Individual Fairness

Statistical/Demographic Parity - Equal selection rate across different groups: $P(\hat{Y} = 1 | S = s_1) = P(\hat{Y} = 1 | S = s_2)$ Equality of Accuracy - Equality of the prediction accuracy (L) across groups: $E[L(\hat{y}, y) | S = s_1] = E[L(\hat{y}, y) | S = s_2]$ Equality of FPR/FNR - Equality of the False Positive Rate (FPR) across groups: $P[\hat{Y}=1|Y =0, S = s1]=P[\hat{Y}=1|Y =0, S = s2]$ - Equality of the False Negative Rate (FNR) across groups: $P[\hat{Y}=0|Y =1, S = s1]=P[\hat{Y}=0|Y =1, S = s2]$ - Equality of Odds: equal FNR and FPR simultaneously Equality of PPV/NPV - Equality of the Positive Predictive Value (PPV) $P[Y =1|\hat{Y}=1, S = s1]=P[Y=1|\hat{Y}=1, S = s2]$ - Equality of the Negative Predictive Value (NPV) $P[Y =0|\hat{Y}=0, S = s1]=P[Y =0|\hat{Y}=0, S = s2]$ - Predictive Value Parity (PVP): equal PPV and NPV simultaneously Common Pros and Cons - Ignoring possible correlation between Y and S. - Allowing for trading off different types of error. - Not considering practical considerations. - e.g., High accuracy difficult to attain for small groups

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Summary of Fairness Notions w. Confusion Matrix

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