## 6 Related Work

Table 9: Comparison of the related work with respect to the desiderata for bias detection presented in Section 2, where \(\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1} \pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@color@rgb@fill{0}{0}{0}\) means “support”, \(\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1} \pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@color@rgb@fill{0}{0}{0}\) “partially support”, \(\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1} \pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@color@rgb@fill{0}{0}{0}\) “no support”. The asterisk (**) indicates that the requirement is only supported by some approaches. evaluate the discriminative power of features exploiting exclusively intrinsic proprieties (e.g., the statistical properties) of the data [35, 36]. The outcome of a filter method can consist of either the set of features showing a correlation with the class above a user-defined threshold (so-called \"univariate\" methods), or groups of features showing the best trade-off in terms of correlations with the class and minimum correlations among each other (named \"multi-variate\" methods) [31, 37, 38]. Another class of feature selection methods consists of _wrapping_ methods. Given a classifier, they look for the subset of features that provide the best results in terms of a classification quality metric, e.g., accuracy [39, 40]. The search is performed either by adding or removing one feature at each iteration, then evaluating the obtained improvements. Wrapper methods usually perform significantly better than filter approaches; however, they are computationally intensive and thus, unsuitable for real-world applications characterized by a large feature space. Finally, _embedded_ methods are feature selection approaches embedded in the classification process itself; namely, these approaches exploit an intrinsic model building metric to assess the importance of features during the construction of decision trees [41]. All three classes of feature selection techniques do not completely meet the desiderata identified in Section 2. Change impact analysis is only addressed by some embedding and filtering approaches, e.g., [42], while wrapping approaches mainly rely on classification accuracy. Only multi-variate filter approaches are data-agnostic. Wrapping and embedding methods only partially meet this desideratum: to obtain the best results, one should know the classifier used for the decisions being analyzed. All feature selection methods require parameter tuning. Analysis at the feature level is fully supported only by wrapping methods. Indeed, many filter and embedded methods only return the correlation values for a single feature; only few methods in these groups allow one to assess correlations between the class and groups of features. It is worth noting that none of the methods support the analysis at the feature value level. A recent model transparency approach alternative to feature selection is presented in [43]. This approach aims to provide explanations related to some _subspace_ of interest, i.e., groups of samples of the population presenting some characteristics of interest, usually represented in terms of itemsets. A set of classification rules is then derived for samples in those groups by means of a multi-objective optimization function taking into account factors such as rules overlapping, fidelity to the original classifiers behaviors, precision, etc. This work, however, has the same advantages and disadvantages of association rule mining (see Section 2.3). Association rule mining has been largely applied to analyze decisional processes, especially for discrimination discovery [4, 22]. Several metrics tailored to measure the impact of sensitive itemsets on the class have been proposed. In a seminal work on discrimination discovery [4], [PERSON] and colleagues introduced the notion of _extended lift_. This metric measures how the rule confidence varies with/without the discriminatory itemset, thus providing an evaluation of the relevance of this itemset.