## 3 Machine Learning Algorithms
### Fairness Notions  
The literature on fair ML algorithms has predominately drawn on the concepts and definition of fairness from legal domain. Popular concepts such as direct discrimination (or \"disparate treatment\") and indirect discrimination (or \"disparate impact\") are based on various antidiscrimination laws that prohibit unfair treatment of individuals based on sensitive attributes such as gender, race, etc. [4]. Disparate treatment occurs when the decision an individual user receives is prone to change with respect to changes in her corresponding sensitive attribute information. Similarly, disparate impact occurs when the decision outcomes disproportionately benefit or hurt members of certain sensitive attribute groups. More formally,  
**Disparate Treatment. ** Given dataset \(D=(A,X,Y)\), with a set of sensitive attributes \(A\) (such as race, gender, etc. ), remaining attributes \(X\), and binary class to be predicted \(Y\), predicted binary class \(\hat{Y}\), disparate treatment is said to exist in data \(D\) if  
\[Pr(\hat{Y}|X)\
eq Pr(\hat{Y}|X,A).\]
**Disparate Impact. ** Given dataset \(D=(A,X,Y)\), with a set of sensitive attributes \(A\) (such as race, gender, etc. ), remaining attributes \(X\), and binary class to be predicted \(Y\), disparate impact is said to exist in data \(D\) if  
\[\frac{Pr(Y=1|A=0)}{Pr(Y=1|A=1)}\leq\tau=0.8\]  
for positive outcome class 1 and majority protected attribute 1 where \(Pr(Y=y|A=a)\) denotes the conditional probability that the class outcome in \(y\in Y\) given sensitive attribute \(a\in A\). For the convenience of the readers, in Table 5, we provide concise summary of various definitions of fairness in literature. In our review, we observed that a majority of recent studies have focused on design of automated decision-making systems that aim at avoiding one or both of these unfairness notions. For example, consider the work of [PERSON] et al. [48], who developed a test for disparate impact as well as methods by which data might be made unbiased. [PERSON] et al. [49] provided a method of discrimination discovery and prevention from a dataset of historical decisions by adopting a variant of k-NN classification. [PERSON] et al. [50] proposed a learning algorithm for fair classification that achieved both group fairness and individual fairness by formulating the fairness as an optimization problem of finding a good representation of the data with two competing goals: to encode data as well as possible while simultaneously obfuscating any information about membership in the protected group. [PERSON] et al. [51] introduced a flexible constraint-based framework to enable the design of fair margin-based classifiers which make use of a general and intuitive measure of decision boundary unfairness. In a more recent work, [PERSON] et al. [52] introduced an alternative notion of unfairness called **disparate mistreatment**. A classifier is said to suffer from disparate mistreatment if the misclassification rates for different groups of individuals having different values of the sensitive attribute \(A\) are different. [PERSON] et al. [52] proposed that disparate mistreatment in binary classification task can be specified with respect to various misclassification measures such as overall misclassification rate, false positive rate, false negative rate, false omission rate, and false discovery rate. We have also witnessed recent works drawing on fairness concepts from economics and social welfare such as equality, Gini distribution, etc., in its conceptualization of fairness. Despite gaining tremendous research attention in recent years, a major feature of fair ML literature has been an extensive set of definitions of fairness to choose from and various empirical and theoretical findings suggesting the impossibility of satisfying various fairness definitions at the same time.