Are decision trees (e.g. C4.5) nonparametric?

Question

I'm relatively new to cars and trying to incorporate decision tree induction into a grandiose scheme of things. Are decision trees (such as those built with C4.5 or ID3) parametric or nonparametric? I would suggest that they can be truly parametric, because the separation points of the solution for real values ​​can be determined from some distribution of characteristic values, for example, average. However, they do not share the nonparametric characteristic of the fact that it is necessary to save all the initial training data (for example, with kNN).

Answer 1

The term “parametric” refers to parameters that define the distribution of data. Since decision trees, such as C4.5, make no assumptions about the distribution of data, they are nonparametric. The Gaussian maximum likelihood classification (GMLC) is parametric because it assumes that the data follows the multidimensional Gaussian distribution (classes are characterized by means and covariances). For your last sentence, storing training data (such as instance-based training) is not common to all nonparametric classifiers. For example, artificial neural networks (ANNs) are considered nonparametric, but they do not store training data.