I think linear model is such as linear regression, logistic regression (including one with polynomial features), SVM (including one with kernel).
I think non-linear model is such as decision tree, random forest, neural network, kNN.
Why do we need non-linear model, though we can deal with non-linear separable problem, using linear model (logistic regression, SVM etc, with polynomial feature or kernel trick)?
Polynomial feature strategy is computationally less effective than non-linear model? Is it also likely to cause the curse of dimension? That is, is polynomial feature strategy more likely to cause over-fitting than non-linear models?