensitive attributes
before they can be applied. However, under UK and EU data protection laws [68] the collection,
processing and storage of personal characteristics should be justified and is held to high standards
of transparency. Often organisations may not collect sensitive attributes due to concerns or
misconceptions around the legality of using them to audit their systems [69]. The relationship
of existing bias mitigation methods to data protection is rarely considered [70].</p>
        </sec>
        <sec id="sec-3-2-3">
          <title>Positive Discrimination</title>
          <p>Existing bias mitigation methods mitigate bias across the (un)privileged groups by changing
classifications for individuals according to their value of a sensitive attribute [ 53]. This could
cause individuals from historically disadvantaged groups to be favoured over others [71],
otherwise known as positive discrimination. In some jurisdictions, such as in the UK under the
UK Equality Act [72, 52], changing any outcome based on sensitive attributes is unlawful except
in special cases. U.S. regulation may have similar implications (although there are more accepted
cases) [66]. Potential positive discrimination resulting from existing bias mitigation methods is
rarely discussed. However, reducing discrimination without positively discriminating [56] is an
important consideration for any method to be applied in a real-world scenario.</p>
        </sec>
        <sec id="sec-3-2-4">
          <title>Transparency and Explainability</title>
          <p>
            Whether regulations such as GDPR [68] enforce a right to an explanation and whether it would
ever be feasible to enforce such a right [73] is debatable. Yet, as more legislation is designed,
transparency and explainability will be crucial in high-impact systems as they are key for
increasing trust [62, 74, 52]. Decisions made by automated systems can be dificult to explain
due to their opacity. Using any of the bias mitigation methods surveyed greater increases the
system’s opacity and adds another layer of automation that requires explanation. The impact the
application of a method may have on the transparency of the system is rarely acknowledged [
            <xref ref-type="bibr" rid="ref20">20</xref>
            ].
          </p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Recommendations</title>
      <p>Whilst the development of bias mitigation methods has enriched the landscape on fairness in AI
research, it remains unclear whether these methods are being used in any real-world scenarios,
and further whether they can actually be efectively and legally deployed. To ensure that new
methods can be practically transferred to real-world applications, we recommend to consider
the following factors when designing a new bias mitigation method:4
Ra1∶ Access to sensitive attributes The number of sensitive attributes available, and whether
those attributes can be binary, multi-valued, or numerical impacts the applicability of methods.
3Illegal discrimination metric [57, 58] corresponds to the fairness notion defined by cond. demographic disparity.
4We denote recommendations related to applicability as   and to regulations as   .</p>
      <p>Ra2∶ Applicability to models Whether a method can be applied in a scenario may depend
on the model and access to that model.</p>
      <p>Ra3∶ Variability of evaluation Experiments on diferent datasets and models, using diferent
fairness metrics can give very diferent results. To understand a method’s efectiveness in various
scenarios, it should be thoroughly evaluated.</p>
      <p>Ra4∶ Trade-ofs after application of method The impact on the system’s performance and
diferences in using various fairness notions/metrics.</p>
      <p>Rr1∶ Conflicts with legal definitions of fairness Legal definitions of fairness may difer
with technical definitions used in ML. Any new method should include which legal definitions
of fairness it does (not) satisfy.</p>
      <p>Rr2∶ Data protection issues Concerns about data protection and privacy may mean it is
not realistic to assume sensitive attributes have been collected or stored.</p>
      <p>Rr3∶ Potential for positive discrimination While bias mitigation methods aim to prevent
negative discrimination, they may unintentionally cause illegal positive discrimination.
Rr4∶ Transparency and explainability rights The right to explainability and the
transparency of a system are increasingly recognised as important aspects of legal and ethical AI.
New bias mitigation methods should work towards this goal, not against it.</p>
      <p>
        In order to consider the context of a system and not rely on pre-specified sensitive attributes
which may not be available, we suggest exploring explainable AI (XAI) methods. Stakeholders
can then consider the reasoning for the system’s classification and decide whether it is fair.
There is a plethora of research into XAI, but its use cases in fairness are limited [
        <xref ref-type="bibr" rid="ref20">20, 75, 76, 77</xref>
        ].
There might still be issues with a stakeholder evaluating the system’s fairness but the concept of
fairness is inherently human-oriented, context-specific and culturally dependent [ 78], meaning
that it is dificult to automate, cannot be reduced to a metric, and requires some level of human
input also for accountability purposes [79].
      </p>
      <p>
        Overall, there is a need for cross-disciplinary considerations on issues such as fairness. Whilst
not a new recommendation [
        <xref ref-type="bibr" rid="ref13 ref18 ref8">8, 13, 18, 80, 81</xref>
        ], it has not yet been universally adopted in current
research around fairness and bias in AI.
      </p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>
        Existing bias mitigation methods for binary classification have significant limitations [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. In
this paper, we identified several that are hurdles to the practical applicability of such methods in
real-world scenarios and proposed a list of recommendations for creating new methods that are
efective, applicable in a wide range of scenarios and legally sound. Our recommendations aim
to guide the advancement of research in this crucial area of AI to ensure that bias mitigation
methods are developed in a more responsible manner.
      </p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>This work was supported by the UK Research and Innovation Centre for Doctoral Training in
Safe and Trusted Artificial Intelligence [Grant number EP/S023356/1]. 5
Data Mining and Knowledge Discovery 21 (2010) 277–292. doi:10.1007/s10618-010-0
190-x.
[44] Y. Bechavod, K. Ligett, Learning fair classifiers: A regularization-inspired approach, arXiv
preprint (2017). arXiv:1707.00044.
[45] B. H. Zhang, B. Lemoine, M. Mitchell, Mitigating unwanted biases with adversarial learning,
in: Proceedings of the 2018 AAAI/ACM Conference on AI, Ethics, and Society, AIES, ACM,
2018, pp. 335–340. doi:10.1145/3278721.3278779.
[46] F. Kamiran, T. Calders, M. Pechenizkiy, Discrimination aware decision tree learning,
in: ICDM, The 10th IEEE International Conference on Data Mining, 2010, pp. 869–874.
doi:10.1109/ICDM.2010.50.
[47] T. Hu, V. Iosifidis, W. Liao, H. Zhang, M. Y. Yang, E. Ntoutsi, B. Rosenhahn, Fairnn - conjoint
learning of fair representations for fair decisions, in: Discovery Science - 23rd International
Conference, DS, volume 12323, 2020, pp. 581–595. doi:10.1007/978-3-030-61527-7\_38.
[48] S. Caton, C. Haas, Fairness in machine learning: A survey, arXiv preprint (2020).</p>
      <p>arXiv:2010.04053.
[49] A. Aggarwal, P. Lohia, S. Nagar, K. Dey, D. Saha, Black box fairness testing of machine
learning models, in: M. Dumas, D. Pfahl, S. Apel, A. Russo (Eds.), Proceedings of the
ACM Joint Meeting on European Software Engineering Conference and Symposium on the
Foundations of Software Engineering, ESEC/SIGSOFT FSE 2019, Tallinn, Estonia, August
26-30, 2019, ACM, 2019, pp. 625–635. doi:10.1145/3338906.3338937.
[50] Y. Savani, C. White, N. S. Govindarajulu, Intra-processing methods for debiasing neural
networks, in: H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, H. Lin (Eds.), Advances in
Neural Information Processing Systems 33: Annual Conference on Neural Information
Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020. URL: https:
//proceedings.neurips.cc/paper/2020/hash/1d8d70dddf147d2d92a634817f01b239-Abstract.
html.
[51] F. Kamiran, T. Calders, Data preprocessing techniques for classification without
discrimination, Knowledge and Information Systems 33 (2011) 1–33. doi:10.1007/s10115-011-0
463-8.
[52] Centre for Data Ethics and Innovation, Review into bias in algorithmic decision-making,
2020. URL: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/a
ttachment_data/file/957259/Review_into_bias_in_algorithmic_decision-making.pdf.
[53] V. Grari, B. Ruf, S. Lamprier, M. Detyniecki, Fair adversarial gradient tree boosting,
in: 2019 IEEE International Conference on Data Mining, ICDM, 2019, pp. 1060–1065.
doi:10.1109/ICDM.2019.00124.
[54] V. Iosifidis, E. Ntoutsi, Adafair: Cumulative fairness adaptive boosting, in: Proceedings
of the 28th ACM International Conference on Information and Knowledge Management,
CIKM, 2019, pp. 781–790. doi:10.1145/3357384.3357974.
[55] E. Krasanakis, E. S. Xioufis, S. Papadopoulos, Y. Kompatsiaris, Adaptive sensitive
reweighting to mitigate bias in fairness-aware classification, in: Proceedings of the
2018 World Wide Web Conference on World Wide Web, WWW, 2018, pp. 853–862.
doi:10.1145/3178876.3186133.
[56] K. Mancuhan, C. Clifton, Combating discrimination using bayesian networks, Artificial</p>
      <p>Intelligence and Law 22 (2014) 211–238. doi:10.1007/s10506-014-9156-4.
[57] F. Kamiran, I. Zliobaite, T. Calders, Quantifying explainable discrimination and removing
illegal discrimination in automated decision making, Knowledge and Information Systems
35 (2013) 613–644. doi:10.1007/s10115- 012- 0584- 8.
[58] I. Zliobaite, F. Kamiran, T. Calders, Handling conditional discrimination, in: 11th IEEE
International Conference on Data Mining, ICDM, 2011, pp. 992–1001. doi:10.1109/ICDM
.2011.72.
[59] R. L. Cardoso, W. M. Jr., V. A. F. Almeida, M. J. Zaki, A framework for benchmarking
discrimination-aware models in machine learning, in: Proceedings of the 2019 AAAI/ACM
Conference on AI, Ethics, and Society, AIES, 2019, pp. 437–444. doi:10.1145/3306618.33
14262.
[60] V. Iosifidis, E. Ntoutsi, Dealing with bias via data augmentation in supervised learning
scenarios, Jo Bates Paul D. Clough Robert Jäschke 24 (2018). URL: https://ceur-ws.org/Vo
l-2103/paper_5.pdf.
