+ Reply to Thread
Results 1 to 3 of 3

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

  1. #1
    Points: 14, Level: 1
    Level completed: 27%, Points required for next Level: 36

    Posts
    2
    Thanks
    1
    Thanked 0 Times in 0 Posts

    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.

    Thanks in advance.

  2. #2
    Points: 3,740, Level: 38
    Level completed: 60%, Points required for next Level: 60
    staassis's Avatar
    Location
    New York
    Posts
    233
    Thanks
    2
    Thanked 42 Times in 40 Posts

    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.

  3. The Following User Says Thank You to staassis For This Useful Post:

    GreggAlexander (07-16-2014)

  4. #3
    Points: 14, Level: 1
    Level completed: 27%, Points required for next Level: 36

    Posts
    2
    Thanks
    1
    Thanked 0 Times in 0 Posts

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


    Quote Originally Posted by staassis View Post
    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.
    Thanks so much for your answer, staassis!

    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?

+ Reply to Thread

           




Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats