If you are starting out in machine learning, the confusion matrix is one of the first tools you must understand. It sounds intimidating, but it is simply a table that shows how often your model was right and wrong — and in what way. Let’s break it down with a clear example.
The four boxes
Imagine a model that predicts whether an email is spam. For every email, there are four possible outcomes:
- True Positive (TP): spam correctly caught as spam.
- True Negative (TN): a normal email correctly left alone.
- False Positive (FP): a normal email wrongly flagged as spam (annoying!).
- False Negative (FN): spam that slipped into the inbox.
A worked example
Suppose we test 100 emails. The model gives us: TP = 40, TN = 45, FP = 5, FN = 10.
| Predicted: Spam | Predicted: Not spam | |
|---|---|---|
| Actually spam | 40 (TP) | 10 (FN) |
| Actually not spam | 5 (FP) | 45 (TN) |
The metrics that come from it
- Accuracy = (TP + TN) / total = (40 + 45) / 100 = 85%
- Precision = TP / (TP + FP) = 40 / 45 = 89% — of all flagged spam, how much really was spam.
- Recall = TP / (TP + FN) = 40 / 50 = 80% — of all real spam, how much we caught.
Accuracy alone can be misleading — precision and recall tell you what kind of mistakes your model makes, which matters far more in the real world.
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