Pushing the docs to dev/ for branch: main, commit 0ad90d51537328b7310741d010e569ca6cd33f78

Author: sklearn-ci

dev/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

@@ -4,7 +4,7 @@
       "cell_type": "markdown",
       "metadata": {},
       "source": [
-        "\n# Precision-Recall\n\nExample of Precision-Recall metric to evaluate classifier output quality.\n\nPrecision-Recall is a useful measure of success of prediction when the\nclasses are very imbalanced. In information retrieval, precision is a\nmeasure of result relevancy, while recall is a measure of how many truly\nrelevant results are returned.\n\nThe precision-recall curve shows the tradeoff between precision and\nrecall for different threshold. A high area under the curve represents\nboth high recall and high precision, where high precision relates to a\nlow false positive rate, and high recall relates to a low false negative\nrate. High scores for both show that the classifier is returning accurate\nresults (high precision), as well as returning a majority of all positive\nresults (high recall).\n\nA system with high recall but low precision returns many results, but most of\nits predicted labels are incorrect when compared to the training labels. A\nsystem with high precision but low recall is just the opposite, returning very\nfew results, but most of its predicted labels are correct when compared to the\ntraining labels. An ideal system with high precision and high recall will\nreturn many results, with all results labeled correctly.\n\nPrecision ($P$) is defined as the number of true positives ($T_p$)\nover the number of true positives plus the number of false positives\n($F_p$).\n\n$P = \\frac{T_p}{T_p+F_p}$\n\nRecall ($R$) is defined as the number of true positives ($T_p$)\nover the number of true positives plus the number of false negatives\n($F_n$).\n\n$R = \\frac{T_p}{T_p + F_n}$\n\nThese quantities are also related to the $F_1$ score, which is the\nharmonic mean of precision and recall. Thus, we can compute the $F_1$\nusing the following formula:\n\n$F_1 = \\frac{2T_p}{2T_p + F_p + F_n}$\n\nNote that the precision may not decrease with recall. The\ndefinition of precision ($\\frac{T_p}{T_p + F_p}$) shows that lowering\nthe threshold of a classifier may increase the denominator, by increasing the\nnumber of results returned. If the threshold was previously set too high, the\nnew results may all be true positives, which will increase precision. If the\nprevious threshold was about right or too low, further lowering the threshold\nwill introduce false positives, decreasing precision.\n\nRecall is defined as $\\frac{T_p}{T_p+F_n}$, where $T_p+F_n$ does\nnot depend on the classifier threshold. This means that lowering the classifier\nthreshold may increase recall, by increasing the number of true positive\nresults. It is also possible that lowering the threshold may leave recall\nunchanged, while the precision fluctuates.\n\nThe relationship between recall and precision can be observed in the\nstairstep area of the plot - at the edges of these steps a small change\nin the threshold considerably reduces precision, with only a minor gain in\nrecall.\n\n**Average precision** (AP) summarizes such a plot as the weighted mean of\nprecisions achieved at each threshold, with the increase in recall from the\nprevious threshold used as the weight:\n\n$\\text{AP} = \\sum_n (R_n - R_{n-1}) P_n$\n\nwhere $P_n$ and $R_n$ are the precision and recall at the\nnth threshold. A pair $(R_k, P_k)$ is referred to as an\n*operating point*.\n\nAP and the trapezoidal area under the operating points\n(:func:`sklearn.metrics.auc`) are common ways to summarize a precision-recall\ncurve that lead to different results. Read more in the\n`User Guide <precision_recall_f_measure_metrics>`.\n\nPrecision-recall curves are typically used in binary classification to study\nthe output of a classifier. In order to extend the precision-recall curve and\naverage precision to multi-class or multi-label classification, it is necessary\nto binarize the output. One curve can be drawn per label, but one can also draw\na precision-recall curve by considering each element of the label indicator\nmatrix as a binary prediction (micro-averaging).\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>See also :func:`sklearn.metrics.average_precision_score`,\n             :func:`sklearn.metrics.recall_score`,\n             :func:`sklearn.metrics.precision_score`,\n             :func:`sklearn.metrics.f1_score`</p></div>\n"
