Regression Metrics MAE, MSE

So far, we have introduced many classification metrics. Next, we'll present some popular regression performance metrics. The most popular regression metrics are mean absolute error, MAE, or mean squared error, MSE. The mean absolute error, MAE, measures the average of the absolute errors, that is the difference between the prediction and the ground truth value. The mean squared error MSE, on the other hand, measures the average of the squared error. MSE is easier to work with because the derivative of the square term is linear, but MSE will greatly affected by outliers because of the square term as well. On the other hand, MAE is more robust against the outliers, but it's harder to work with because this absolute value is not differentiable.

Here are some visual illustrations. The X axis is the grand truth value and the Y axis is the prediction. As the amount of noise increases from left to right, both MAE and MSE increase. You can also notice that MSE increased a lot faster because the square of error term.