The mean squared error as defined below is a common way
to measure the error of the estimation of some parameter, or,
more generally, the performance of a supervised learning algorithm
(for either regression or classification). Let
an estimator of the parameter of a data model. Then
mean squared error (MSE) of this estimator is
caused by the oversensitivity of a learning algorithm to small fluctuations in the training dataset due to random noise rather than the intended property of the data, a problem called overfitting.
caused by the under-sensitivity of a learning algorithm to the dominanting variation in the training dataset representing the essential relationship in the training dataset, a problem called underfitting.