+        "\n# Precision-Recall\n\nExample of Precision-Recall metric to evaluate classifier output quality.\n\nPrecision-Recall is a useful measure of success of prediction when the\nclasses are very imbalanced. In information retrieval, precision is a\nmeasure of the fraction of relevant items among actually returned items while recall\nis a measure of the fraction of items that were returned among all items that should\nhave been returned. 'Relevancy' here refers to items that are\npostively labeled, i.e., true positives and false negatives.\n\nPrecision ($P$) is defined as the number of true positives ($T_p$)\nover the number of true positives plus the number of false positives\n($F_p$).\n\n\\begin{align}P = \\frac{T_p}{T_p+F_p}\\end{align}\n\nRecall ($R$) is defined as the number of true positives ($T_p$)\nover the number of true positives plus the number of false negatives\n($F_n$).\n\n\\begin{align}R = \\frac{T_p}{T_p + F_n}\\end{align}\n\nThe precision-recall curve shows the tradeoff between precision and\nrecall for different thresholds. A high area under the curve represents\nboth high recall and high precision. High precision is achieved by having\nfew false positives in the returned results, and high recall is achieved by\nhaving few false negatives in the relevant results.\nHigh scores for both show that the classifier is returning\naccurate results (high precision), as well as returning a majority of all relevant\nresults (high recall).\n\nA system with high recall but low precision returns most of the relevant items, but\nthe proportion of returned results that are incorrectly labeled is high. A\nsystem with high precision but low recall is just the opposite, returning very\nfew of the relevant items, but most of its predicted labels are correct when compared\nto the actual labels. An ideal system with high precision and high recall will\nreturn most of the relevant items, with most results labeled correctly.\n\nThe definition of precision ($\\frac{T_p}{T_p + F_p}$) shows that lowering\nthe threshold of a classifier may increase the denominator, by increasing the\nnumber of results returned. If the threshold was previously set too high, the\nnew results may all be true positives, which will increase precision. If the\nprevious threshold was about right or too low, further lowering the threshold\nwill introduce false positives, decreasing precision.\n\nRecall is defined as $\\frac{T_p}{T_p+F_n}$, where $T_p+F_n$ does\nnot depend on the classifier threshold. Changing the classifier threshold can only\nchange the numerator, $T_p$. Lowering the classifier\nthreshold may increase recall, by increasing the number of true positive\nresults. It is also possible that lowering the threshold may leave recall\nunchanged, while the precision fluctuates. Thus, precision does not necessarily\ndecrease with recall.\n\nThe relationship between recall and precision can be observed in the\nstairstep area of the plot - at the edges of these steps a small change\nin the threshold considerably reduces precision, with only a minor gain in\nrecall.\n\n**Average precision** (AP) summarizes such a plot as the weighted mean of\nprecisions achieved at each threshold, with the increase in recall from the\nprevious threshold used as the weight:\n\n$\\text{AP} = \\sum_n (R_n - R_{n-1}) P_n$\n\nwhere $P_n$ and $R_n$ are the precision and recall at the\nnth threshold. A pair $(R_k, P_k)$ is referred to as an\n*operating point*.\n\nAP and the trapezoidal area under the operating points\n(:func:`sklearn.metrics.auc`) are common ways to summarize a precision-recall\ncurve that lead to different results. Read more in the\n`User Guide <precision_recall_f_measure_metrics>`.\n\nPrecision-recall curves are typically used in binary classification to study\nthe output of a classifier. In order to extend the precision-recall curve and\naverage precision to multi-class or multi-label classification, it is necessary\nto binarize the output. One curve can be drawn per label, but one can also draw\na precision-recall curve by considering each element of the label indicator\nmatrix as a binary prediction (`micro-averaging <average>`).\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>See also :func:`sklearn.metrics.average_precision_score`,\n             :func:`sklearn.metrics.recall_score`,\n             :func:`sklearn.metrics.precision_score`,\n             :func:`sklearn.metrics.f1_score`</p></div>\n"
       ]
     },
     {

dev/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip

@@ -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::