# Thread: What are the advantages of the mean squared error versus the mean absolute error?

1. ## What are the advantages of the mean squared error versus the mean absolute error?

I understand the formulas for each, but don't understand the advantages of using one over the other.

If you could provide a situation that would be better suited for each error metric, it would be greatly appreciated.

2. ## Re: What are the advantages of the mean squared error versus the mean absolute error?

The main advantage of the mean-square error is the analytical tractability that comes with it. Many problems have simple solutions, either as closed-form formulas or semi-closed-form algorithms... The mathematical ease is related to the fact that problems phrased in terms of minimizing the mean-square error are equivalent to calculating projections in linear functional spaces.

On the other hand, mean absolute error ensures a much more robust estimation, insensitive to outliers and errors in the data. Applying mean absolute error in the context of variable selection allows you to substantially reduce the number of predictors you have to worry about.

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4. ## Re: What are the advantages of the mean squared error versus the mean absolute error?

Originally Posted by staassis
The main advantage of the mean-square error is the analytical tractability that comes with it. Many problems have simple solutions, either as closed-form formulas or semi-closed-form algorithms... The mathematical ease is related to the fact that problems phrased in terms of minimizing the mean-square error are equivalent to calculating projections in linear functional spaces.

On the other hand, mean absolute error ensures a much more robust estimation, insensitive to outliers and errors in the data. Applying mean absolute error in the context of variable selection allows you to substantially reduce the number of predictors you have to worry about.

If it's not too much trouble, could your provide an example situation where you'd want to use the mean-square error over the mean absolute error; and vice-versa?

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