Math behind, MSE = bias^2 + variance

Based on the deeplearningbook:

$$MSE = E[(\theta_m^{-} - \theta)^2]$$

$$equals$$

$$Bias(\theta_m^{-})^2 + Var(\theta_m^{-})$$

where m is the number of samples in training set, $\theta$ is the actual parameter in the training set and $\theta_m^{-}$ is the estimated parameter.

I can't get to the second equation. Further, I don't understand how the first expression is gained.

Note:

$Bias(\theta_m^{-})^2 = E(\theta_m^{-2}) - \theta^2$

Also how bias and variance evaluated in classification.?

Topic mse bias variance estimators

Category Data Science


The proof for this has been clearly explained on wikipedia link

enter image description here

For more detailed discussion please refer to this Question on stackexchange

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