Update README.md

README.md

@@ -12,20 +12,22 @@ license: apache-2.0
 
 # Bias AUC
 
-## Description
+## Description of Metric
 
-Suite of threshold-agnostic metrics that provide a nuanced view
-of this unintended bias, by considering the various ways that a
-classifier’s score distribution can vary across designated groups.
+Suite of threshold-agnostic metrics that provide a nuanced view of this unintended bias, by considering the various ways that a classifier’s score distribution can vary across designated groups.
 
-The following are computed:
+The following are computed where $D^{-}$ is the negative examples in the background set, $D^{+}$ is the positive examples in the background set, $D^{-}_{g}$
+is the negative examples in the identity subgroup, and $D^{+}_{g}$ is the positive examples in the identity subgroup:
 
-- Subgroup AUC
-- BPSN (Background Positive, Subgroup Negative) AUC
-- BNSP (Background Negative, Subgroup Positive) AUC
-- GMB (Generalized Mean of Bias) AUC
+$$
+\begin{aligned}
+\text{Subgroup AUC} &= \text{AUC} (D^{-}_{g} + D^{+}_{g} ) &(1)\\
+\text{BPSN AUC} &= \text{AUC} (D^{+} + D^{-}_{g} ) &(2)\\
+\text{BNSP AUC} &= \text{AUC} (D^{-} + D^{+}_{g} ) &(3)
+\end{aligned}
+$$
 
-## How to use
+## How to Use
 
 ```python
 from evaluate import load