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The mean square error is the expected value that reflects the degree of difference between the estimated value and the true value. It is often used to evaluate the degree of change in data and predict the accuracy of data.

Assume that there is a parameter ${ \theta }$ , and its estimation function is $\text{[math]}$ , then ${MSE{ \left( {T} \right) }\text{ }=\text{ }E{ \left( {{ \left( {T\text{ }-\text{ } \theta } \right) }\mathop{{}}\nolimits^{{2}}} \right) }}$ , the squared expected value of the "error".

The mean squared error satisfies the equation ${MSE{ \left( {T} \right) }\text{ }=\text{ }var{ \left( {T} \right) }\text{ }+\text{ }{ \left( {bias{ \left( {T} \right) }} \right) }\mathop{{}}\nolimits^{{2}}}$ , where ${bias{ \left( {T} \right) }\text{ }=\text{ }E{ \left( {T} \right) }\text{ }-\text{ } \theta }$ , that is, the bias ${bias{ \left( {T} \right) } }$ is the difference between the expected value of the estimated function and the unobservable parameter.

Since the square form is easy to derive, the mean square error is often used as the loss function for linear regression.

Mean Squared Error