DOC: Updates to Macro vs micro-averaging in plot_roc.py (#29845)

Co-authored-by: Xiao Yuan <yuanx749@gmail.com>
Co-authored-by: Lucy Liu <jliu176@gmail.com>

examples/model_selection/plot_roc.py

@@ -218,6 +218,12 @@
 # Obtaining the macro-average requires computing the metric independently for
 # each class and then taking the average over them, hence treating all classes
 # equally a priori. We first aggregate the true/false positive rates per class:
+#
+# :math:`TPR=\frac{1}{C}\sum_{c}\frac{TP_c}{TP_c + FN_c}` ;
+#
+# :math:`FPR=\frac{1}{C}\sum_{c}\frac{FP_c}{FP_c + TN_c}` .
+#
+# where `C` is the total number of classes.
 
 for i in range(n_classes):
     fpr[i], tpr[i], _ = roc_curve(y_onehot_test[:, i], y_score[:, i])
@@ -441,7 +447,17 @@
 # global performance of a classifier can still be summarized via a given
 # averaging strategy.
 #
-# Micro-averaged OvR ROC is dominated by the more frequent class, since the
-# counts are pooled. The macro-averaged alternative better reflects the
-# statistics of the less frequent classes, and then is more appropriate when
-# performance on all the classes is deemed equally important.
+# When dealing with imbalanced datasets, choosing the appropriate metric based on
+# the business context or problem you are addressing is crucial.
+# It is also essential to select an appropriate averaging method (micro vs. macro)
+# depending on the desired outcome:
+#
+# - Micro-averaging aggregates metrics across all instances, treating each
+#   individual instance equally, regardless of its class. This approach is useful
+#   when evaluating overall performance, but note that it can be dominated by
+#   the majority class in imbalanced datasets.
+#
+# - Macro-averaging calculates metrics for each class independently and then
+#   averages them, giving equal weight to each class. This is particularly useful
+#   when you want under-represented classes to be considered as important as highly
+#   populated classes.