This version of the ontology contains fairness concepts for classification, regression, and clustering. It is the combination of FMO-Class (AKA FMO-C), FMO-R, and FMO-Clust. To aid in the development of fair ML models, and provide guidance to researchers on how best to utilize fairness notions and metrics, we present the Fairness Metrics Ontology (FMO). FMO is a comprehensive knowledge resource which defines each fairness notion and metric, describes their use cases, and details the relationships between them. FMO also includes related concepts for describing ML models, such as the statistical metrics used to evaluate them, and defines how each fairness notion can be derived from these metrics. Although FMO can be used as a standalone resource by itself, it is also designed to be used to model fairness information for specific ML models in a Resource Description Framework (RDF) knowledge graph, and can be combined with a reasoner to infer fairness notions a model satisfies according to its evaluation metrics. Deborah L. McGuinness Hannah Powers Jonathan Li David Qiu Jamie McCusker Kristin P. Bennett Mohamed Ghalwash Jade S. Franklin 2022-08-02 2024-04-18 Fairness Metrics Ontology mathematical definition A definition for a mathematical concept, formally defined in LaTeX. probabilistic definition A definition for a mathematical concept, formally defined using a probalistic expression. prioritizes A fairness notion prioritizes some evaluation metric(s) if comparisons made with the given evaluation metric(s) are the primary way that fairness is determined with this notion. PREV prevalence PPV positive predictive value P( Y = 1 | Ŷ=1 ) https://www.techtarget.com/whatis/definition/machine-learning-algorithm ML Algorithm The method by which a machine learning model operates or is created by. Clustering Algorithm Area under the ROC curve AUC The area under the ROC (receiver operating characteristic) curve, created by plotting the true positive rate against the false positive rate at various thresholds. Area under the ROC curve model result AUC model result The area under the ROC curve calculated from the distribution of outputs of a regression model. https://doi.org/10.1109/ACCESS.2021.3114099 Deep Clustering Deep clustering is the combination of deep learning paradigms to the classical clustering approaches in unsupervised learning. The approaches used are different from traditional clustering, and usually require the existence of labels in the testing phase to evaluate the deep learning models using metrics. https://arxiv.org/pdf/1910.05113.pdf FairKM Fair k-Means An in-processing ML algorithm that is a modified form of the k-means clustering algorithm. https://doi.org/10.48550/arXiv.1910.05113 FairKM clustering objective The clustering objective used in the FairKM algorithm. Calculated as the group-specific deviation of each cluster summed over all protected groups, weighted by the square of the cluster's fractional representation over the entire dataset, and summed over all clusters. https://doi.org/10.48550/arXiv.1908.09041 Jung et al individual fairness Jung individual fairness A clustering is fair if each center serves approximately the same number of data points and the center for each data point is no farther than the n/kth farthest other data point. K-S test KS test Kolmogorov–Smirnov distance KS-distance The distance between the empirical distribution function of a sample and the cumulative distribution function of a reference distribution. https://doi.org/10.48550/arXiv.2006.07286 Kolmogorov-Smirnov statistical parity KS statistical parity The maximum difference between the cumulative distribution function of the group predictions and the overall predictions. This metric for statistical parity is defined as \(h(cdf(f(X);s), cdf(f(X)))\) for Kolmogorov-Smirnov test \(h\). The corresponding fairness notion is Statistical Parity. https://doi.org/10.48550/arXiv.2006.04960 Kleindessner individual fairness A data point is individually fair if the average distance from it to the other points in its cluster is not greater than the average distance from it to points in other clusters. https://doi.org/10.48550/arXiv.2102.12013 accuracy parity The absolute difference in expected loss for each group is bounded above to satisfy accuracy parity. Accuracy Parity requires that the absolute difference in expected loss for each group is bounded above to satisfy accuracy parity. We define the bound as \(8M^2d_{tv}(Y_0,Y_1)+3M\min(E[ E[f(X) | S=0] - E[f(X) | S=1] | S=0], E[ E[f(X) | S=0] - E[f(X) | S=1] | S=1])\) where \(M\) is the bound on \(Y\) and the uniform norm of \(f\) and \(d_{tv}\) is the maximum absolute difference of the probability distributions of \(Y\) for \(S=0\) and \(S=1\). doi.org/10.1145/3278721.3278779 adversarial mitigation Two models: the predictor which learns to predict Y from X and the adversary which predicts S from f(X), the goal is for the adversary to perform poorly https://doi.org/10.48550/arXiv.2106.05423 aggregational fairness Every point j has a set of points S that it percieves as similar to itself. A fair clustering will give point j an alpha close treatment as those in S. A clustering is fair if the quality of service j recieves(distance from center) is at most a times the average quality in S. https://doi.org/10.1109/ACCESS.2021.3114099 algorithm-agnostic clustering fairness notion A fairness notion that is not derived from some specifiic clustering objective or ML algorithm for clustering. https://doi.org/10.1109/ACCESS.2021.3114099 algorithm-agnostic fairness algorithm-agnostic fairness notion A fairness notion that is not restricted to use with some specific ML algorithm(s) (beyond requirements for modeling output as classificaiton, clustering, etc.) https://doi.org/10.1109/ACCESS.2021.3114099 algorithm-specific clustering fairness notion A fairness notion that is derived from some specifiic clustering objective or ML algorithm for clustering. https://doi.org/10.1109/ACCESS.2021.3114099 algorithm-agnostic fairness algorithm-specific fairness notion A fairness notion that is not restricted to use with some specific ML algorithm(s) (beyond requirements for modeling output as classificaiton, clustering, etc.) https://doi.org/10.1145/3457607 algorithmic bias Algorithmic bias is when the bias is not present in the input data and is added purely by the algorithm. https://doi.org/10.48550/arXiv.2007.07384 alpha-pairwise fairness A clustering is Alpha pairwise Fair if every pair of points has a probability of at least alpha of being assigned to different centers where alpha is a function of distance between the points. https://doi.org/10.1109/ICDM.2013.114 area under the ROC curve fairness metric AUC parity The predictions of two groups is not dependent on the sensitive attribute, i.e. there is zero attribute effect. The AUC metric is the area under the ROC curve of the continuous predicted output partitioned by sensitive attribute: $$\sum_{(x,y)\in G_i,(x',y')\in G_j}\frac{I(y>y')}{|G_i|\times|G_j|}.