[61] L. Oneto, M. Donini, A. Elders, M. Pontil, Taking advantage of multitask learning for
fair classification, in: Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and
Society, AIES, 2019, pp. 227–237. doi:10.1145/3306618.3314255.
[62] European Commission, Proposal for a regulation of the european parliament and of the
council laying down harmonised rules on artificial intelligence (artificial intelligence act)
and amending certain union legislative acts, 2021. URL: https://eur-lex.europa.eu/legal-c
ontent/EN/TXT/?uri=CELEX:52021PC0206.
[63] A. Ruoss, M. Balunovic, M. Fischer, M. T. Vechev, Learning certified individually fair
representations, in: Advances in Neural Information Processing Systems 33: Annual
Conference on Neural Information Processing Systems NeurIPS, 2020. URL: https://procee
dings.neurips.cc/paper/2020/hash/55d491cf951b1b920900684d71419282-Abstract.html.
[64] S. Schelter, Y. He, J. Khilnani, J. Stoyanovich, Fairprep: Promoting data to a first-class citizen
in studies on fairness-enhancing interventions, in: Proceedings of the 23rd International
Conference on Extending Database Technology, EDBT, 2020, pp. 395–398. doi:10.5441/
002/edbt.2020.41.
[65] F. Kamiran, A. Karim, X. Zhang, Decision theory for discrimination-aware classification,
in: 12th IEEE International Conference on Data Mining, ICDM, 2012, pp. 924–929. doi:10
.1109/ICDM.2012.45.
[66] A. Xiang, I. D. Raji, On the legal compatibility of fairness definitions, arXiv preprint (2019).</p>
      <p>arXiv:1912.00761.
[67] R. Xenidis, Tuning EU equality law to algorithmic discrimination: Three pathways to
resilience, Maastricht Journal of European and Comparative Law 27 (2020) 736–758.
doi:10.1177/1023263X20982173.
[68] GDPR, General Data Protection Regulation (GDPR) – Oficial Legal Text, 2016. URL:
https://gdpr-info.eu/.
[69] Centre for Data Ethics and Innovation, Enabling responsible access to demographic data to
make AI systems fairer, 2023. URL: https://www.gov.uk/government/publications/enablin
g-responsible-access-to-demographic-data-to-make-ai-systems-fairer/report-enabling-r
esponsible-access-to-demographic-data-to-make-ai-systems-fairer#executive-summary.
[70] M. A. Haeri, K. A. Zweig, The crucial role of sensitive attributes in fair classification,
in: IEEE Symposium Series on Computational Intelligence, SSCI, 2020, pp. 2993–3002.
doi:10.1109/SSCI47803.2020.9308585.
[71] S. Wachter, B. Mittelstadt, C. Russell, Bias preservation in machine learning: the legality
of fairness metrics under EU non-discrimination law, W. Va. L. Rev. 123 (2020) 735. URL:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3792772.
[72] UK Public General Acts, Equality Act 2010, 2010. URL: https://www.legislation.gov.uk/ukp
ga/2010/15/contents.
[73] S. Wachter, B. Mittelstadt, L. Floridi, Why a right to explanation of automated
decisionmaking does not exist in the general data protection regulation, International Data Privacy
Law 7 (2017) 76–99. doi:10.1093/idpl/ipx005.
[74] J. Schöfer, Y. Machowski, N. Kuehl, A study on fairness and trust perceptions in automated
decision making, in: D. Glowacka, V. R. Krishnamurthy (Eds.), Joint Proceedings of the
ACM IUI 2021 Workshops co-located with 26th ACM Conference on Intelligent User
Interfaces (ACM IUI 2021), College Station, United States, April 13-17, 2021, volume 2903
of CEUR Workshop Proceedings, CEUR-WS.org, 2021. URL: https://ceur-ws.org/Vol-2903/
IUI21WS-TExSS-12.pdf.
[75] T. Begley, T. Schwedes, C. Frye, I. Feige, Explainability for fair machine learning, arXiv
preprint (2020). arXiv:2010.07389.
[76] P. A. Grabowicz, N. Perello, A. Mishra, Marrying fairness and explainability in
supervised learning, in: FAccT ’22: 2022 ACM Conference on Fairness, Accountability, and
Transparency, Seoul, Republic of Korea, June 21 - 24, 2022, ACM, 2022, pp. 1905–1916.
doi:10.1145/3531146.3533236.
[77] R. Calegari, F. Sabbatini, The psyke technology for trustworthy artificial intelligence,
in: A. Dovier, A. Montanari, A. Orlandini (Eds.), AIxIA 2022 – Advances in Artificial
Intelligence, Springer International Publishing, Cham, 2023, pp. 3–16.
[78] C. Barabas, C. Doyle, J. B. Rubinovitz, K. Dinakar, Studying up: reorienting the study
of algorithmic fairness around issues of power, in: M. Hildebrandt, C. Castillo, L. E.
Celis, S. Ruggieri, L. Taylor, G. Zanfir-Fortuna (Eds.), FAT* ’20: Conference on Fairness,
Accountability, and Transparency, Barcelona, Spain, January 27-30, 2020, ACM, 2020, pp.
