What is an advantage of mean absolute error (MAE) over mean squared error (MSE)?

Mean absolute error (MAE) is preferred in certain scenarios because it provides a linear score that is directly related to the average error. This means that each individual error contributes to the overall error metric in a linear way, preserving the original scale of the data without exaggerating larger errors. This characteristic allows MAE to effectively reflect the average magnitude of errors without the influence of the square function, which can significantly increase the impact of outliers.

For many practical applications, this linearity makes MAE a more straightforward metric to interpret when the goal is to understand typical error sizes in a more intuitive way. Unlike mean squared error (MSE), which squares each error term, MAE provides a direct average of absolute error sizes. This property can offer valuable insights, particularly when outliers are present, as it avoids overly penalizing these extreme values.

In contrast, the emphasis placed on larger errors through squaring in MSE can lead to distorted performance insights if outliers are part of the dataset. This is why MAE is often chosen for scenarios where a robust performance measure is needed without the disproportionate influence of outliers.