The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error approaches zero. The MSE is a measure of the quality of an estimator. In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. MSE is a risk function, corresponding to the expected value of the squared error loss. In statistics, the mean squared error ( MSE) or mean squared deviation ( MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors-that is, the average squared difference between the estimated values and the actual value. Not to be confused with Mean squared displacement.
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