167–176. doi:10.1145/3351095.3372859.
[79] M. Veale, M. V. Kleek, R. Binns, Fairness and accountability design needs for algorithmic
support in high-stakes public sector decision-making, in: R. L. Mandryk, M. Hancock,
M. Perry, A. L. Cox (Eds.), Proceedings of the 2018 CHI Conference on Human Factors in
Computing Systems, CHI 2018, Montreal, QC, Canada, April 21-26, 2018, ACM, 2018, p.
440. doi:10.1145/3173574.3174014.
[80] X. F. Aran, T. van Nuenen, J. M. Such, M. Coté, N. Criado, Bias and discrimination in AI: A
cross-disciplinary perspective, IEEE Technol. Soc. Mag. 40 (2021) 72–80. doi:10.1109/MTS.
2021.3056293.
[81] L. Cheng, K. R. Varshney, H. Liu, Socially responsible AI algorithms: Issues, purposes, and
challenges, J. Artif. Intell. Res. 71 (2021) 1137–1181. doi:10.1613/jair.1.12814.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>Shared</given-names>
            <surname>Intelligence</surname>
          </string-name>
          and Local Government Association,
          <article-title>Using predictive analytics in local public services</article-title>
          ,
          <year>2020</year>
          . URL: https://www.local.gov.uk
          <article-title>/using-predictive-analytics-local-pub lic-services.</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>C. E.</given-names>
            <surname>Church</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. J.</given-names>
            <surname>Fairchild</surname>
          </string-name>
          ,
          <article-title>In search of a silver bullet: child welfare's embrace of predictive analytics</article-title>
          ,
          <source>Juvenile and Family Court Journal</source>
          <volume>68</volume>
          (
          <year>2017</year>
          )
          <fpage>67</fpage>
          -
          <lpage>81</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <surname>Deloitte</surname>
          </string-name>
          ,
          <source>AI and Automated Decision Making</source>
          ,
          <year>2021</year>
          . URL: https://www2.deloitte.com/uk/e n/pages/deloitte-analytics/articles/ai-and
          <article-title>-automated-decision-making</article-title>
          .
          <source>html.</source>
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>Z.</given-names>
            <surname>Engin</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P. C.</given-names>
            <surname>Treleaven</surname>
          </string-name>
          ,
          <article-title>Algorithmic government: Automating public services and supporting civil servants in using data science technologies</article-title>
          ,
          <source>Computer Journal</source>
          <volume>62</volume>
          (
          <year>2019</year>
          )
          <fpage>448</fpage>
          -
          <lpage>460</lpage>
          . doi:
          <volume>10</volume>
          .1093/comjnl/bxy082.
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <surname>Northpointe</surname>
          </string-name>
          ,
          <article-title>Practitioner's Guide to</article-title>
          COMPAS Core,
          <year>2019</year>
          . URL: https://s3.documentcloud .org/documents/2840784/
          <article-title>Practitioner-s-Guide-to-COMPAS-Core</article-title>
          .pdf.
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>J.</given-names>
            <surname>Larson</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Mattu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Kirchner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Angwin</surname>
          </string-name>
          ,
          <source>How We Analyzed the COMPAS Recidivism Algorithm</source>
          ,
          <year>2016</year>
          . URL: https://www.propublica.org/article/how
          <article-title>-we-analyzed-the-compa s-recidivism-algorithm.</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>J.</given-names>
            <surname>Dastin</surname>
          </string-name>
          ,
          <article-title>Amazon scraps secret AI recruiting tool that showed bias against women</article-title>
          ,
          <year>2018</year>
          . URL: https://www.reuters.com/article/us-amazon
          <article-title>-com-jobs-automation-insight-idUSK CN1MK08G</article-title>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>S.</given-names>
            <surname>Wachter</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B. D.</given-names>
            <surname>Mittelstadt</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Russell</surname>
          </string-name>
          ,
          <article-title>Why fairness cannot be automated: Bridging the gap between EU non-discrimination law</article-title>
          and
          <source>AI</source>
          ,
          <source>Comput. Law Secur. Rev</source>
          .
          <volume>41</volume>
          (
          <year>2021</year>
          )
          <article-title>105567</article-title>
          . doi:
          <volume>10</volume>
          .1016/j.clsr.
          <year>2021</year>
          .
          <volume>105567</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>M.</given-names>
            <surname>Waller</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Waller</surname>
          </string-name>
          ,
          <article-title>Why predictive algorithms are so risky for public sector bodies</article-title>
          ,
          <year>2020</year>
          . URL: https://tinyurl.com/SoRisky.
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>M.</given-names>
            <surname>Waller</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Rodrigues</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Cocarascu</surname>
          </string-name>
          ,
          <article-title>Bias mitigation methods for binary classification decision-making systems: Survey and recommendations</article-title>
          , arXiv preprint (
          <year>2023</year>
          ). arXiv:
          <volume>2305</volume>
          .
          <fpage>20020</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>D.</given-names>
            <surname>Pessach</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Shmueli</surname>
          </string-name>
          ,
          <article-title>A review on fairness in machine learning</article-title>
          ,
          <source>ACM Comput. Surv</source>
          .
