Accuracy, Precision, Recall, F1 Score, Sensitivity, Specificity

Considering a system in diagnosis of disease, we can depict these terms with the rate involved.

(1)   \begin{equation*} % Table generated by Excel2LaTeX from sheet 'Sheet1' \begin{tabular}{cll} & \multicolumn{2}{c}{Actual} \\ {Prediction} & \textcolor[rgb]{ 1, 0, 0}{\textbf{TP}} & \textbf{FP} \\ & \textbf{FN} & \textbf{TN} \\ \end{tabular}% \end{equation*}

Accuracy The rate of all the correctly predicted people in all the people.

(2)   \begin{equation*} \text{Accuracy} = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{TN} + \text{FP} + \text{FN}} \end{equation*}

Precision The rate of people who really get the disease in predicted people with disease.

(3)   \begin{equation*} \text{Precision} = \frac{\text{TP}}{\text{TP}+\text{FP}} \end{equation*}

Recall or Sensitivity For all the actual positives, it’s the rate of how many people with disease are finally predicted.

(4)   \begin{equation*} \text{Recall} = \text{Sensitivity} = \text{True positive rate} = \frac{\text{TP}}{\text{TP}+\text{FN}} \end{equation*}

Specificity For all the healthy people, it’s the rate how many healthy people are identified.

(5)   \begin{equation*} \text{Specificity} = \text{True negative rate} = \frac{\text{TN}}{\text{TN}+\text{FP}} \end{equation*}

F1 Score

(6)   \begin{equation*} \begin{aligned} \text{F1 Score} = & \frac{1}{ \frac{1}{2} (\frac{1}{Recall} + \frac{1}{Precision}) } \\ = & \frac{\text{TP}}{ \text{TP} + \frac{1}{2}(\text{FP}+\text{FN}) } \end{aligned} \end{equation*}

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