$$ average cohort clustering objective cost The average clustering objective cost over all points in one specific dataset cohort. average distance from the center The average distance of a point from its assigned cluster's centroid, for all points in a clustering. https://doi.org/10.4230/LIPIcs.ITCS.2017.43 balance for negative class For each protected group, subjects from the negative class have equal average probability score S. https://doi.org/10.4230/LIPIcs.ITCS.2017.43 balance for positive class For each protected group, subjects from the positive class have equal average probability score S. https://doi.org/10.48550/arXiv.2007.07384 beta-community preserving fairness A clustering is Beta community preserving if every community has a probability of at most beta of being split into more than t clusters where beta is an increasing function of diameter D and a decreasng function of clusters t. A community is a subset of points with diameter D and does not need to be known or identified. https://www.lexico.com/en/definition/bias bias Prejudice in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair. https://doi.org/10.1016/j.jbusres.2022.01.076 unfairness mitigation method bias mitigation method A method of training or using a machine learning model to mitigate the effects of bias. https://doi.org/10.1145/3292500.3330987 bounded representation fairness A cluster is fair if, for all protected classes, the proportion of members of those classes are within a defined bound and at most 0.5(preventing dominance). https://doi.org/10.48550/arXiv.1905.12843 bounded group loss All group losses fall within the same threshold. A predictor \(f\) satisfies bounded group loss at level \(\zeta\) under a distribution over \((X,S,Y)\) if \(E[l(Y,f(X))|S=s]\leq\zeta\) for all \(s\in S\)” \cite{Agarwaletal_2019}. This means that the model will perform equally well for the protected and unprotected groups. {\bf KPB Maybe here we can the idea of thresholded metrics from the original ML ontology paper}. There is a generic idea of converting a notion to a threshold notion in that ML ontology and probably we should describe above in our notation. https://doi.org/10.1109/ACCESS.2021.3114099 Center-Based Clustering These approaches aim to partition the input dataset into clusters by minimizing an error metric between data samples assigned to a cluster, and their corresponding cluster centers https://doi.org/10.1109/ACCESS.2021.3114099 classification fairness notion A notion of fairness used to define a classification or classification model as fair. S classification probability score A predicted score (S) returned by an ML model for some specific input, corresponding to the likelihood of classification as the positive or negative class. classification statistical metric A metric used to evaluate a classification model, based only on statistical methods. Typically based on the confusion matrix of results generated by a standard evaluation of a machine learning classification model. Cᵢ https://doi.org/10.1109/ACCESS.2021.3114099 cluster An assignment of points in a dataset to a subset (cluster). In a hard clustering, each point assigned to a cluster is not a member of any other cluster in the clustering. 1 per-cluster fairness metric A fairness metric computed for one specific cluster in a clustering. exclude hide https://doi.org/10.48550/arXiv.1802.05733 cluster balance The balance of the cluster is a measurement of a cluster's representation of two cohorts, such that a cluster consisting entirely of one cohort is unfair and a cluster evenly divided between two cohorts is fair. The balance is calculated as the minimum ratio between members of a cohort and non-members of a cohort, for both cohorts. \min{\frac{Y \in a_i}{Y \notin a_i}} \forall a_i \in A https://doi.org/10.48550/arXiv.1802.05733 cluster balance equality A clustering is considered fair according to this notion if each cluster has an equal number of each cohort. https://openaccess.thecvf.com/content_CVPR_2020/papers/Li_Deep_Fair_Clustering_for_Visual_Learning_CVPR_2020_paper.pdf cluster entropy A cluster's entropy reflects its distribution of predictions as well as how unfair the cluster is. Low entropy reveals that one subgroup of samples only assigns to a few clusters. A cluster has a high entropy if it is independent of protected attributes. -\sum_i^{\frac{|C_i ∩ X_g|}{n_{i+})log\frac{|Ci ∩ Xg|}{n_{i+}} https://doi.org/10.1109/CVPR42600.2020.00909 deep fairness for clustering cluster entropy fairness A clustering is considered fair according to this notion if it is group invariant and independent of protected attributes. https://doi.org/10.48550/arXiv.1802.05733 clustering objective cost The cost of a clustering. Typically, this cost is minimized in a clustering algorithm, and is calculated differently according to which clustering objective(s) are selected. \min{\frac{Y \in a_i}{Y \notin a_i}} \forall a_i \in A https://doi.org/10.48550/arXiv.1910.05113 https://doi.org/10.48550/arXiv.2106.07239 Abraham et al Group Fairness cluster proportion preservation A clustering is considered fair according to this notion if each cluster preserves the proportional representation of each cohort in the original dataset and in each cluster. https://arxiv.org/pdf/1910.05113.pdf cluster proportion violation A measurement of a cluster's violation of the proportionality constraint, calculated as the maximum absolute value of the ratio in each cluster between the actual proportion of a cohort to the expected proportion of the cohort (based on known proportions in the data). \max{\frac{\frac{Y \in a_i}{Y \notin a_i}{\frac{X \in a_i}{X \notin a_i}} - 1} \forall a_i \in A 'C' clustering A set of clusters defined over some specific dataset. In a "hard clustering," every point in the dataset is assigned to exactly one cluster, whereas in a "soft clustering" every point is assigned to at least one cluster. The superset of all points in all clusters is equal to the set of all points in the clustering and dataset. https://doi.org/10.1109/ACCESS.2021.3114099 C = {C₁,C₂,...,Cₖ}, C₁∪C₂∪...∪Cₖ = X https://doi.org/10.48550/arXiv.1802.05733 clustering balance The balance of a clustering as a whole is defined as the minimum balance value across all clusters. \min{balance(C_i)} \forall C_i \in C https://openaccess.thecvf.com/content_CVPR_2020/papers/Li_Deep_Fair_Clustering_for_Visual_Learning_CVPR_2020_paper.pdf clustering entropy A clustering's entropy as a whole is the maximum of the entropy of each of its clusters. \max{entropy(C_i)} \forall C_i \in C https://doi.org/10.1109/ACCESS.2021.3114099 clustering fairness metric A metric to measure the fairness of a set of clusters, with regards to some specific cohort(s). exclude hide https://doi.org/10.1109/ACCESS.2021.3114099 clustering fairness notion A definition of fairness used to define a clustering or clustering model as fair. exclude clustering statistical metric A statistical metric which accepts as input an entire clustering. https://doi.org/10.1109/ACCESS.2021.3114099 Combinatorial Search-based Clustering Exactly solving most clustering optimization objectives can be NP-Hard as there often exists an exponential search space of clustering solutions. Thus, the clustering problem can be reformulated as a combinatorial optimization problem, and local search approaches can be used to approximate the optimal clustering solution. N condition negative The number of real negative cases in the data. P condition positive The number of real positive cases in the data. https://doi.org/10.1145/3194770.3194776 conditional statistical parity Each protected class has the same positive rate when controlling for a set of legitimate attributes L. overall predictive parity https://doi.org/10.1145/3194770.3194776 conditional use accuracy equality Each protected class has the same positive and negative predictive value; in other words, the probability of subjects with positive predictive value to truly belong to the positive class and the probability of subjects with negative predictive value to truly belong to the negative class is the same among all protected classes. constrained optimization mitigation Difference in pairwise predictive accuracy between any two groups must fall within some bound when optimizing max_{f} AUC(f) s.t. A_{Gi>Gj}(f) - A_{Gk>Gl}(f) <= eps forall i != j, k!