Mean squared error

lastmod 2018-08-17created 2015-12-276 edits

In statistics, the mean squared error (MSE) of an estimator measures the average of the squares of the "errors", that is, the difference between the estimator and what is estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or quadratic loss. The difference occurs because of randomness or because the estimator doesn't account for information that could produce a more accurate estimate.

Predictor

If \(\hat{Y}\) is a vector of \(n\) predictions, and \(Y\) is the vector of observed values corresponding to the inputs to the function which generated the predictions, then the MSE of the predictor can be estimated by

\[ \operatorname{MSE}=\frac{1}{n}\sum_{i=1}^n(\hat{Y_i} - Y_i)^2 \]

See also

• Machine learning
• Root-mean-square deviation
• Loss function

Favorite site

• Wikipedia (en) explanation of Mean squared error
• Wikipedia (en) explanation of Mean absolute error
• Least Mean Squares Method
• Regularization – Cost Function (regularization methods for the Cost Function)
• Machine Learning, Week 1 (explanation of the formula in the Cost Function)