F1 Score is Overrated. Instead, use this!
When it comes to evaluating the performance of machine learning models, the F1 score has long been hailed as the go-to metric. However, I dare to challenge the status quo and argue that the F1 score is overrated. In this article, we will explore an alternative metric that deserves more attention and recognition: the Matthews Correlation Coefficient (MCC).
Brace yourself as we dissect the F1 score, uncover its limitations, and unveil the hidden gem that is MCC.
The F1 Score: A Flawed Hero
Ah, the F1 score — the metric that seems to be on every machine learning practitioner’s lips. Calculated by harmonizing precision and recall, the F1 score is intended to strike a balance between the two. But does it always deliver accurate results? Let’s find out.
Precision, Recall, and a Harmonious Blend
To understand the F1 score, we need to take a step back and look at its components: precision and recall. Precision measures how many correctly predicted positive instances out of all predicted positive instances. Recall, on the other hand, quantifies how many positive instances were correctly identified out of all actual positive instances. Both metrics have their merits, but blending them together might not always be the best idea.
Example: When F1 Score Falls Short
Consider a hypothetical scenario where you’re building a model to detect a rare disease. Suppose we have a dataset with the following confusion matrix for a binary classification problem:
In this scenario, the dataset represents a medical test for a rare disease where only a small number of positive cases exist compared to negative cases. The confusion matrix suggests that the model has a high True Negative (TN) rate but a low True Positive (TP) rate. Here are the calculations for precision, recall, and F1 score:
In this case, the F1 score is around 0.769, which might seem like a reasonable performance. However, the low number of True Positives is a concern, especially in the context of medical diagnostics. The rare nature of the disease means that even a small number of missed positive cases can have significant real-world consequences.
F1 score, are you really the superhero we thought you were?
Introducing the Matthews Correlation Coefficient (MCC)
Amidst the F1 score’s limitations, a silent hero awaits its time to shine: the Matthews Correlation Coefficient. Named after its creator, Brian Matthews, this coefficient ranges from -1 to +1, providing a holistic measure of a model’s performance. It takes into account true positives, true negatives, false positives, and false negatives, all wrapped up in a single number. Isn’t that impressive?
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Formulating the MCC : Let’s break down the MCC formula step by step:
MCC = (TP * TN - FP * FN) / sqrt((TP + FP) * (TP + FN) * (TN + FP) * (TN + FN))
Let’s take the same example above and see how MCC is better than F1.
Using the values from the confusion matrix:
Substituting these values into the MCC formula:
MCC = (25 * 9000 - 10 * 5) / sqrt((25 + 10) * (25 + 5) * (9000 + 10) * (9000 + 5))
MCC ≈ 0.517
The MCC value is approximately 0.517.
The Matthews Correlation Coefficient takes into account all four elements of the confusion matrix and considers the balance between true positives, true negatives, false positives, and false negatives. Unlike the F1 score, the MCC considers the relative sizes of different classes in the dataset and is suitable for imbalanced datasets or situations where the consequences of false positives and false negatives are not equal.
As we bid farewell to the F1 score, let’s acknowledge its merits as a starting point for evaluation. However, in the ever-evolving landscape of machine learning, we must embrace alternatives that can better capture the nuances of our models’ performance. The Matthews Correlation Coefficient (MCC) shines as a comprehensive metric, accommodating imbalanced datasets and considering all possible outcomes. So, let’s set aside our F1 score goggles and give MCC the recognition it truly deserves.