= l https://fairlearn.org/main/user_guide/mitigation/preprocessing.html#correlation-remover https://www.microsoft.com/en-us/research/uploads/prod/2020/05/Fairlearn_WhitePaper-2020-09-22.pdf correlation remover Removes correlation between sensitive and non-sensitive features min sum(||zi - xi||^2) subject to avg(zi(si-s*)^T)=0 for nonsensitive attributes Z and sensitive attributes S and original features X with s* being avg s?, new features X_tfm = aX_filt+(1-a)X_orig https://doi.org/10.48550/arXiv.1706.02409 cross-pair group fairness The squared average of a weighted difference between all samples in two groups. The Cross-Pair Group Fairness is a metric of Statistical Parity which takes the squared average of a weighted difference between all samples in two groups of the protected class. We may write this in mathematical notation as $$\Big(\frac{1}{|G_i|\times|G_j|}\sum_{(x,y)\in G_i,(x',y')\in G_j}d(y,y')\cdot(f(x)-f(x'))\Big)^2$$ where \(d\) is a distance function which decreases as \(|y-y'|\) increases. https://agrovoc.fao.org/browse/agrovoc/en/page/?uri=c_13accfa8 dataset cohort A subset of subjects in an ML dataset who share one or more attributes (such as race, gender, etc.) https://openaccess.thecvf.com/content_CVPR_2020/papers/Li_Deep_Fair_Clustering_for_Visual_Learning_CVPR_2020_paper.pdf Deep Fair Clustering A method of finding fair clusters, via an objective function that takes into account cluster balance and cluster entropy. https://doi.org/10.1145/3468507.3468511 difference-based fairness metric A measurement of any fairness notion, calculated by the relative differences of measurements of cohorts within a dataset. Δ https://doi.org/10.1145/2090236.2090255 difference metric A metric to compute the difference between two values, such that highly similar values are 0 and highly dissimilar values are 1. disparate impact The ratio comparing the rate at which an unprivileged group recieves a positive outcome, compared to the rate at which a privileged group recieves a positive outcome. It is calculated as the positive rate of the protected cohort divided by the positive rate of the unprotect cohort. In general, the industry standard is that disparate impact must be no less than 0.80 in order for the assignment of the positive condition to be fair. distance from the center The distance of a point from some cluster centroid https://doi.org/10.48550/arXiv.2006.12589 distributional individual fairness A clustering is fair if the statistical distance of the f-divergence of the distribution of each pair of samples is smaller than the distance using the F metric that measures fairness between pairs of points. https://doi.org/10.48550/arXiv.2106.11696 diversity-aware fairness A diversity aware fair clustering should contain at least a center from every group. https://doi.org/10.48550/arXiv.2106.07239 egalitarian FCBC egalitarian fair clustering under a bounded cost The fundamental idea of fair clustering under a bounded cost (FCBC) is to minimize a measure of unfairness subject to an upper bound on the clustering cost. https://doi.org/10.1609/aaai.v34i04.5970 equal accuracy for regression Error is independent of sensitive attribute(s). A predictor \(f\) satisfies Equal Accuracy if \(P[f(X) = Y | S = s_i] = P[f(X) = Y | S = s_j]\) for any two groups \(s_i,s_j\) of the protected class. That is, the model’s accuracy in correctly estimating \(Y\) is independent of the protected attribute. (Chi et al, 2021) E[ l(f(X),Y) | S = s] = E[ l(f(X),Y) ] for any s in S https://doi.org/10.1111/papa.12189 equal negative predictive value Each protected class has equal negative predicted value; in other words, the predicted percentage of individuals predicted to be negative who are actually negative is the same for each relevant group. false negative error rate balance https://doi.org/10.1145/3194770.3194776 equal opportunity Each protected class has the same true positive rate; in other words, the positive outcome is given equally across members of all protected classes which should qualify for it. https://doi.org/10.1609/aaai.v34i04.5970 equal opportunity for regression Probability of predicted outcome being greater than the actual outcome is independent of the sensitive attribute. conditional procedure accuracy equality disparate mistreatment https://doi.org/10.1145/3194770.3194776 equalized odds Each protected class has the same true positive rate and the same false positive rate: in other words, all classes are classified correctly and classified incorrectly at equal rates. https://doi.org/10.48550/arXiv.1706.02409 error gap The absolute difference in expected loss for each group assuming there is just two groups. false positive to false negative ratio FP:FN https://doi.org/10.1097/EDE.0b013e31821b506e error type ratio The ratio of false positive outcomes to false negative outcomes. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.18 essential cluster fairness A cluster is essentially fair if there exists a fractional fair cluster where for each color h, the number of color h points in C differ by at most 1 from the mass of color h points in C'. evaluation metric A measurement used to evaluate a machine-learning model or dataset. EV expected value The probable value of a random variable. model EV expected value of model The expected value of the model's prediction. https://doi.org/10.48550/arXiv.1803.02453 exponentiation gradient Exponentiates the gradient of the loss and normalizes it, uses Bounded Group Loss as constraint during fit. https://doi.org/10.48550/arXiv.2106.07239 FCBC fair clustering under a bounded cost The fundamental idea of fair clustering under a bounded cost (FCBC) is to minimize a measure of unfairness subject to an upper bound on the clustering cost. https://doi.org/10.48550/arXiv.1901.08628 fair summary fairness A clustering is fair if the protected group are equally represented in the summary (set of centroids). https://doi.org/10.48550/arXiv.1802.05733 fairlet decomposition A method of finding fair clusters, according to the balance for clustering metric. The method models the problem as a minimum-cost flow problem, and provides an algorithm for solving the problem. https://doi.org/10.1007/s10664-022-10116-7 fairness degree The maximum absolute difference between identical individuals of different groups. We defined this as the maximum absolute difference in predicted output for individuals with identical features and different values for their protected attribute, or \(|y-y'|\) such that \(x=x'\) and \(s\neq s'\). https://doi.org/10.1145/3468507.3468511 fairness metric A measurement of some fairness notion in a machine-learning model or dataset, with regards to some specific cohort(s). hide https://doi.org/10.1145/3468507.3468511 criterion fairness notion A formal definition of fairness that can be observed as a property of a predictive model, in relation to that model's treatment of different cohorts. fairness notion categorization A scheme for organizing fairness notions into categories. fairness notion subcategorization A non-top-level scheme for organizing fairness notions into categories. https://doi.org/10.48550/arXiv.1706.02409 fairness penalty The average weighted distance in predictions. The Fairness Penalty metric is the weighted average of the squared difference in predictions, which is written as $$\frac{1}{|G_i|\times|G_j|}\sum_{(x,y)\in G_i,(x',y')\in G_j}d(y,y')\cdot(f(x)-f(x'))^2$$ https://doi.org/10.1145/2090236.2090255 FTA fairness through awareness The similarity of individuals is defined via a distance metric; for fairness to hold, the distance between the distributions of outputs for individuals should be at most the distance between the (unprotected attributes of) individuals. E[Δʸ(Ŷ₁,Ŷ₂)] ≤ Δˣ( X₁,X₂) | X₁,X₂∈X, X₁,X₂∉A, Ŷ₁,Ŷ₂∈Ŷ https://doi.org/10.1145/2090236.2090255 FTU blindness fairness through unawareness A classifier satisfies this definition if no sensitive attributes are explicitly used in the decision-making process. (However, there may be causal relationships between sensitive attributes and unprotected attributes, such that sensitive attributes may still influence the prediction.) ∀a ∈ A, a ∉ X FDR false discovery rate the fraction of negative cases incorrectly predicted to be in the positive class out of all predicted positive cases. P(Y=0 | Ŷ = 1) FN false negative count The number of false negatives (type II errors) observed in an evaluation. FOR false omission rate The fraction of positive cases incorrectly predicted to be in the negative class out of all predicted negative cases. P(Y=1 | Ŷ = 0) FP false positive count The number of false positives (type I errors) observed in an evaluation. https://doi.org/10.1109/ACCESS.2021.3114099 Fuzzy Clustering Fuzzy clustering algorithms consist of soft clustering approaches where data samples have fuzzy memberships (a grade of membership between 0 and 1) to clusters instead of binary cluster assignments. https://doi.org/10.1109/ACCESS.2021.3114099 Graph-Based Clustering Graph-based clustering approaches utilize concepts from graph theory to cluster the data. This first requires translating the original dataset into a graph problem, by treating data samples as nodes/vertices in a graph, and creating edges between samples using a dissimilarity/similarity metric. The dissimilarity/similarity metric is usually defined using a distance metric between points. Then, edges can be created between nodes if points are within a certain distance threshold, often using a k-nearest-neighbor graph https://doi.org/10.48550/arXiv.1803.02453 grid search Performs Grid Search for model constrained with Bounded Group Loss https://doi.org/10.1145/3468507.3468511 group fairness group-level fairness notion A family of fairness notions with the common objective to ensure that groups who differ by their sensitive attributes are treated equally. (Note: Occasionally, "group fairness" is used to refer to statistical parity specifically, instead of the broader meaning as defined here). https://arxiv.org/pdf/1910.05113.pdf group egalitarian clustering A group's egalitarian clustering measurement is the maximum proportion violation across all clusters. \max{proportional_violation(C_i)} \forall C_i \in C https://arxiv.org/pdf/1910.05113.pdf group leximin clustering A group's leximin clustering measurement is the sum of all proportion violations across all clusters. \sum{proportional_violation(C_i)} \forall C_i \in C https://doi.org/10.1109/ICDM.2013.114 group mean difference The difference between the mean group prediction and the mean overall prediction The metric is defined as the difference in the average predictions for each group, that is, \(E[f(X)|S=s]-E[f(X)]\) for all \(s\) for expected value function \(E\) such as mean or weighted average. https://arxiv.org/pdf/1910.05113.pdf group utilitarian clustering A group's egalitarian clustering measurement is the maximum proportion violation across all clusters, but subject to an upper bound and lower bound on the clustering constraint. A proportional violation is the largest deviation from the bounds. Minimize all proportional violations starting from the largest. \max{utilitarian_proportional_violation(C_i)} \forall C_i \in C hard clustering In a hard clustering, every point is assigned to exactly one cluster. C₁∪C₂∪...∪Cₖ = X, C₁∩C₂∩...∩Cₖ = ∅ https://doi.org/10.1145/3457607 historical bias Historical bias is caused by already existing bias and socio-technical issues in the world, and can seep into from the data generation process even given a perfect sampling and feature selection. in-processing bias mitigation method An in-processing bias mitigation method operates during the process to create the ML model, and may be its own ML algorithm in its own right. https://doi.org/10.1109/ACCESS.2021.3114099 https://doi.org/10.1145/3468507.3468511 independence The fairness property satisfied when the predicted outcome variable is independent from protected attributes. Independence Ŷ ⊥ A https://doi.org/10.1145/2090236.2090255 individual fairness Individual fairness imposes the constraint that similar individuals must be treated similarly: in order to satisfy individual fairness, an ML model cannot treat a pair of similar individuals more differently than it would treat more different indiivduals. Note that this is a looser constraint than strict fairness through awareness, which is also sometimes called individual fairness, as FTA compares input and output distributions directly. Individual Fairness E[Δʸ(Ŷ₁,Ŷ₂)] ≤ E[Δʸ(Ŷ₁,Ŷ₃)] | Δˣ(X₁,X₂) ≤ Δˣ(X₁,X₃), X₁,X₂,X₃∈D, Ŷ₁,Ŷ₂,Ŷ₃∈Ŷ https://doi.org/10.48550/arXiv.1706.02409 individual fairness for regression Outcomes are linearly dependent on how similar individuals are, such that identical individuals recieve the same outcome, similar individuals recieve almost the same outcome, and more different individuals recieve more different outcomes. Exclude protected characteristics when determining the similarity between indiivduals. Individual Fairness requires that the outcome for all identical individuals of different group for the protected attribute receive equivalent outcomes. This can be written as \(f(x_i)=f(x_j)\) for all \(i,j\) such that \(x_i=x_j\) and \(s_i\neq s_j\). (Berk et al, 2017) f(xi) = f(xj) for all i,j such that xi = xj and si != sj Δˣ https://doi.org/10.1145/2090236.2090255 input difference metric A metric to compute the difference between two input individuals, such that highly similar individuals are 0 and highly dissimilar individuals are 1. https://doi.org/10.1145/3468507.3468511 intersectional bias Intersectional bias is a type of bias that occurs due to the combination of multiple sensitive factors. https://doi.org/10.48550/arXiv.2106.07239 leximin FCBC leximin fair clustering under a bounded cost The fundamental idea of fair clustering under a bounded cost (FCBC) is to minimize a measure of unfairness subject to an upper bound on the clustering cost. l https://www.datarobot.com/blog/introduction-to-loss-functions/ cost function loss function loss A function that maps one or more variables onto a real number intuitively representing some "cost" associated with the event. In general, an ML model seeks to minimize the loss of the predicted and actual outcome variables. https://doi.org/10.1609/aaai.v34i04.5970 loss fairness loss-based fairness A loss-based fairness notion is satisfied when the loss between the predicted and actual outcome variables is independent of protected attributes. It is exclusively used for regression models, but closely related to the ideas of separation and sufficiency used for classification models. Loss l(Ŷ,Y) ⟂ A D https://isbndb.com/book/9780521766333 ML dataset A dataset used in the process of creating or evaluating a machine learning model. Broadly, it is defined as a set of points (X), and, in supervised learning, a target value (Y). D = (X, Y) M https://isbndb.com/book/9780521766333 ML model A predictive model which has been trained via a process of machine learning. Ŷ = M(X) https://isbndb.com/book/9780521766333 ML model evaluation An evaluation of a specific machine learning model on a set of dataset cohorts. https://doi.org/10.1145/3468507.3468511 masking bias Masking is a form of intentional discrimination that allows decision makers with prejudicial views to mask their intentions, typically by exploiting how fairness notions are defined. max-over-clusters clustering fairness metric A measurement of fariness for a clustering, with regards to some fairness notion