Mean Squared Error (MSE) vs. Mean Absolute Error (MAE)

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The choice between minimizing squared error (mean squared error, MSE) and minimizing absolute error (mean absolute error, MAE) often depends on the characteristics of the data and the goals of the modeling task. Here are some key differences between the two error metrics and situations where each might be more appropriate:

I. Minimizing Squared Error (MSE):

1. Sensitivity to Outliers:

• MSE penalizes large errors more heavily than smaller errors. As a result, it is more sensitive to outliers in the data. Outliers can disproportionately influence the model’s performance by increasing the impact of their squared errors.

2. Mathematical Properties:

• MSE is associated with the assumption that errors are normally distributed and follows the maximum likelihood estimation under Gaussian noise assumptions.

3. Smoothness and Continuity:

• MSE tends to yield smoother and more continuous solutions. It is sensitive to the variance of errors, which may be beneficial when noise is expected to be normally distributed.

4. Optimal under Gaussian Assumptions: