Regression error metrics

Link: Supervised learning

What is regression? §

Regression is a task to predict continous values instead of categorial values. E.g. predict housing prices

What is regression error metrics §

Mean Absolute Error (MAE) §

The mean of absolute value of errors

$$\text{MAE}=\frac{1}{n}\sum _{i=1}^n|y_i-{\hat{y}}_i|$$

The problem of MAE §

It wont punish large errors (the + and - will cancel out). So we introduce the Mean Squared Error.

Mean Squared Error MSE §

The mean of the squared errors. More popular than MAE due to it demonstrates the large errors.

$$\text{MSE}=\frac{1}{n}\sum _{i=1}^n(y_i-{\hat{y}}_i{)}^2$$

The problem of MSE §

The unit will also be squared. E.g. the unit of housing price will become $to$²

Root Mean Square Error (RMSE) §

The root of MSE It has the advantages of MSE and don’t have the unit problem.

$$\text{RMSE}=\sqrt{\frac{1}{n}\sum _{i=1}^n(y_i-{\hat{y}}_i{)}^2}$$

Because it’s continous value, whether it’s good or not depends on the context. Domain knowledge plays an important role to understand the context as we need to compare the error metrics vs the average of y values.