Precision

Precision is a metric used in machine learning to measure the quality of a classifier.

In the context of a binary classification problem (where the outcomes are classified into one of two classes, labeled as positive(1) and negative(0)), precision is the proportion of true positive predictions (TP) out of all positive predictions. This means it's the proportion of correctly predicted positive observations to the total predicted positives.

Mathematically, precision is defined as:

Precision = True Positives / (True Positives + False Positives)

Here,

True Positives (TP) are the cases when the actual class of the observation is 1 (Positive) and the prediction is also 1 (Positive)
False Positives (FP) are the cases when the actual class of the observation is 0 (Negative) but the prediction is 1 (Positive)
So in simple terms, precision answers the question: "What proportion of positive identifications was actually correct?"

A high precision means that an algorithm returned substantially more relevant results than irrelevant, while low precision means that the algorithm produced a lot of false positives (misclassified the negative examples as positive).

It's important to note that precision is not the only metric to evaluate the performance of a classifier. While precision gives you an idea of how many false positives are classified, it doesn't give you any information about the false negatives. Therefore, precision is often used in conjunction with recall (also known as sensitivity) which provides information about the false negatives. Additionally, the F1 Score might be used as it combines both precision and recall.