Performing polynomial expansion
Simple models, such as linear and logistic regression, can capture complex patterns if we feed them the right features. Sometimes, we can create powerful features by combining the variables in our datasets with themselves or with other variables. For example, in the following figure, we can see that the target, y, has a quadratic relation with the variable, x, and as shown in the left panel, a linear model is not able to capture that relationship accurately:
Figure 8.4 – A linear model fit to predict a target, y, from a feature, x, which has a quadratic relationship to the target, before and after squaring x. In the left panel: the model offers a poor fit by using the original variable; in the right panel, the model offers a better fit, based on the square of the original variable
This linear model has a quadratic relationship to the target, before and after squaring x. However, if we square x, or, in other words...
