They’re not equivalent if the distribution is skewed, because if you use a Laplace-distributed prediction, you maximize accuracy by guessing at the median value, rather than at the mean value.
Agreed, More importantly the two distribution have different kurtosis, so their tails are very different a few sigmas away
I do think the Laplace distribution is a better beginner distribution because of its fat tails, but advocating for people to use a distribution they have never heard of seems like a to tough sell :)
They’re not equivalent if the distribution is skewed, because if you use a Laplace-distributed prediction, you maximize accuracy by guessing at the median value, rather than at the mean value.
Agreed, More importantly the two distribution have different kurtosis, so their tails are very different a few sigmas away
I do think the Laplace distribution is a better beginner distribution because of its fat tails, but advocating for people to use a distribution they have never heard of seems like a to tough sell :)