which assigns a fairness value to each cluster. It is calculated by taking the minimum cluster-specific fairness value over all clusters in the clustering. hide https://doi.org/10.48550/arXiv.2005.03197 max fairness cost A clustering is fair if each group's proportion in each cluster is close to their respectively defined ideal proportion. https://doi.org/10.1109/ICDM.2013.114 max mean difference The maximum absolute difference between each mean group predictions and the means overall prediction across all the groups. https://doi.org/10.1109/ICDM.2013.114 mean difference The expected value of the predicted output is independent of sensitive attribute(s). A predictor \(f\) satisfies mean difference if the expected outcome of an individual is independent of the protected attribute. We write this as \(E[f(X)|S=s]=E[f(X)]\) for all \(s\in S\). (Derived from Calders et al, 2013) E[f(X) | S = s] = E[f(X)] min-over-clusters clustering fairness metric A measurement of fariness for a clustering, with regards to some fairness notion which assigns a fairness value to each cluster. It is calculated by taking the minimum cluster-specific fairness value over all clusters in the clustering. hide https://doi.org/10.1109/ACCESS.2021.3114099 Mixture Model-Based Clustering Mixture model-based clustering refers to a probabilistic clustering approach where points are assigned to clusters in a soft manner, and do not have hard memberships. Furthermore, data points are assumed to originate (and belong to) some mixture of probability distributions. naive mitigation Resamples data to limit disproportional impact due to sample size negative prediction An ML model's prediction of the negative class for a specific input. NR negative rate negative prediction rate The fraction of a group which recieves a negative outcome (either true negative or false negative) P(Ŷ = 0) NPV negative predictive value The fraction of negative cases correctly predicted to be in the negative class out of all predicted negative cases. P(Y=0 | Ŷ = 0) https://doi.org/10.1145/3457607 omitted variable bias Omitted variable bias occurs when one or more important variables are left out of a model. class prediciton A classification predicted by a model, given some specific input. outcome outcome count a statistical metric derived from the confusion matrix, counting the number of outcomes of various types predicted by a classification model. Δʸ https://doi.org/10.1145/2090236.2090255 output difference metric A metric to compute the difference between two output values, such that highly similar values are 0 and highly dissimilar values are 1. https://doi.org/10.1145/3194770.3194776 overall accuracy equality Each protected class is predicted with equal accuracy. pairwise difference The average of the difference between each sample in two groups https://doi.org/10.1609/aaai.v34i04.5970 pairwise equal accuracy The probability of correctly predicting an individual has a better outcome than another within the same group is equal for all groups. Pairwise Equal Accuracy requires that the probability of correctly predicting an individual of one group has a better outcome than an individual in the same group is the same for all groups of the protected class. This is equivalent to \(P[f(X)>f(X')|Y>Y',(X,Y),(X',Y')\in G_i]=\kappa\) for some \(\kappa\in[0,1]\) and all \(i\). This is another notion which relies on ranking. (Narasimhan et al, 2020) P(f(X) > f(X') | Y > Y', (X',Y'),(X,Y)∈Di) = κ for some κ∈[0,1] for all i https://doi.org/10.1609/aaai.v34i04.5970 pairwise equal accuracy difference The probability of correctly predicting the better outcome for all pairs in a group is above the same bound for all groups. Pairwise Equal Accuracy Difference requires the probability of correctly predicting the better outcome for all pairs in a group is above the same bound for all groups, or \(P[f(X) > f(X') | Y > Y', (X',Y'),(X,Y)\in G_i]\geq\kappa\) for some \(\kappa\in[0,1]\) for all \(i\). https://doi.org/10.1609/aaai.v34i04.5970 pairwise equal opportunity The probability of correctly predicting an individual has a better outcome between two groups is the same for all pairs of groups of the protected class. Pairwise Equal Opportunity requires the probability of correctly predicting that an individual of one group has a better outcome than an individual of another is the same for any two groups of the protected class. Equivalently, we write it as \(P[f(X) > f(X') | Y > Y', (X,Y)\in G_i,(X',Y")\in G_j]\) for some \(\kappa\in[0,1]\) and \(i\neq j\). (Narasimhan et al, 2020) P(f(X) > f(X') | Y > Y', (X,Y)∈Di, (X',Y')∈Dj) = κ for some κ∈[0,1] for all i≠j https://doi.org/10.1609/aaai.v34i04.5970 pairwise equal opportunity difference The probability of correctly predicting the better outcome for all individuals in one group as compared to another group is above the same bound for all groups The Pairwise Equal Opportunity metric is a thresholded version of the Pairwise Equal Opportunity notion which requires The probability of correctly predicting the better outcome for all individuals in one group as compared to another group is above the same bound for all groups. We rewrite this as \(P[f(X) > f(X') | Y > Y', (X,Y)\in G_i, (X',Y')\in G_j] \geq\kappa\) for some \(\kappa\in[0,1]\) for all \(i\neq j\). (Narasimhan et al, 2020) https://doi.org/10.1609/aaai.v34i04.5970 pairwise fairness notion A notion of fairness defined via pairwise comparisons of individuals within the same cohort. pairwise statistical metric A pairwise function performed between two elements of the dataset or model output. f(dᵢ,dⱼ) | dᵢ,dⱼ ∈D∪Ŷ https://doi.org/10.1609/aaai.v34i04.5970 pairwise statistical parity The probability of predicting a better outcome for individuals in one group over individuals from another is the same for all pairs of groups. The ranking equivalent of Statistical Parity, this notion requires that \(P[f(X) > f(X') | (X,Y)\in G_i,(X',Y')\in G_j]=\kappa\) for some \(\kappa\in[0,1]\) for all \(i\neq j\). We can think of this as requiring the probability of predicting a better outcome for individuals in one group over individuals from another is the same for any two groups of the protected class. P(f(X) > f(X') | (X,Y)∈Di, (X',Y')∈Dj) = κ for some κ∈[0,1] for all i≠j https://doi.org/10.1609/aaai.v34i04.5970 pairwise statistical parity difference The difference between the probability of correctly predicting the better outcome of all pairs of individuals between two different groups and the same probability for two groups (can be the same two groups as the first probability) is bounded above by the same threshold for all differences Pairwise Statistical Parity Difference relaxes the notion of Pairwise Statistical Parity so we no longer require strict equality for all probabilities and instead require the difference between the probability of correctly predicting the better outcome of all pairs of individuals between two different groups and the same probability for two groups (can be the same two groups as the first probability) is bounded above by the same threshold for all differences. This can be rewritten as \(P[f(X)>f(X')|(X,Y)\in G_i,(X',Y')\in G_j]-P[f(X)>f(X')|(X,Y)\in G_k,(X',Y')\in G_l]\leq\epsilon\) for some \(\epsilon>0\) for \(i\neq j,k\neq l\). This is a Thresholded metric. 