Mean squared error

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
• 평균 제곱근 편차 (Root-mean-square deviation)
• Loss function

Favorite site

• Wikipedia (en) Mean squared error에 대한 설명
• Wikipedia (en) Mean absolute error에 대한 설명
• 최소 평균 제곱법 (Least Mean Squares Method)
• Regularization – Cost Function (Cost Function에 정규화 방법)
• Machine Learning, Week 1 (Cost Function에서 공식에 대한 설명)