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Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true positives and true negatives) among the total number of cases examined. [10]
In a classification task, the precision for a class is the number of true positives (i.e. the number of items correctly labelled as belonging to the positive class) divided by the total number of elements labelled as belonging to the positive class (i.e. the sum of true positives and false positives, which are items incorrectly labelled as belonging to the class).
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 ...
Precision takes all retrieved documents into account. It can also be evaluated considering only the topmost results returned by the system using Precision@k. Note that the meaning and usage of "precision" in the field of information retrieval differs from the definition of accuracy and precision within other branches of science and statistics.
For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent of the prevalence or skew (how often each class occurs in the population), and metrics that depend on the prevalence – both types are useful, but ...
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Another reason the precision matrix may be useful is that if two dimensions and of a multivariate normal are conditionally independent, then the and elements of the precision matrix are . This means that precision matrices tend to be sparse when many of the dimensions are conditionally independent, which can lead to computational efficiencies ...
Examples of the exact sciences are mathematics, optics, astronomy, [3] and physics, which many philosophers from Descartes, Leibniz, and Kant to the logical positivists took as paradigms of rational and objective knowledge. [4] These sciences have been practiced in many cultures from antiquity [5] [6] to modern times.