What is mean absolute error (MAE)?

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🔹 What is Mean Absolute Error (MAE)?

The Mean Absolute Error (MAE) is a regression metric that measures the average absolute difference between actual values and predicted values.

It answers: “On average, how far off are my predictions from the true values?”

🔹 Formula

$$MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|$$

Where:

• $n$ = number of data points

• $y_i$ = actual value

• $\hat{y}_i$ = predicted value

• $| \cdot |$ = absolute value (ignores sign)

🔹 Example

Actual values ($y$): [3, 5, 2]
Predicted values ($\hat{y}$): [2.5, 4.8, 2.2]

$$MAE = \frac{|3-2.5| + |5-4.8| + |2-2.2|}{3}$$ $$= \frac{0.5 + 0.2 + 0.2}{3} = 0.3$$

👉 The model’s MAE = 0.3, meaning predictions are off by 0.3 units on average.

🔹 Key Characteristics

✅ Advantages

• Easy to interpret (same units as the target variable).

• Less sensitive to outliers compared to MSE.

⚠️ Disadvantages

• Doesn’t penalize large errors as heavily as MSE.

• Not differentiable at zero (slight drawback for some optimization methods).

🔹 Comparison with Other Metrics

Metric	Formula	Error Scale	Sensitivity to Outliers
MAE	Avg. of (	y - ŷ	)
MSE	Avg. of $(y - ŷ)^2$	Squared units	High
RMSE	$\sqrt{MSE}$	Original units	High

✅ In short:
MAE tells you the average magnitude of prediction errors in the same units as the data, making it highly interpretable, but less punishing of large errors than MSE/RMSE.

Read more :

What is mean squared error (MSE)?

What is R² score in regression?

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