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by abhgh 805 days ago
"nonparametric" is somewhat of a (confusing!) misnomer in that it doesn't mean no parameters, but lots of them where the # of parameters grows with # of instances [1]. In all of these cases the models have some general parameter(s) as well.

Some simple examples would be the bin-width and bandwidth in the histogram and the kernel density estimator. A somewhat complex example would be Dirichlet Process-based Mixture Models [2]; this has a "concentration" parameter. The terminology is used outside of density estimation too, e.g., Support Vector Machines (SVM) and k-Nearest Neighbors are considered nonparametric [3].

[1] For ex, see https://stats.stackexchange.com/a/268646, or https://youtu.be/I7bgrZjoRhM?si=VOEENs773SXlEMxm&t=300

[2] https://www.gatsby.ucl.ac.uk/~ywteh/research/npbayes/dp.pdf

[3] https://stats.stackexchange.com/a/237704