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A precision-recall curve plots precision as a function of recall; usually precision will decrease as the recall increases. Alternatively, values for one measure can be compared for a fixed level at the other measure (e.g. precision at a recall level of 0.75) or both are combined into a single measure.
Precision and recall. In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all samples predicted to be positive, including those not identified correctly ...
An F-score is a combination of the precision and the recall, providing a single score. There is a one-parameter family of statistics, with parameter β, which determines the relative weights of precision and recall. The traditional or balanced F-score is the harmonic mean of precision and recall:
The F-score combines precision and recall into one number via a choice of weighing, most simply equal weighing, as the balanced F-score . Some metrics come from regression coefficients : the markedness and the informedness , and their geometric mean , the Matthews correlation coefficient .
By computing a precision and recall at every position in the ranked sequence of documents, one can plot a precision-recall curve, plotting precision () as a function of recall . Average precision computes the average value of p ( r ) {\displaystyle p(r)} over the interval from r = 0 {\displaystyle r=0} to r = 1 {\displaystyle r=1} : [ 7 ]
F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer).
is the true positive rate, also called sensitivity or recall, and is the positive predictive rate, also known as precision. The minimum possible value of the Fowlkes–Mallows index is 0, which corresponds to the worst binary classification possible, where all the elements have been misclassified.
The precision of 10 / 10 + 990 = 1% reveals its poor performance. As the classes are so unbalanced, a better metric is the F1 score = 2 × 0.01 × 1 / 0.01 + 1 ≈ 2% (the recall being 10 + 0 / 10 = 1).