Why is the f1-score the harmonic mean of precision and recall rather than the arithmetic mean?

Precision, Recall, and F1-Score: Metrics for Evaluating Classifier Performance

Classification is a typical job in machine learning in which we attempt to predict the class labels of given data. However, simply creating a classifier is insufficient. We must also assess its performance to determine how well it is performing. There are various measures for measuring a classifier’s performance, but in this blog, we will focus on precision, recall, and F1-score.

What is Precision?

Precision is the fraction of correctly predicted positive instances out of all predicted positives. In other words, it tells us how many of the predicted positive instances are actually positive. It is given by the formula:

where True Positives (TP) are the number of correctly classified positive instances, and False Positives (FP) are the number of negative instances that were incorrectly classified as positive.

What is Recall?

Recall is the fraction of correctly predicted positive instances out of all actual positives. In other words, it tells us how many of the actual positive instances were correctly identified as positive. It is given by the formula:

where False Negatives (FN) are the number of positive instances that were incorrectly classified as negative.

What is F1-Score?

F1-score is the harmonic mean of precision and recall. It gives us an overall measure of classifier performance by balancing both the precision and recall values. It is given by the formula

It ranges from 0 to 1, with 1 being the best possible score.

Why is the f1-score the harmonic mean of precision and recall rather than the arithmetic mean?

The arithmetic mean of precision and recall is not an appropriate measure to evaluate classifier performance because it does not account for cases where one value is much lower than the other. For example, if a classifier has a very high precision but a low recall, its overall performance would not be good. The harmonic mean in F1-Score gives more weight to the lower value, which means that a low value in either precision or recall will result in a low F1-score.

Let’s say we have a binary classification problem where we want to predict if a person has diabetes or not based on some medical tests. We have a dataset of 1000 patients, out of which 100 have diabetes (positive class) and 900 do not have diabetes (negative class). Now, we build a classifier and evaluate its performance using precision, recall, and F1-score.

Suppose our classifier predicts that 50 people have diabetes and 40 of them actually have diabetes. Then:

Precision = 40 / (40 + 10) = 0.8

In this case, we have 40 true positive cases and 10 false positive cases, which gives us a precision of 0.8 or 80%. This means that out of all the predicted positive cases, 80% of them were actually true positive cases.

Recall = 40 / (40 + 60) = 0.4

In this case, we have identified 40 out of a total of 100 positive cases, which gives us a recall of 0.4 or 40%. This means that out of all the actual positive cases in the dataset, our model was able to correctly identify only 40% of them.

F1-Score = 2 * (0.8 * 0.4) / (0.8 + 0.4) = 0.533

In this case, we have a precision of 0.8 and a recall of 0.4, which gives us an F1-score of 0.533. This score indicates that our model’s performance is not optimal and it needs further improvement.

Conclusion:

In this blog, we discussed precision, recall, and F1-score — three important metrics for evaluating classifier performance. They provide us with a balanced view of how well our classifier is doing in predicting different classes. It is important to remember that these metrics are not perfect and should be used in concert with other metrics to fully evaluate the performance of a classifier.

We’ve reached the end of this blog. I hope you found the information in this article useful.❤

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