1 per-cohort statistical metric A statistical metric which accepts as input a single cohort. https://doi.org/10.48550/arXiv.2106.05423 per-point fairness Every point j has a set of points S that it percieves as similar to itself. A fair clustering will give point j an α-close treatment as those in S. A clustering is fair if every point satisfies α-close, where the quality of service j recieves (distance from center) is at most α times the best quality in S. 1 per-point statistical metric A statistical metric which accepts as input a single data point. positive prediction An ML model's prediction of the positive class for a specific input. PR positive rate positive prediction rate The fraction of a group which recieves a positive outcome (either true positive or false positive). P(Ŷ = 1) post-processing bias mitigation method A ppost-processing bias mitigation method operates after the process of creating the ML model through some other ML algorithm. https://doi.org/10.1109/ACCESS.2021.3114099 pre-processing bias mitigation method A pre-processing bias mitigation method operates prior to the use of some main ML algorithm to create the ML model. https://doi.org/10.1109/ACCESS.2021.3114099 PN prediction negative The number of negative predictions reported by a model. PP prediction positive The number of positive predictions reported by a model. equal mis-opportunity false positive error rate balance predictive equality Each protected class has equal false positive rate; in other words, the positive outcome is (incorrectly) given equally across members of all protected classes which should not qualify for it. equal positive predictive value outcome test predictive parity Each protected class has equal positive predicted value; in other words, predictions for all predicted classes are made with equal precision. propensity mitigation Data is stratified via propensity scoring by sensitive attribute, the model then requires that mean predictions (or residuals) must be the same for all groups in a strata min sum_i in S(w*xi-ti)^2 subject to w*d=0 where d = avg_S+(xi)-avg_S-(xi) or w*d-b=0 where b=avg_S+(ti)-avg_S-(ti) for strata S and sensitive group denoted by +/- A https://www.archives.gov/eeo/terminology.html protected cohort protected class A group protected from employment discrimination by law, due to their sensitive attributes. https://doi.org/10.1145/3468507.3468511 ratio-based fairness metric A measurement of any fairness notion, calculated by the relative ratios of measurements of cohorts within a dataset. regression fairness metric hide https://doi.org/10.1109/ACCESS.2021.3114099 regression fairness notion A notion of fairness, as designed to evaluate a clustering relative to its dataset. regression statistical metric A metric used to evaluate a regression model (i.e., a model for predicting a continuous value), based only on statistical methods. https://doi.org/10.1145/3468507.3468511 relaxed fairness notion A fairness notion which is a relaxed version of another fairness notion. https://doi.org/10.1145/3457607 representation bias Representation bias arises from the use of a skewed or otherwise non-representative sample from a population during data collection process. https://doi.org/10.1214/22-AOS2198 risk measure The weighted average of the mean squared error of each class. The Risk Measure metric is the weighted sum of the expected losses for each group of the protected class. We can write this as \(\sum_{s_i\in S}w_i\cdot E[(f(X)-Y)^2|S=s_i]\) where \(w_i\) is the probability of protected attribute value \(s_i\). robust optimization mitigation Lower bound of the AUC curve for the model is also a lower bound of the pairwise predictive accuracy for the model max_{zeta,f} zeta s.t. zeta <= AUC(f), zeta <= A_{Gi>Gj}(f) forall i != j https://doi.org/10.1145/3457607 sampling bias Similarly to representation bias, sampling bias arises due to non-random sampling of subgroups https://doi.org/10.1145/3468507.3468511 separation The fairness property satisfied when the predicted outcome variable is independent of protected attributes, conditionally on the actual outcome variable. Ŷ ⊥ A | Y https://doi.org/10.1145/3442188.3445906 social fairness A clustering is socially fair if it has minimum average center-based clustering objectives for each protected group. In other words, nearby clusters are similar and a representative exists for each cluster. https://doi.org/10.48550/arXiv.1802.05733 social fairness cost The social fairness cost of a clustering as a whole is defined as the maximum average clustering objective value across the set of all protected groups. In other words, the social cost of a clustering is the error for the protected group with the highest error value. \max{objective(U, X_a)/{\lvert X_a \rvert}} \forall a \in A https://doi.org/10.1145/3468507.3468511 statistical fairness notion A fairness notion that can be computed from the statistical metrics used to evaluate an ML model, such as the confusion matrix of results generated by a typical model evaluation of a classification model. https://doi.org/10.1145/3468507.3468511 statistical fairness test A measurement of any fairness notion, calculated by a statistical fairness test of the likelihood of some cohorts within a dataset exhibiting the fairness notion according to their measurements (i,e, comparison of p-values), https://doi.org/10.1145/3468507.3468511 statistical metric A measurement used to evaluate the performance of a machine-learning model or dataset, based only on statistical methods. acceptance rate benchmarking demographic parity https://doi.org/10.1145/3194770.3194776 statistical parity Each protected class has the same positive rate: in other words, the positive outcome is given equally to all protected classes. (Note: Occasionally, "group fairness" is used to refer to statistical parity specifically, instead of the broader meaning as defined in this ontology.) https://doi.org/10.48550/arXiv.1905.12843 statistical parity for regression The distribution of predicted output is independent of the sensitive attribute. A predictor \(f\) satisfies statistical parity under a distribution over \((X,S,Y)\) if \(f(X)\) is independent of the protected attribute \(S\), i.e. \(f(X) \perp S\). For regression, this can be redefined using the cumulative distribution function of \(f(x)\). Specifically \(P[f(X) \leq z | S = s] = P[f(X) \leq z]\) for all \(s\in S\) and \(z\) in the range of the outcome. The probability of an outcome is not dependent on whether the individual is in the protected group or not. (Agarwal et al., 2019) P[f(X) >= z | S = s] = P[f(X) >= z] for all z in range(Y) https://doi.org/10.1145/3468507.3468511 sufficiency The fairness property satisfied when a target variable is independent of protected attributes, conditionally on the predicted outcome variable. Y ⊥ A | Ŷ max-over-cohorts fairness metric A measurement of fariness for a clustering, with regards to some fairness notion which assigns a fairness value to each cohort. It is calculated by taking the maximum fairness value across all clusters in the clustering. exclude hide sum-over-clusters clustering fairness metric A measurement of fairness for a clustering, with regards to some fairness notion which assigns a fairness value to each cluster. It is calculated by taking the sum of the fairness values across all clusters in the clustering. hide https://doi.org/10.1609/aaai.v34i04.5970 symmetric equal accuracy The probability of correctly predicting an individual has a better outcome than one from a different group is equal for all groups. Symmetric Equal Accuracy requires \(P[f(X)>f(X')|Y>Y',(X,Y)\in G_i]+P[f(X)>f(X')|Y>Y',(X',Y')\in G_i]=\kappa\) for some \(\kappa\in[0,1]\) for all \(i\). We can state this as the probability of correctly predicting that an individual in a group has a better outcome than individuals in all other groups and the probability of correctly predicting that an individual in the same group has a worse outcome than individuals in all other groups is the same for all groups of the protected class.