Accuracy

Accuracy

Accuracy is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct.

Definition

$\text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}$

Where:

• TP = True Positives
• TN = True Negatives
• FP = False Positives
• FN = False Negatives

Accuracy answers the question: "Out of all predictions made by the model, how many were actually correct?"

Simple Example

Let’s say a model is used to detect whether emails are spam. Out of 100 emails:

• 60 are correctly identified as spam (TP)
• 30 are correctly identified as not spam (TN)
• 5 are incorrectly marked as spam (FP)
• 5 are incorrectly marked as not spam (FN)

Then:

$\text{Accuracy}=\frac{60+30}{60+30+5+5}=\frac{90}{100}=90\mathrm{\%}$

When is Accuracy Useful?

Accuracy is useful when the dataset is **balanced** (i.e., both classes occur in roughly equal numbers).

Limitations of Accuracy

Accuracy can be misleading in cases of Imbalanced Data.

Example: Fraud Detection

Imagine 1000 transactions:

• Only 10 are fraudulent.
• A model labels all as “not fraud” and gets 990 correct.

$\text{Accuracy}=\frac{990}{1000}=99\mathrm{\%}$

Even with 99% accuracy, the model is useless because it failed to detect any fraud.

Related Metrics

• Precision – Focuses on correct positive predictions
• Recall – Focuses on correctly identifying actual positives
• F1 Score – Harmonic mean of Precision and Recall
• Confusion Matrix – Underlying table for all classification metrics

Real-World Applications

• Image classification (e.g., cat vs dog detection)
• Email spam filters
• Sentiment analysis (positive vs negative review)

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