Which loss function punishes large errors more heavily than small errors?

Which loss function punishes large errors more heavily than small errors?

• A. MAE
• B. MAPE
• C. MSE
• D. RMSE

Answer: (C)

Squaring the error makes bigger deviations stand out more. In a loss that averages squared deviations, a mistake of size 2 contributes 4 to the loss, while a mistake of size 1 contributes only 1. Doubling the error more than doubles the penalty, so large errors are punished disproportionately compared to small ones. This direct emphasis comes from the squared-error approach, which is what mean squared error uses. By contrast, mean absolute error grows linearly with error, so large and small errors are penalized more evenly; RMSE applies a square root to those squared errors, reducing the emphasis a bit; mean absolute percentage error is based on relative error, not just magnitude. So the function that weights large mistakes most strongly is the squared-error loss.

Squaring the error makes bigger deviations stand out more. In a loss that averages squared deviations, a mistake of size 2 contributes 4 to the loss, while a mistake of size 1 contributes only 1. Doubling the error more than doubles the penalty, so large errors are punished disproportionately compared to small ones. This direct emphasis comes from the squared-error approach, which is what mean squared error uses. By contrast, mean absolute error grows linearly with error, so large and small errors are penalized more evenly; RMSE applies a square root to those squared errors, reducing the emphasis a bit; mean absolute percentage error is based on relative error, not just magnitude. So the function that weights large mistakes most strongly is the squared-error loss.