(Narasimhan et al, 2020) P(f(X) > f(X') | Y > Y', (X,Y)∈Di)+P(f(X) > f(X') | Y > Y', (X',Y')∈Di) = κ for some κ∈[0,1] for all i https://doi.org/10.1609/aaai.v34i04.5970 symmetric equal accuracy difference The probability of correctly predicting the better outcome for all individuals in a group compared to all individuals not within the group is above the same bound for all groups. We require that the probability of correctly predicting the better outcome for all individuals in a group compared to all individuals not within the group is above the same bound for all groups for the metric of Symmetric Equal Accuracy. We can write this as \(P[f(X) > f(X') | Y > Y', (X,Y)\in G_i]+P[f(X) > f(X') | Y > Y', (X',Y')\in G_i)\geq\kappa\) for some \(\kappa\in[0,1]\) for all \(i\). calibration matching conditional frequencies https://doi.org/10.4230/LIPIcs.ITCS.2017.43 test-fairness For any predicted probability score S, each protected group is predicted with equal precision; in other words, the fraction of correct positive predictions is the same for all groups for any value of S. https://isbndb.com/book/9780521766333 testing dataset A dataset used to evaluate the outcomes of a machine learning model. https://doi.org/10.1145/3468507.3468511 thresholded fairness notion A fairness notion which is satisfied if another fairness notion is within a certain threshold. https://doi.org/10.1145/3468507.3468511 total fairness The highly stringent fairness notion that is satisfied when independence, separation, and sufficiency are satisfied; in other words, the proportions of false positives, true positives, false negatives, and true negatives are the same among all protected classes. n total outcome count The total number of observed outcomes (whether TN,TP,FN,FP). https://isbndb.com/book/9780521766333 training dataset A dataset used to train a model through the process of machine learning. https://doi.org/10.1145/3194770.3194776 treatment equality Each group has an equal ratio of false negatives and false positives. TN true negative count The number of true negatives (correct rejections) observed in an evaluation. TP true positive count The number of true positives (hits) observed in an evaluation. https://arxiv.org/pdf/1910.05113.pdf bounded cluster proportion violation utilitarian cluster proportion violation A measurement of a cluster's violation of the proportionality constraint, calculated as the maximum absolute value of the ratio in each cluster between the actual proportion of a cohort to the expected proportion of the cohort (based on known proportions in the data). \max{\bounds_{LB.UB}{\frac{\frac{Y \in a_i}{Y \notin a_i}{\frac{X \in a_i}{X \notin a_i}}} - 1} \forall a_i \in A https://doi.org/10.48550/arXiv.2106.07239 utilitarian FCBC utlitarian fair clustering under a bounded cost The fundamental idea of fair clustering under a bounded cost (FCBC) is to minimize a measure of unfairness subject to an upper bound on the clustering cost. https://isbndb.com/book/9780521766333 validation dataset A dataset used to validate the predictive capability of a machine learning model during its development. https://doi.org/10.4230/LIPIcs.ITCS.2017.43 well calibration For any predicted probability score S, subjects in each protected group are correctly predicted to be in the positive class with a probability equal to S. Linear Regression Search-based fairness testing for regression-based machine learning systems Overcoming the pitfalls and perils of algorithms: A classification of machine learning biases and mitigation methods The False-positive to False-negative Ratio in Epidemiologic Studies An Overview of Fairness in Clustering Deep fair clustering for visual learning Controlling Attribute Effect in Linear Regression On statistical criteria of algorithmic fairness Fairness through Awareness Fairness definitions explained Clustering without Over-Representation Socially Fair k-Means Clustering A Survey on Bias and Fairness in Machine Learning On the Applicability of Machine Learning Fairness Notions A minimax framework for quantifying risk-fairness trade-off in regression Pairwise Fairness for Ranking and Regression On the Cost of Essentially Fair Clusterings Inherent Trade-Offs in the Fair Determination of Risk Scores On the (im)possibility of fairness A Convex Framework for Fair Regression Fair Clustering Through Fairlets Fair k-Center Clustering for Data Summarization Fair Regression: Quantitative Definitions and Reduction-based Algorithms A Center in Your Neighborhood: Fairness in Facility Location Fairness in Clustering with Multiple Sensitive Attributes Fair Algorithms for Hierarchical Agglomerative Clustering A Notion of Individual Fairness for Clustering Fair Regression with Wasserstein Barycenters Distributional Individual Fairness in Clustering A Pairwise Fair and Community-preserving Approach to k-Center Clustering Understanding and Mitigating Accuracy Disparity in Regression A New Notion of Individually Fair Clustering: α-Equitable k-Center Fair Clustering Under a Bounded Cost Diversity-aware k-median : Clustering with fair center representation Data Mining and Analysis: Fundamental Concepts and Algorithms Algorithm-Agnostic A fairness notion is algorithm-agnostic if it can work with any ML algorithm, provided that the ML algorithm targets the same problem as it. Algorithm-Specific An algorithm-specific fairness notion is designed to only work with specific, predetermined algorithms, rather than any ML algorithm. Algorithm Specificity A fairness notion may be designed to only work with specific ML algorithms, or it may be broadly applicable to any ML algorithm (that addresses the same format of problem). 4 ?notion_uri rdfs:subClassOf+ ?category_uri. exclude https://www.techtarget.com/whatis/definition/machine-learning-algorithm ML Algorithm The method by which a machine learning model operates or is created by. ?notion_uri rdfs:subClassOf+ [a owl:Restriction; owl:onProperty sio:000011; owl:someValuesFrom [a owl:Restriction; owl:onProperty sio:000632; owl:someValuesFrom ?category_uri]]. prioritized evaluation metric The evaluation metric relied on primarily to compute whether or not a notion of fairness has been satisfied. Prioritized Evaluation Metric ?notion_uri rdfs:subClassOf+ [a owl:Restriction; owl:onProperty sio:000011; owl:someValuesFrom [a owl:Restriction; owl:onProperty sio:000632; owl:someValuesFrom ?category_uri]]. 579.0 664.0 5828.0 326.0 247.0 500.0 6228.0 628.0 test_unit Test_unit FPR P(Ŷ = 1 | Y=0 ) false positive rate fall-out probability of false alarm TNR selectivity true negative rate P(Ŷ = 0 | Y=0 ) P(Ŷ = 0 | Y=1 ) FNR miss rate false negative rate true positive rate hit rate P(Ŷ = 1 | Y=1 ) TPR P(Ŷ = Y) accuracy ACC P[Ŷ = Y] https://doi.org/10.1109/ACCESS.2021.3114099 Hierarchical clustering approaches aim to partition the dataset into hierarchies, with the clustering output represented as a binary tree. The root node represents the entire dataset while the leaf nodes comprise of the singular samples of the dataset. The remaining nodes of the tree represent clusters, and in this way, a hierarchy of clusters is obtained. Hierarchical Clustering https://isbndb.com/book/9780521766333 A classification problem is a problem where, for a given set of input features, an ML model must output a class (label) from a predetermined set of classes. Classification Problem Ŷ = M(X) | Ŷ ∈ {c₁,c₂,...,cₖ} Clustering is the task of partitioning the data points into natural groups called clusters, such that points within a group are very similar, whereas points between different groups are as dissimilar as possible. exclude Clustering Problem Ŷ = M(X) | Ŷ = {C₁,C₂,...,Cₖ}, C₁∪C₂∪...