### Model Bias and Variance

- Over fitting
- Low Bias with High Variance
- Low training error – ‘Low Bias’
- High testing error
- Unstable model – ‘High Variance’
- The coefficients of the model change with small changes in the data
- Under fitting
- High Bias with low Variance
- High training error – ‘high Bias’
- testing error almost equal to training error
- Stable model – ‘Low Variance’
- The coefficients of the model doesn’t change with small changes in the data

### The Bias-Variance Decomposition

\[Y = f(X)+\epsilon\] \[Var(\epsilon) = \sigma^2\] \[Squared Error = E[(Y -\hat{f}(x_0))^2 | X = x_0 ]\] \[= \sigma^2 + [E\hat{f}(x_0)-f(x_0)]^2 + E[\hat{f}(x_0)-E\hat{f}(x_0)]^2\] \[= \sigma^2 + (Bias)^2(\hat{f}(x_0))+Var(\hat{f}(x_0 ))\]

**Overall Model Squared Error = Irreducible Error + \(Bias^2\) + Variance**

### Bias-Variance Decomposition

**Overall Model Squared Error = Irreducible Error + \(Bias^2\) + Variance**- Overall error is made by bias and variance together
- High bias low variance, Low bias and high variance, both are bad for the overall accuracy of the model
- A good model need to have low bias and low variance or at least an optimal where both of them are jointly low
- How to choose such optimal model. How to choose that optimal model complexity