# Precision and Recall ## Precision Precision measures how accurate is your predictions. i.e. the percentage of your predictions are correct. $ \text { Precision }=\frac{T P}{T P+F P} $ or simply, **Precision = TP / predicted positives** i.e. out of our predicted positives how many did we get right. ## Recall Recall measures how good you find all the positives. For example, we can find 80% of the possible positive cases in our top K predictions. $ \text { Recall }=\frac{T P}{T P+F N} $ or simply, **Recall = TP / all positives** i.e. out of all positives how many did we catch. ## Average Precision AP = Average of precisions at relevant documents It can also be obtained from the AUC of [[Classification Metrics and Evaluation#PR curve]]. $ \begin{aligned} &\begin{array}{cccc} \text { Rank } & \text { Rel. } & \text { Precision } & \text { Recall } \\ 1 & \mathrm{R} & 1 / 1 & 1 / 10 \\ 2 & \mathrm{~N} & 1 / 2 & 1 / 10 \\ 3 & \mathrm{R} & 2 / 3 & 2 / 10 \\ 4 & \mathrm{R} & 3 / 4 & 3 / 10 \\ 5 & \mathrm{~N} & \ldots & \ldots \\ 6 & \mathrm{R} & 4 / 6 & 4 / 10 \\ 7 & \mathrm{~N} & & \\ 8 & \mathrm{~N} & \cdots & \ldots \\ 9 & \mathrm{~N} & & \\ 10 & \mathrm{R} & 5 / 10 & 5 / 10 \\ \ldots & \ldots & \ldots & \ldots \\ \infty & \mathrm{R} & 0 & 10 / 10 \end{array}\\ &A P=\frac{\frac{1}{1}+\frac{2}{3}+\frac{3}{4}+\frac{4}{6}+\frac{5}{10}+\ldots}{10} \end{aligned} $ --- ## References