∪Cₖ = X https://isbndb.com/book/9780521766333 Fair-ML Paradigm 2 A paradigm is a set of fairness notions that all follow the same principle about how fairness should be achieved: at the group level, at the individual level, or at a combination of both. Define fairness according to any of these ML fairness paradigms: https://doi.org/10.1145/2090236.2090255 ?notion_uri rdfs:subClassOf+ [a owl:Restriction; owl:onProperty sio:000095; owl:someValuesFrom ?category_uri]. Fair-ML Paradigm https://isbndb.com/book/9780521766333 A result output by a model, given some specific input. ?notion_uri rdfs:subClassOf+ [a owl:Restriction; owl:onProperty sio:000011; owl:someValuesFrom [a owl:Restriction; owl:onProperty sio:000632; owl:someValuesFrom ?category_uri]]. ML model result Model Output Ŷ Ŷ = M(X) Apply to ML models modeling any of these ML problems: ML Problem An ML problem is a problem that an MLmodel is designed to solve. Broadly, these fall into categories based on the kind of output the model needs to prodiuce, such as a label (for classification), continuous value (for regression), or set (for clustering). 1 Machine Learning Problem ?notion_uri rdfs:subClassOf+ [a owl:Restriction; owl:onProperty sio:000011; owl:someValuesFrom [a owl:Restriction; owl:onProperty sio:000632; owl:someValuesFrom ?category_uri]]. https://isbndb.com/book/9780521766333 Regression Problem https://isbndb.com/book/9780521766333 Ŷ = M(X) | Ŷ ∈ ℝ A regression problem is a problem where, for a given set of input features, an ML model must output a continuous value. We're All Equal Let CS = (X, dX) with measure µX be partitioned into groups X1, . . . , Xk. There exists some ε > 0 such that for all i, j, WdX(Xi, Xj) < ε. Fairness notions in the "We're All Equal" worldview assumes that any unfairness present in ground truth data is due to structural inequality or other biases, and that therefore individuals should be assumed to be inherently equal without these biases. https://doi.org/10.48550/arXiv.1609.07236 WAE There exists a mapping f : CS → OS such that the distortion ρf is at most e for some small e > 0. Or equivalently, the distortion ρ between CS and OS is at most e. Fairness notions in the "What You See is What You Get" worldview assume that any unfairness present in ground truth data is to be trusted and used as-is. https://doi.org/10.48550/arXiv.1609.07236 WYSIWYG What You See is What You Get continous value prediction A continous value prediction, as output by a regression ML model. false negative outcome type II error An input incorrectly classified to be false, in relation to some testing dataset which classifies it as true. miss false alarm type I error false positive outcome An input incorrectly classified to be true, in relation to some testing dataset which classifies it as false. group fairness paradigm https://doi.org/10.1145/2090236.2090255 The paradigm of fairness that follows the principle that " groups who differ by their sensitive attributes are treated equally." 1 Group Fairness High-Level Notion Are descended from any of these high-level notions (group fairness only): high-level fairness notion A high-level notion is a broader and more generalized fairness notion used to group more specialized notions into classifications. It is still mathematically defined, however, and is therefore a full-fledged fairness notion in its own right. We group relaxed, strengthened, or otherwise varied forms of some high-level notions together in the same category of fairness notion classification for ease of understanding, though we provide a separate concept for the high-level notion itself (e.g., there are concepts for both the more relaxed "Independence-class notion" and the stricter "Independence"). high-level notion 3 ?notion_uri rdfs:subClassOf+ ?category_uri. 3 Hybrid Fairness https://doi.org/10.1145/2090236.2090255 exclude The paradigm of fairness that combines elements from both group and individual fairness. hybrid fairness paradigm https://doi.org/10.1145/3468507.3468511 A fairness notion that is a relaxed, strengthened, or otherwise related form of Independence: the fairness property satisfied when the predicted outcome variable is independent from protected attributes. In other words, the model's expected output should not differ for different protected attributes, regardless of other factors such as underlying differences in ground truth data. This notion is closely related to statistical parity: the model should predict the same rates of success for each group. 1 independence-class fairness notion Independence Individual Fairness A family of fairness notions with the common objective to ensure that similar individuals are treated similarly by a model. Some notions in this group may be a relaxed version of "strict" individual fairness (i.e., they may treat similar indivduals differently under certain conditions). https://doi.org/10.1145/3468507.3468511 individual-level fairness notion 5 hide Individual Fairness https://doi.org/10.1145/2090236.2090255 2 individual fairness paradigm The paradigm of fairness that follows the principle of "similar individuals should be treated similarly." k-Center k-Medoids https://doi.org/10.1609/aaai.v34i04.5970 A fairness notion that is a relaxed, strengthened, or otherwise related form of loss-based fairness. Loss <i>(regression only)</i> 4 loss-class fairness notion Loss Separation https://doi.org/10.1145/3468507.3468511 Fairness notions in this class are relaxed, strengthened, or otherwise related form of Separation: the fairness property satisfied when the predicted outcome variable is independent of protected attributes, conditionally on the actual outcome variable. In other words, the actual outcome separates the predicted outcome from the sensitive attributes; for each possible actual outcome, the model's prediction must be independent from sensitive attributes. This is closely related to the notion of error parity or equalized odds: the model should predict the target variable in similar ways for each group, with false positive and false negative rates not varying. separation-class fairness notion 2 Sufficiency sufficiency-class fairness notion 3 https://doi.org/10.1145/3468507.3468511 Fairness notions in this class are relaxed, strengthened, or otherwise related forms of Sufficiency: the fairness property satisfied when the ground truth variable is independent of protected attributes, conditionally on the predicted outcome variable. In other words, the model's prediction should be sufficient to predict the ground truth variable by itself -- including the sensitive attributes is unnecesary and will not change the prediction. This is closely related to the notion of group-calibration: for each group, the model's prediction should give a good prediction of the target variable. Sufficiency (<i>classification only</i>) true negative outcome An input correctly classified to be false, in relation to some testing dataset which classifies it as false. correct rejection hit An input correctly classified to be true, in relation to some testing dataset which classifies it as true. true positive outcome ?notion_uri rdfs:subClassOf+ [a owl:Restriction; owl:onProperty sio:000095; owl:someValuesFrom ?category_uri]. Worldview A mapping f : CS → DS is said to be fair if objects that are close in CS are also close in DS. Specifically, fix two thresholds e, e0. Then f is defined as (e, e0)- fair if for any x, y ∈ P, dP(x, y) ≤ e =⇒ dO(f(x), f(y)) ≤ e0. https://doi.org/10.48550/arXiv.1609.07236 worldview exclude A worldview is a set of fairness notions that make the same assumptions about the data used to determine whether a model is fair: either that the data should be taken as-is, or that the data is itself unfair and further assumptions must be made about what it would look like if it wasn't fair. 3