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# Mean Absolute Error

## Mean Absolute Error Explained

Mean Absolute Error (MAE) is defined as the mean of the absolute discrepancies between predictions and actual outcomes, without considering the direction of these discrepancies. It represents the average absolute gap between the actual values and those predicted by the model, and is commonly used to gauge the performance of a regression model.

MAE=n1​∑i=1n​∣yi​−y^​i​∣

In this formula:

• n signifies the total number of observations in the dataset.
• y_i indicates the actual value.
• ŷ_i is the value predicted by the model.

MAE is characterized by its linear nature, which implies that each individual discrepancy is of equal importance in the overall average. This metric offers a rough estimation of the error size but does not provide direction (i.e., whether the forecast is over or under).

## Why is MAE important?

MAE's significance lies in its capacity as an essential indicator for evaluating the accuracy of regression models. Its simplicity and interpretability make it particularly valuable. Here are some of the reasons:

• It is less sensitive to outliers compared to other measures like the Mean Squared Error (MSE), which makes it a more suitable metric for datasets prone to extreme values.
• As a linear score, it gives equal weight to all individual differences, simplifying the comparison between different models or various iterations of the same model.
• The straightforwardness of MAE makes it easily understandable even by those without technical expertise.
• The metric is expressed in the same units as the output variable, aiding clarity in understanding the magnitude of prediction errors.
• MAE finds application across various fields such as finance, engineering, and meteorology, where it is often considered a standard metric.
• It provides insights into the magnitude of error, aiding in model selection and improvement.

Ultimately, the MAE stands out as a widely applied and crucial metric for regression models due to its user-friendly nature, resistance to outliers, and the valuable error size information it provides.

## Computing Mean Absolute Error Using Python

When implementing Mean Absolute Error in Python, the `mean_absolute_error()` method from the `sklearn.metrics` module offers a straightforward approach:

This example demonstrates the use of the `mean_absolute_error()` function, providing actual values (`y_true`) and predicted values (`y_pred`) to compute the MAE, which offers a measure of the accuracy of the predictive models. The code requires the Scikit-learn library in the Python environment and can also accommodate multi-output problems, enhancing its versatility in different scenarios and applications.

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