Precision, also known as Positive-Predictive Value, is an important evaluation metric and is defined as True Positives / (True Positives + False Positives), i.e., among recognized outcomes (labels), what % are correct (actual) outcomes.

This is important especially when tasks need to be certain that a positive prediction is actually a True Positive. 

Precision is important in many tasks that directly impact consumers (as a False Positive would not be good). Some examples include search engine classification, sentiment analysis, and movie/item recommendation services.



Precision of a Classification Model

Recall, also known as the True Positive Rate (TPR), is defined as True Positives / (True Positives + False Negatives), i.e., what % of actual outcomes (labels) are correctly recognized.

Recall is important in tasks that required as many possible positives to be identified.

Recall is especially important in medicinal and legal applications (ex: fraud detection and tumor detection), and it is occasionally paired with someone who manually filters out all of the False Positives. Recall is also related to F1 Score and ROC Curves.


Recall of a Classification Model

The false negative (FN), together with false positive (FP), is a type of inaccurately predicted outcome, meaning that the prediction does not match the true observation/ condition in terms of the class (positive/ negative).  
 
FN occurs when a negative class prediction (classification) was inaccurately made when a positive class prediction, when accurately predicted, should have been made.  


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- True Positive (TP)
- True Negative (TN)
- False Positive (FP)
- False Negative (FN)

Components of Confusion Matrix

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

https://developers.google.com/machine-learning/crash-course/classification/true-false-positive-negative



Classification: True vs. False and Positive vs. Negative

The true positive (TP), together with true negative (TN) (*) is a type of accurately predicted outcome, meaning that the prediction matches the true observation/ condition in terms of the class (positive/ negative).  
 
TP occurs when a positive class prediction (classification) was accurately made.  


True Positive (TP)

The true negative (TN), together with true positive (TP), is a type of accurately predicted outcome, meaning that the prediction matches the true observation/ condition in terms of the class (positive/ negative).  
 
TN occurs when a negative class prediction (classification) was accurately made.  




True Negative (TN) 

The false positive (FP), together with false negative (FN) (*), is a type of inaccurately predicted outcome, meaning that the prediction does not match the true observation/ condition in terms of the class (positive/ negative).  
 
FP occurs when a positive class prediction (classification) was inaccurately made when a negative class prediction, when accurately predicted, should have been made.  

In the example of the mammogram: 
If the woman who is tested positive for breast cancer does not actually have the disease, such an incorrect prediction is called FP.   



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