          <volume>55</volume>
          (
          <year>2023</year>
          )
          <volume>51</volume>
          :
          <fpage>1</fpage>
          -
          <lpage>51</lpage>
          :
          <fpage>44</fpage>
          . doi:
          <volume>10</volume>
          .1145/3494672.
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>J.</given-names>
            <surname>Dunkelau</surname>
          </string-name>
          ,
          <article-title>Fairness-aware machine learning: An extensive overview</article-title>
          ,
          <year>2020</year>
          . URL: https: //www.sozwiss.hhu.de/fileadmin/redaktion/Fakultaeten/Philosophische_Fakultaet/Sozial wissenschaften/Kommunikations-_und_Medienwissenschaft_I/Dateien/Dunkelau___Leus chel__
          <year>2019</year>
          _
          <article-title>_Fairness-Aware_Machine_Learning</article-title>
          .pdf.
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>M.</given-names>
            <surname>Hort</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Z.</given-names>
            <surname>Chen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. M.</given-names>
            <surname>Zhang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Sarro</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Harman</surname>
          </string-name>
          ,
          <article-title>Bias mitigation for machine learning classifiers: A comprehensive survey</article-title>
          , arXiv preprint (
          <year>2022</year>
          ). arXiv:
          <volume>2207</volume>
          .
          <fpage>07068</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14] The United States Department of Justice,
          <source>The Equal Credit Opportunity Act</source>
          ,
          <year>2015</year>
          . URL: https://www.justice.gov/crt/equal
          <article-title>-credit-opportunity-act-3.</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15] The United States Department of Justice,
          <source>The Fair Housing Act</source>
          ,
          <year>2015</year>
          . URL: https://www. justice.gov/crt/fair-housing
          <source>-act-1.</source>
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <surname>R. K. E. Bellamy</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          <string-name>
            <surname>Dey</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          <string-name>
            <surname>Hind</surname>
            ,
            <given-names>S. C.</given-names>
          </string-name>
          <string-name>
            <surname>Hofman</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Houde</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          <string-name>
            <surname>Kannan</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          <string-name>
            <surname>Lohia</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Martino</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Mehta</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Mojsilovic</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Nagar</surname>
            ,
            <given-names>K. N.</given-names>
          </string-name>
          <string-name>
            <surname>Ramamurthy</surname>
            ,
            <given-names>J. T.</given-names>
          </string-name>
          <string-name>
            <surname>Richards</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          <string-name>
            <surname>Saha</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          <string-name>
            <surname>Sattigeri</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          <string-name>
            <surname>Singh</surname>
            ,
            <given-names>K. R.</given-names>
          </string-name>
          <string-name>
            <surname>Varshney</surname>
          </string-name>
          , Y. Zhang,
          <source>AI</source>
          fairness
          <volume>360</volume>
          :
          <article-title>An extensible toolkit for detecting, understanding, and mitigating unwanted algorithmic bias, arXiv preprint (</article-title>
          <year>2018</year>
          ). arXiv:
          <year>1810</year>
          .
          <year>01943</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <given-names>T. L.</given-names>
            <surname>Quy</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Roy</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Iosifidis</surname>
          </string-name>
          ,
          <string-name>
            <given-names>W.</given-names>
            <surname>Zhang</surname>
          </string-name>
          , E. Ntoutsi,
          <article-title>A survey on datasets for fairness-aware machine learning</article-title>
          ,
          <source>WIREs Data Mining and Knowledge Discovery</source>
          <volume>12</volume>
          (
          <year>2022</year>
          ). doi:
          <volume>10</volume>
          .1002/ widm.1452.
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <surname>T. Van Nuenen</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          <string-name>
            <surname>Ferrer</surname>
            ,
            <given-names>J. M.</given-names>
          </string-name>
          <string-name>
            <surname>Such</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          <string-name>
            <surname>Coté</surname>
          </string-name>
          , Transparency for whom?
          <source>Assessing discriminatory Artificial Intelligence, Computer</source>
          <volume>53</volume>
          (
          <year>2020</year>
          )
          <fpage>36</fpage>
          -
          <lpage>44</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <given-names>C.</given-names>
            <surname>Dwork</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Hardt</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T.</given-names>
            <surname>Pitassi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Reingold</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. S.</given-names>
            <surname>Zemel</surname>
          </string-name>
          ,
          <article-title>Fairness through awareness</article-title>
          ,
          <source>in: Innovations in Theoretical Computer Science</source>
          ,
          <year>2012</year>
          , pp.
          <fpage>214</fpage>
          -
          <lpage>226</lpage>
          . doi:
          <volume>10</volume>
          .1145/2090236. 2090255.
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <given-names>J.</given-names>
            <surname>Chakraborty</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Peng</surname>
          </string-name>
          , T. Menzies,
          <article-title>Making fair ML software using trustworthy explanation</article-title>
          ,
          <source>in: 35th IEEE/ACM International Conference on Automated Software Engineering</source>
          ,
          <string-name>
            <surname>ASE</surname>
          </string-name>
          , IEEE,
          <year>2020</year>
          , pp.
