Mean Squared Error

machine-learning statistics regression

Definition

Mean Squared Error

The mean squared error (MSE) is the average quadratic loss over a dataset. For targets and predictions with residuals ,

Squaring makes every deviation non-negative and penalises large residuals disproportionately: an error of size contributes , four times the contribution of an error of size . The square root yields the RMSE, which restores the target’s units.

Decomposition

For an estimator of a quantity , the MSE decomposes into a bias term and a variance term:

A biased estimator can therefore attain a lower MSE than an unbiased one, by trades a small bias for a larger reduction in variance.