scikit-learn
diff --git a/‎examples/model_selection/plot_precision_recall.py
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+28-28Lines changed: 28 additions & 28 deletions b/‎examples/model_selection/plot_precision_recall.py
Copy file name to clipboardExpand all lines: examples/model_selection/plot_precision_recall.py
+28-28Lines changed: 28 additions & 28 deletions
@@ -7,55 +7,55 @@
 
 Precision-Recall is a useful measure of success of prediction when the
 classes are very imbalanced. In information retrieval, precision is a
-measure of result relevancy, while recall is a measure of how many truly
-relevant results are returned.
-
-The precision-recall curve shows the tradeoff between precision and
-recall for different threshold. A high area under the curve represents
-both high recall and high precision, where high precision relates to a
-low false positive rate, and high recall relates to a low false negative
-rate. High scores for both show that the classifier is returning accurate
-results (high precision), as well as returning a majority of all positive
-results (high recall).
-
-A system with high recall but low precision returns many results, but most of
-its predicted labels are incorrect when compared to the training labels. A
-system with high precision but low recall is just the opposite, returning very
-few results, but most of its predicted labels are correct when compared to the
-training labels. An ideal system with high precision and high recall will
-return many results, with all results labeled correctly.
+measure of the fraction of relevant items among actually returned items while recall
+is a measure of the fraction of items that were returned among all items that should
+have been returned. 'Relevancy' here refers to items that are
+postively labeled, i.e., true positives and false negatives.
 
 Precision (:math:`P`) is defined as the number of true positives (:math:`T_p`)
 over the number of true positives plus the number of false positives
 (:math:`F_p`).
 
-:math:`P = \\frac{T_p}{T_p+F_p}`
+.. math::
+    P = \\frac{T_p}{T_p+F_p}
 
 Recall (:math:`R`) is defined as the number of true positives (:math:`T_p`)
 over the number of true positives plus the number of false negatives
 (:math:`F_n`).
 
-:math:`R = \\frac{T_p}{T_p + F_n}`
+.. math::
+    R = \\frac{T_p}{T_p + F_n}
 
-These quantities are also related to the :math:`F_1` score, which is the
-harmonic mean of precision and recall. Thus, we can compute the :math:`F_1`
-using the following formula:
+The precision-recall curve shows the tradeoff between precision and
+recall for different thresholds. A high area under the curve represents
+both high recall and high precision. High precision is achieved by having
+few false positives in the returned results, and high recall is achieved by
+having few false negatives in the relevant results.
+High scores for both show that the classifier is returning
+accurate results (high precision), as well as returning a majority of all relevant
+results (high recall).
 
-:math:`F_1 = \\frac{2T_p}{2T_p + F_p + F_n}`
+A system with high recall but low precision returns most of the relevant items, but
+the proportion of returned results that are incorrectly labeled is high. A
+system with high precision but low recall is just the opposite, returning very
+few of the relevant items, but most of its predicted labels are correct when compared
+to the actual labels. An ideal system with high precision and high recall will
+return most of the relevant items, with most results labeled correctly.
 
-Note that the precision may not decrease with recall. The
-definition of precision (:math:`\\frac{T_p}{T_p + F_p}`) shows that lowering
+The definition of precision (:math:`\\frac{T_p}{T_p + F_p}`) shows that lowering
 the threshold of a classifier may increase the denominator, by increasing the
 number of results returned. If the threshold was previously set too high, the
 new results may all be true positives, which will increase precision. If the
 previous threshold was about right or too low, further lowering the threshold
 will introduce false positives, decreasing precision.
 
 Recall is defined as :math:`\\frac{T_p}{T_p+F_n}`, where :math:`T_p+F_n` does
-not depend on the classifier threshold. This means that lowering the classifier
+not depend on the classifier threshold. Changing the classifier threshold can only
+change the numerator, :math:`T_p`. Lowering the classifier
 threshold may increase recall, by increasing the number of true positive
 results. It is also possible that lowering the threshold may leave recall
-unchanged, while the precision fluctuates.
+unchanged, while the precision fluctuates. Thus, precision does not necessarily
+decrease with recall.
 
 The relationship between recall and precision can be observed in the
 stairstep area of the plot - at the edges of these steps a small change
@@ -82,7 +82,7 @@
 average precision to multi-class or multi-label classification, it is necessary
 to binarize the output. One curve can be drawn per label, but one can also draw
 a precision-recall curve by considering each element of the label indicator
-matrix as a binary prediction (micro-averaging).
+matrix as a binary prediction (:ref:`micro-averaging <average>`).
 
 .. note::