          <fpage>1229</fpage>
          -
          <lpage>1233</lpage>
          . doi:
          <volume>10</volume>
          .1145/3324884.3418932.
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <given-names>S. A.</given-names>
            <surname>Friedler</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Scheidegger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Venkatasubramanian</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Choudhary</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E. P.</given-names>
            <surname>Hamilton</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Roth</surname>
          </string-name>
          ,
          <article-title>A comparative study of fairness-enhancing interventions in machine learning</article-title>
          ,
          <source>in: Proceedings of the Conference on Fairness, Accountability, and Transparency</source>
          ,
          <year>2019</year>
          , pp.
          <fpage>329</fpage>
          -
          <lpage>338</lpage>
          . doi:
          <volume>10</volume>
          .1145/3287560.3287589.
        </mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation>
          [22]
          <string-name>
            <given-names>G.</given-names>
            <surname>Ristanoski</surname>
          </string-name>
          , W. Liu,
          <string-name>
            <given-names>J.</given-names>
            <surname>Bailey</surname>
          </string-name>
          ,
          <article-title>Discrimination aware classification for imbalanced datasets</article-title>
          ,
          <source>in: 22nd ACM International Conference on Information and Knowledge Management</source>
          ,
          <string-name>
            <surname>CIKM</surname>
          </string-name>
          ,
          <year>2013</year>
          , pp.
          <fpage>1529</fpage>
          -
          <lpage>1532</lpage>
          . doi:
          <volume>10</volume>
          .1145/2505515.2507836.
        </mixed-citation>
      </ref>
      <ref id="ref23">
        <mixed-citation>
          [23]
          <string-name>
            <given-names>W.</given-names>
            <surname>Zhang</surname>
          </string-name>
          , E. Ntoutsi,
          <article-title>FAHT: an adaptive fairness-aware decision tree classifier</article-title>
          ,
          <source>in: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI</source>
          ,
          <year>2019</year>
          , pp.
          <fpage>1480</fpage>
          -
          <lpage>1486</lpage>
          . doi:
          <volume>10</volume>
          .24963/ijcai.
          <year>2019</year>
          /205.
        </mixed-citation>
      </ref>
      <ref id="ref24">
        <mixed-citation>
          [24]
          <string-name>
            <given-names>B.</given-names>
            <surname>Fish</surname>
          </string-name>
          , J. Kun, Á. D.
          <string-name>
            <surname>Lelkes</surname>
          </string-name>
          ,
          <article-title>A confidence-based approach for balancing fairness and accuracy</article-title>
          ,
          <source>in: Proceedings of the 2016 SIAM International Conference on Data Mining</source>
          ,
          <year>2016</year>
          , pp.
          <fpage>144</fpage>
          -
          <lpage>152</lpage>
          . doi:
          <volume>10</volume>
          .1137/1.9781611974348.17.
        </mixed-citation>
      </ref>
      <ref id="ref25">
        <mixed-citation>
          [25]
          <string-name>
            <given-names>P. K.</given-names>
            <surname>Lohia</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K. N.</given-names>
            <surname>Ramamurthy</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Bhide</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Saha</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K. R.</given-names>
            <surname>Varshney</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Puri</surname>
          </string-name>
          ,
          <article-title>Bias mitigation post-processing for individual and group fairness</article-title>
          ,
          <source>in: IEEE International Conference on Acoustics, Speech and Signal Processing</source>
          , ICASSP,
          <year>2019</year>
          , pp.
          <fpage>2847</fpage>
          -
          <lpage>2851</lpage>
          . doi:
          <volume>10</volume>
          .1109/ICAS SP.
          <year>2019</year>
          .
          <volume>8682620</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref26">
        <mixed-citation>
          [26]
          <string-name>
            <given-names>T.</given-names>
            <surname>Calders</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Karim</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Kamiran</surname>
          </string-name>
          ,
          <string-name>
            <given-names>W.</given-names>
            <surname>Ali</surname>
          </string-name>
          ,
          <string-name>
            <surname>X. Zhang,</surname>
          </string-name>
          <article-title>Controlling attribute efect in linear regression</article-title>
          ,
          <source>in: 2013 IEEE 13th International Conference on Data Mining</source>
          ,
          <year>2013</year>
          , pp.
          <fpage>71</fpage>
          -
          <lpage>80</lpage>
          . doi:
          <volume>10</volume>
          .1109/ICDM.
          <year>2013</year>
          .
          <volume>114</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref27">
        <mixed-citation>
          [27]
          <string-name>
            <given-names>R.</given-names>
            <surname>Berk</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Heidari</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Jabbari</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Joseph</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. J.</given-names>
            <surname>Kearns</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Morgenstern</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Neel</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Roth</surname>
          </string-name>
          ,
          <article-title>A convex framework for fair regression</article-title>
          , arXiv preprint (
          <year>2017</year>
          ). arXiv:
          <volume>1706</volume>
          .
