Math behind, $MSE = bias^2 + variance$

Question

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.?

Answer 1

The proof for this has been clearly explained on wikipedia link

For more detailed discussion please refer to this Question on stackexchange