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

1

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.?

5

See this. the proof is explained https://en.wikipedia.org/wiki/Mean_squared_error#Proof_of_variance_and_bias_relationship

– Kasra Manshaei – 2019-06-14T07:24:59.227