          <fpage>02409</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref28">
        <mixed-citation>
          [28]
          <string-name>
            <given-names>E.</given-names>
            <surname>Chzhen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Denis</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Hebiri</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Oneto</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Pontil</surname>
          </string-name>
          ,
          <article-title>Fair regression via plug-in estimator and recalibration with statistical guarantees</article-title>
          ,
          <source>in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems NeurIPS</source>
          ,
          <year>2020</year>
          . URL: https://proceedings.neurips.cc/paper/2020/hash/ddd808772c035aed516d42ad3559be5 f-Abstract.html.
        </mixed-citation>
      </ref>
      <ref id="ref29">
        <mixed-citation>
          [29]
          <string-name>
            <given-names>P.</given-names>
            <surname>Putzel</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
          <article-title>Blackbox post-processing for multiclass fairness</article-title>
          ,
          <year>2022</year>
          . URL: http://ceur -ws.org/Vol-
          <volume>3087</volume>
          /paper_36.pdf.
        </mixed-citation>
      </ref>
      <ref id="ref30">
        <mixed-citation>
          [30]
          <string-name>
            <given-names>W.</given-names>
            <surname>Alghamdi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Hsu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Jeong</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Wang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P. W.</given-names>
            <surname>Michalak</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Asoodeh</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. P.</given-names>
            <surname>Calmon</surname>
          </string-name>
          ,
          <article-title>Beyond adult and COMPAS: fairness in multi-class prediction, arXiv preprint (</article-title>
          <year>2022</year>
          ). arXiv:
          <volume>2206</volume>
          .
          <fpage>07801</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref31">
        <mixed-citation>
          [31]
          <string-name>
            <given-names>F.</given-names>
            <surname>Chierichetti</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Kumar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Lattanzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Vassilvitskii</surname>
          </string-name>
          ,
          <article-title>Fair clustering through fairlets</article-title>
          ,
          <source>in: Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems</source>
          ,
          <year>2017</year>
          , pp.
          <fpage>5029</fpage>
          -
          <lpage>5037</lpage>
          . URL: https://proceedings.neurips.cc /paper/2017/hash/978fce5bcc4eccc88ad48ce3914124a2-Abstract.html.
        </mixed-citation>
      </ref>
      <ref id="ref32">
        <mixed-citation>
          [32]
          <string-name>
            <given-names>I. M.</given-names>
            <surname>Ziko</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Yuan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Granger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>I. B.</given-names>
            <surname>Ayed</surname>
          </string-name>
          ,
          <article-title>Variational fair clustering</article-title>
          ,
          <source>in: Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI</source>
          ,
          <year>2021</year>
          , pp.
          <fpage>11202</fpage>
          -
          <lpage>11209</lpage>
          . URL: https: //ojs.aaai.org/index.php/AAAI/article/view/17336.
        </mixed-citation>
      </ref>
      <ref id="ref33">
        <mixed-citation>
          [33]
          <string-name>
            <given-names>M.</given-names>
            <surname>Abbasi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Bhaskara</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Venkatasubramanian</surname>
          </string-name>
          , Fair clustering via equitable group representations,
          <source>in: FAccT '21: 2021 ACM Conference on Fairness, Accountability, and Transparency</source>
          ,
          <year>2021</year>
          , pp.
          <fpage>504</fpage>
          -
          <lpage>514</lpage>
          . doi:
          <volume>10</volume>
          .1145/3442188.3445913.
        </mixed-citation>
      </ref>
      <ref id="ref34">
        <mixed-citation>
          [34]
          <string-name>
            <given-names>A.</given-names>
            <surname>Backurs</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Indyk</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Onak</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Schieber</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Vakilian</surname>
          </string-name>
          , T. Wagner,
          <article-title>Scalable fair clustering</article-title>
          ,
          <source>in: Proceedings of the 36th International Conference on Machine Learning</source>
          , ICML, volume
          <volume>97</volume>
          <source>of Proceedings of Machine Learning Research</source>
          ,
          <year>2019</year>
          , pp.
          <fpage>405</fpage>
          -
          <lpage>413</lpage>
          . URL: http://proceedings. mlr.press/v97/backurs19a.html.
        </mixed-citation>
      </ref>
      <ref id="ref35">
        <mixed-citation>
          [35]
          <string-name>
            <given-names>C.</given-names>
            <surname>Rösner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Schmidt</surname>
          </string-name>
          ,
          <article-title>Privacy preserving clustering with constraints</article-title>
          ,
          <source>in: 45th International Colloquium on Automata, Languages, and Programming</source>
          ,
          <string-name>
            <surname>ICALP</surname>
          </string-name>
          , volume
          <volume>107</volume>
          of LIPIcs,
          <year>2018</year>
          , pp.
          <volume>96</volume>
          :
          <fpage>1</fpage>
          -
          <lpage>96</lpage>
          :
          <fpage>14</fpage>
          . doi:
          <volume>10</volume>
          .4230/LIPIcs.ICALP.
          <year>2018</year>
          .
          <volume>96</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref36">
        <mixed-citation>
          [36]
          <string-name>
            <given-names>S. K.</given-names>
            <surname>Bera</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Chakrabarty</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Flores</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Negahbani</surname>
          </string-name>
          ,
          <article-title>Fair algorithms for clustering</article-title>
          ,
          <source>in: Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems</source>
          <year>2019</year>
          , NeurIPS,
          <year>2019</year>
          , pp.
