Mean Absolute Error

What is the Mean Absolute Error?

Mean Absolute Error (MAE) is a measure of the average size of the mistakes in a collection of predictions, without taking their direction into account. It is measured as the average absolute difference between the predicted values and the actual values and is used to assess the effectiveness of a regression model.

The MAE loss function formula:

  • MAE = (1/n) Σ(i=1 to n) |y_i – ŷ_i|


  • n is the number of observations in the dataset.
  • y_i is the true value.
  • ŷ_i is the predicted value.

The MAE is a linear score, meaning all individual differences contribute equally to the mean. It provides an estimate of the size of the inaccuracy, but not its direction (e.g., over or under-prediction).

The importance of MAE

The Mean Absolute Error (MAE) is a crucial performance statistic for regression models since it is an easy-to-understand, interpretable, and reliable tool for assessing the accuracy of predictions. Among the many reasons, these are the most significance:

  • Resiliency to outliers. The MAE is not as impacted by extreme results as other metrics, such as Mean Squared Error (MSE), are. This makes it an appropriate measure for datasets that include outliers or extreme values.
  • Linear score. All individual differences are given equal weight in the average. This makes it simple to compare the performance of several models or variations of the same model.
  • Straightforward. The MAE interpretation is a basic and obvious statistic that represents the average magnitude of the forecasts’ mistakes. It is simple for non-technical stakeholders to comprehend.
  • Same units as the response variable. The ML MAE is expressed in the same units as the response variable, making it simple to comprehend the size of the prediction error. This is important when trying to understand the performance of the model in the context of the issue you’re attempting to solve.
  • Used in several disciplines. MAE is used in finance, engineering, and meteorology. It is even regarded as a standard measure in some instances.
  • Offer information about the size of the error. MAE provides information about the magnitude of the error produced by the model. It allows for model comparison and the selection of the best one, as well as the improvement of a model by determining the predicted mean absolute percentage error.

In conclusion, MAE is a commonly used and significant performance metric for regression models because it is intuitive, interpretable, resistant to outliers, and offers information about the error size.

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Mean Absolute Error in Python

The mean absolute error() method of the sklearn.metrics module in Python may be used to compute the MAE of a series of predictions.

The following demonstrates how to use the mean absolute error() function:

from sklearn.metrics import mean_absolute_error 
import numpy as np

# Generate some sample data
y_true = np.array([1, 2, 3, 4, 5])
y_pred = np.array([1.5, 2.5, 2.8, 4.2, 4.9])

# Calculate the MAE
mae = mean_absolute_error(y_true, y_pred)
print("Mean Absolute Error:", mae)

This example provides some sample data and then uses the mean absolute error() function to determine the MAE of the forecasts. The first argument represents the actual values, while the second represents the expected values.

This code requires the Scikit-learn package to be installed in your Python environment.

The mean absolute error() method may also be used to determine MAE for multi-output issues. The first input is an array of actual values, while the second is of anticipated values.