          <fpage>4955</fpage>
          -
          <lpage>4966</lpage>
          . URL: https://proceedi ngs.neurips.cc/paper/2019/hash/fc192b0c0d270dbf41870a63a8c76c2f-Abstract.html.
        </mixed-citation>
      </ref>
      <ref id="ref37">
        <mixed-citation>
          [37]
          <string-name>
            <given-names>V.</given-names>
            <surname>Iosifidis</surname>
          </string-name>
          , E. Ntoutsi, FABBOO
          <article-title>- online fairness-aware learning under class imbalance</article-title>
          ,
          <source>in: Discovery Science - 23rd International Conference, DS</source>
          , volume
          <volume>12323</volume>
          of Lecture Notes in Computer Science,
          <year>2020</year>
          , pp.
          <fpage>159</fpage>
          -
          <lpage>174</lpage>
          . doi:
          <volume>10</volume>
          .1007/978- 3-
          <fpage>030</fpage>
          - 61527- 7\_
          <fpage>11</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref38">
        <mixed-citation>
          [38]
          <string-name>
            <given-names>A.</given-names>
            <surname>Roy</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Horstmann</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Ntoutsi</surname>
          </string-name>
          <article-title>, Multi-dimensional discrimination in law and machine learning - A comparative overview</article-title>
          ,
          <source>in: Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency</source>
          ,
          <source>FAccT</source>
          <year>2023</year>
          , Chicago, IL, USA, June 12-15,
          <year>2023</year>
          , ACM,
          <year>2023</year>
          , pp.
          <fpage>89</fpage>
          -
          <lpage>100</lpage>
          . doi:
          <volume>10</volume>
          .1145/3593013.3593979.
        </mixed-citation>
      </ref>
      <ref id="ref39">
        <mixed-citation>
          [39]
          <string-name>
            <surname>M. B. Zafar</surname>
            , I. Valera,
            <given-names>M.</given-names>
          </string-name>
          <string-name>
            <surname>Gomez-Rodriguez</surname>
            ,
            <given-names>K. P.</given-names>
          </string-name>
          <string-name>
            <surname>Gummadi</surname>
          </string-name>
          ,
          <article-title>Fairness constraints: Mechanisms for fair classification</article-title>
          ,
          <source>in: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics</source>
          , AISTATS, volume
          <volume>54</volume>
          ,
          <year>2017</year>
          , pp.
          <fpage>962</fpage>
          -
          <lpage>970</lpage>
          . URL: http://proceedings.mlr.press/v54/zafar17a.html.
        </mixed-citation>
      </ref>
      <ref id="ref40">
        <mixed-citation>
          [40]
          <string-name>
            <given-names>Y.</given-names>
            <surname>Choi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Farnadi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Babaki</surname>
          </string-name>
          ,
          <string-name>
            <surname>G.</surname>
          </string-name>
          <article-title>V. den Broeck, Learning fair naive bayes classifiers by discovering and eliminating discrimination patterns</article-title>
          ,
          <source>in: The Thirty-Fourth AAAI Conference on Artificial Intelligence</source>
          ,
          <string-name>
            <surname>AAAI</surname>
          </string-name>
          , AAAI Press,
          <year>2020</year>
          , pp.
          <fpage>10077</fpage>
          -
          <lpage>10084</lpage>
          . URL: https://ojs.aaai.org/index.php/AAAI/article/view/6565.
        </mixed-citation>
      </ref>
      <ref id="ref41">
        <mixed-citation>
          [41]
          <string-name>
            <given-names>N.</given-names>
            <surname>Quadrianto</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Sharmanska</surname>
          </string-name>
          ,
          <article-title>Recycling privileged learning and distribution matching for fairness</article-title>
          ,
          <source>in: Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems</source>
          ,
          <year>2017</year>
          , pp.
          <fpage>677</fpage>
          -
          <lpage>688</lpage>
          . URL: https://proceedings. neurips.cc/paper/2017/hash/250cf8b51c773f3f8dc8b4be867a9a02-Abstract.html.
        </mixed-citation>
      </ref>
      <ref id="ref42">
        <mixed-citation>
          [42]
          <string-name>
            <given-names>M.</given-names>
            <surname>Feldman</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S. A.</given-names>
            <surname>Friedler</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Moeller</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Scheidegger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Venkatasubramanian</surname>
          </string-name>
          ,
          <article-title>Certifying and removing disparate impact</article-title>
          ,
          <source>in: Proceedings of the 21th ACM SIGKDD</source>
          ,
          <year>2015</year>
          , pp.
          <fpage>259</fpage>
          -
          <lpage>268</lpage>
          . doi:
          <volume>10</volume>
          .1145/2783258.2783311.
        </mixed-citation>
      </ref>
      <ref id="ref43">
        <mixed-citation>
          [43]
          <string-name>
            <given-names>T.</given-names>
            <surname>Calders</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Verwer</surname>
          </string-name>
          ,
          <article-title>Three naive bayes approaches for discrimination-free classification,</article-title>
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>